Sports competitions are widely researched in computer and social science, with the goal of understanding how players act under uncertainty. Although there is an abundance of computational work on player metrics prediction based on past performance, very few attempts to incorporate out-of-game signals have been made. Specifically, it was previously unclear whether linguistic signals gathered from players’ interviews can add information that does not appear in performance metrics. To bridge that gap, we define text classification tasks of predicting deviations from mean in NBA players’ in-game actions, which are associated with strategic choices, player behavior, and risk, using their choice of language prior to the game. We collected a data set of transcripts from key NBA players’ pre-game interviews and their in-game performance metrics, totalling 5,226 interview-metric pairs. We design neural models for players’ action prediction based on increasingly more complex aspects of the language signals in their open-ended interviews. Our models can make their predictions based on the textual signal alone, or on a combination of that signal with signals from past-performance metrics. Our text-based models outperform strong baselines trained on performance metrics only, demonstrating the importance of language usage for action prediction. Moreover, the models that utilize both textual input and past-performance metrics produced the best results. Finally, as neural networks are notoriously difficult to interpret, we propose a method for gaining further insight into what our models have learned. Particularly, we present a latent Dirichlet allocation–based analysis, where we interpret model predictions in terms of correlated topics. We find that our best performing textual model is most associated with topics that are intuitively related to each prediction task and that better models yield higher correlation with more informative topics.1

Decision theory is a well-studied field, with a variety of contributions in economics, statistics, biology, psychology, and computer science (Einhorn and Hogarth 1981; Berger 1985). Although substantial progress has been made in analyzing the choices that agents make, prediction in decision-making is not as commonly researched, partly due to its challenging nature (Gilboa 2009). Particularly, defining and assessing the set of choices in a real-world scenario is difficult, as the full set of options that an agent faces is usually unobserved, and her decisions are only inferred from their outcomes.

One domain where the study of human action is well defined and observable is sports, in our case, basketball. Professional athletes are experts in decision-making under uncertainty, and their actions, along with their outcomes, are well-documented and extensively studied. While there are many attempts to predict game outcomes in basketball, including win probability, players’ marginal effects, and the strengths of specific lineups (Coate 2012; Ganguly and Frank 2018), they are less focused on the decisions of individual players.

Individual player actions are difficult to predict as they are not made in lab conditions and are also a function of “soft” factors such as their subjective feelings regarding their opponents, teammates, and themselves. Moreover, such actions are often made in response to the decisions that their opponents and teammates make. Currently, sports analysts and statisticians who try to predict such actions do so mostly through past performances, and their models do not account for factors such as those mentioned above (Kaya 2014).

However, there is an additional signal, ingrained in fans’ demand for understanding the players’ current state: pre-game interviews. In widely successful sports such as baseball, football, and basketball, top players and coaches are regularly interviewed before and after games. These interviews are usually conducted to get a glimpse of how players and coaches are currently feeling and allow them to share their thoughts, given the specifics of the upcoming game and the baggage they are carrying from previous games. Following the sports psychology literature, we wish to use these interviews to gain insight about the players’ emotional state and its relation to actions (Uphill, Groom, and Jones 2014).2

In the sports psychology literature, there is a long-standing attempt to map the relationship between what this literature defines as “emotional state” and performance. The most popular account of such a relationship is the model of Individual Zones of Optimal Functioning (IZOF) (Hanin 1997). IZOF proposes that there are individual differences in the way athletes react to their emotional state, with each having an optimal level of intensity for each emotion for achieving top performance. IZOF suggests viewing emotions from a utilitarian perspective, looking at their helpfulness in achieving individual and team goals, and aims to calibrate the optimal emotional state for each player to perform at her best.

In this paper we build on that literature and aim to predict actions in basketball, using the added signal provided in the interviews. We explore a multimodal learning scheme, exploiting player interviews alongside performance metrics or without them. We build models that use as input the text alone, the metrics, and both modalities combined. As we wish to test for the predictive power of language, alone or in combination with past performance metrics, we look at all three settings, and discuss the learned representation of the text modality with respect to the “emotional state” that could be captured through the model.

We treat the player’s deviation from his mean performance measure in recent games as an indication to the actions made in the current game. By learning a mapping from players’ answers to underlying performance changes, we hope to integrate a signal about their thoughts into the action prediction process. Our choice to focus on deviations from the mean performance, and not on absolute performance values, is also useful from a machine learning perspective: It allows us to generalize across players, despite the differences in their absolute performance. We leave a more in-depth discussion of the formulation of our prediction task for later in the article (Section 4).

Being interested in the added behavioral signal hidden in the text, we focus on the task (Section 4) of predicting metrics that are associated in the literature with in-game behavior and are endogenous to the player’s strategic choices and mental state: shot success share on the offensive side, and fouls on the defensive side (Goldman and Rao 2011). We further add our own related metrics: the player’s mean shot location, his assists to turnovers ratio, and his share of 2-point to 3-point shot attempts. We choose to add those metrics as they are measurable on a play-by-play basis, and are interesting measures of relative risk. We believe our proposed measures can isolate to some extent the risk associated with specific types of decisions, such as when to pass, when to shoot, and where to do it.

Almost no single play result is a function of only one player’s action; yet, our positive results from models that exploit signals from individual players only (Section 7) indicate that meaningful predictions can be made even without direct modeling of inter-player interactions. As this is a first report on the topic, we leave for future work an exploration of how player interactions can be learned, noting that such an attempt will surely entail a more complex model.3 Also, we believe that if the interviews provide a strong signal regarding players’ in-game decisions, it should be observed even when interactions are not explored. Hopefully, our work will encourage future research that considers interactions as well.

We collected (Section 3) a data set of 1,337 interviews with 36 major NBA players during a total of 14 seasons. Each interview is augmented with performance measures of the player in each period (quarter) of the corresponding game. To facilitate learnability, we focus on NBA all-stars as they are consistently interviewed before games, and have played key roles throughout their career. Also, the fact that many players in our data set are still active and are expected to remain so in the following years, gives us an opportunity to measure our model’s performance and improve it in the future.

We start by looking at a regression model as a baseline for both the text-only and the metrics-only schemes. Then, we experiment with structure-aware neural networks for their feature learning capabilities and propose (Section 5) models based on long short-term memory (LSTM) (Hochreiter and Schmidhuber 1997) and convolutional neural network (CNN) (LeCun et al. 1998). Finally, to better model the interview structure and to take advantage of recent advancements in contextual embeddings, we also use a BERT-based architecture (Vaswani et al. 2017; Devlin et al. 2019) and explore the trade-off between a light-weight attention mechanism and more parameter-heavy alternatives (Section 5).

Our results (Sections 6, 7) suggest that our text-based models are able to learn from the interviews to predict the player’s performance metrics, while the performance-based baselines are not able to predict much better than a coin flip or the most common class, a phenomenon we try to explain in Section 7.

Interestingly, the models that exploit both the textual signal and the signal from past performance metrics improve on some of the most challenging predictions. These results are consistent with the hypothesized relationship of mental state and performance, and support claims in the literature that such an “emotional state” has predictive power on player performance (Lazarus 2000; Hanin 2007).

Our contributions to the sports analytics and natural language processing (NLP) literature are as follows: (1) We provide the first model, as far as we know, that predicts player actions from language. (2) Our model is the first that can predict relative player performance without relying on past performance. (3) On a more conceptual level, our results suggest that the player’s “emotional state” is related to player performance.

We support our findings with a newly proposed approach to qualitative analysis (Section 8). As neural networks are notoriously difficult to directly interpret, we choose to analyze text-based neural network models via topic modeling of the texts associated with the model’s predictions. Alternative approaches for model explanations do not allow for reasoning over higher-level concepts such as topics. Hence, we believe this could be a beneficial way to examine many neural models in NLP and view this as an additional contribution we present in this paper.

This analysis includes a comparison of our best performing models and finds that our BERT-based model is most associated with topics that are intuitively related to each prediction task, suggesting that the hypothesized “emotional state” from the sports psychology literature could have been learned. Additionally, we find that this correlation becomes stronger as the confidence of the model in its prediction increases, meaning that a higher probability for such topics corresponds to higher model confidence. Finally, we compare our models and observe that better performing models yield higher correlation with more informative topics.

In conclusion, we believe that this article provides evidence for the transmission of language into human actions. We demonstrate that our models are able to predict real-world variables via text, extending a rich NLP tradition and literature about tasks such as sentiment analysis, stance classification, and intent detection that also extract information regarding the text author. We hope this research problem and the high-level topic will be of interest to the NLP community. To facilitate further research we also release our data and code.

Previous work on the intersection of language, behavior, and sports is limited because of the rarity of relevant textual data (Xu, Yu, and Hoi 2015). However, there is an abundance of research on predicting human decision-making (e.g., Hartford, Wright, and Leyton-Brown 2016; Plonsky et al. 2017; Rosenfeld and Kraus 2018), on using language to predict human behavior (Niculae et al. 2015; Sim, Routledge, and Smith 2016), and on predicting outcomes in basketball (Cervone et al. 2014; Ganguly and Frank 2018). Because we aim to bridge the gap between the different disciplines, we survey the relevant work in each.

### 2.1 Prediction and Decision-Making

Previous decision-making work is both theoretical—modeling the incentives individuals face and the equilibrium observed given their competing interests (Gilboa 2009), and empirical—aiming to disentangle causal relationships that can shed light on what could be driving actions observed in the world (Kahneman and Tversky 1979; Angrist and Pischke 2008).

There are some interesting attempts at learning to better predict human action (Erev and Roth 1998; Wright and Leyton-Brown 2010; Hartford, Wright, and Leyton-Brown 2016), but the task at hand is usually addressed in lab conditions or using synthetic data. In a noisy environment it becomes much harder to define the choice set, that is, the alternatives the agent faces, and to observe a clear outcome, the result of the action taken. In our setting we can only observe proxies to the choices made, and they can only be measured discretely, whenever a play is complete. Moreover, we cannot easily disentangle the outcome of the play from the choices that drove it, because actions are dependent on both teammates and adversaries.

Our work attempts to integrate linguistics signals into a decision prediction process. Language usage seems to be informative about the speaker’s current state of mind (Wardhaugh 2011) and his personality (Fasold and Stephens 1990). Yet this is rarely explored in the context of decision-making (Gilboa 2009). Here, we examine whether textual traces can facilitate predictions in decision-making.

### 2.2 NLP and Prediction of Human Behavior

NLP algorithms, and particularly deep neural networks (DNNs), often learn a low-dimensional language representation with respect to a certain objective and in a manner that preserves valuable information regarding the text or the agent producing it. For example, in sentiment analysis (Pang, Lee, and Vaithyanathan 2002) text written by different authors is analyzed with respect to the same objective of determining whether the text conveys positive or negative sentiment. This not only reveals something about the text, but also about the author—her personal stance regarding the subject she was writing about. One can view our task to share some similarity with sentiment classification as both tasks aim to learn something about the emotional state of the author of a given text.

A key difference between the two tasks, however, that poses a greater challenge in our case, is that in our task the signal we are aiming to capture is not clearly visible in the text, and requires inferring more subtle or abstract concepts than positive or negative sentiment. Given a movie review, an observer can guess if it is positive or negative rather easily. In our case, it is unclear where in the text the clue is regarding the players’ mental state, and it is even less clear how it will correspond to their actions. Moreover, the text in our task involves a form of structured dialog between two speakers (the player and the interviewer), which entails an additional level of complexity on top of the internal structures present for each speaker independently.

In a sense, our question is actually broader. We want to examine whether textual traces can help us in the challenging problem of predicting human action. There is a longstanding claim in the social sciences that one could learn information about a person’s character and his behavior from their choice of language (Fasold and Stephens 1990; Bickerton 1995; Wardhaugh 2011), but this claim was not put to test in a real-world setting such as those we are testing in. Granted, understanding character from language and predicting actions from language are quite different. However, if it is the case that neural networks could learn a character-like context using the final action as the supervision sign, it could have substantial implications for language processing and even the social sciences.

In the emerging field of computational social science, there is a substantial effort to harness linguistic signals to better answer scientific questions (Danescu-Niculescu-Mizil et al. 2013). This approach, also known as text-as-data, has led to many advancements in the prediction of stock prices (Kogan et al. 2009), understanding of political discourse (Field et al. 2018), and analysis of court decisions (Goldwasser and Daumé III 2014; Sim, Routledge, and Smith 2016). Our work adds another facet to this literature, trying to identify textual signals that enable the prediction of actions that are not explicitly mentioned in the text.

### 2.3 Prediction and Analysis in Basketball

Basketball is at the forefront of sports analytics. In recent decades, there have been immense efforts to document every aspect of the game in real-time, and currently for every game there are data capturing each play’s result, player and ball movements, and even crowd generated noise. Researchers have used this data to solve prediction tasks about game outcomes (Kvam and Sokol 2006; Ganguly and Frank 2018), points and performance (Cervone et al. 2014; Sampaio et al. 2015), and possession outcome (Cervone et al. 2016).

Recent work has also explored mechanisms that facilitate the analysis of the decisions that players and coaches make in a given match (Bar-Eli and Tractinsky 2000; Kaya 2014). Some have tried to analyze the efficiency and optimality of decisions across the game (Goldman and Rao 2011; Wang et al. 2018), whereas others have focused on the decisions made in the final minutes of the game, when they are most critical (McFarlane 2018). Also, attempts have been made to model strategic in-game interactions in order to simulate and analyze counterfactual scenarios (Sandholtz and Bornn 2018) and to understand the interplay in dynamic space creation between offense and defense (Lamas et al. 2015). We complement this literature by making text-based decision-related predictions. We address the player’s behavior and current mental state as a factor in analyzing his actions, whereas previous work in sports analytics focused only on optimality considerations. Following the terminology of the sports psychology literature, we attempt to link players’ emotional/mental state, as manifested in the interviews, to the performance, actions, and risk-taking in the game (Hanin 1997; Uphill, Groom, and Jones 2014).

We created our data set with the requirement that we have enough data on both actions and language, from as many NBA seasons as possible and for a variety of players. Although the number of seasons is constrained by the availability of transcribed interviews, we had some flexibility in choosing the players. To be able to measure a variety of actions and the corresponding interviews across time, we chose to focus on players who were important enough to be interviewed repeatedly and crucial enough for their team so that they play throughout most of the game. These choices allowed us to measure player performance not only at the game level, but also in shorter increments, such as the period level.

Our data set is therefore a combination of two resources: (1) a publicly available play-by-play data set, collected from basketball-reference.com; and (2) the publicly available interviews at ASAPsports.com, collected only for players who were interviewed in more than three different seasons. Interviews were gathered from the 2004–2005 basketball season up until June 2018. As this data set comes from a fairly unexplored domain with regard to NLP, we follow here with a basic description of the different sources. For a more detailed description and advanced statistics such as common topics, interview length, and player performance distributions, please see Tables 2, 3 and 4.

We processed the play-by-play data to extract individual metrics for each player in each game for which that player was interviewed. The metrics were collected at both the game and the period level (see Section 4 for the description of the metrics). We aggregated the performance metrics at the period level to capture performance at different parts of the game and reduce the effects of outliers.4 This is important because performance in the first quarter could have a different meaning than performance in the last quarter, where every mistake could be irreversible. Each interview consists of question-answer pairs for one specific player, and hence properties like the interview length and the length of the different answers are player-specific. Key players are interviewed before each game, but we have data mostly for playoff games, because they were the ones that were transcribed and uploaded.5 This bias makes sense since playoff interviews are more in-depth and they attract a larger audience. Overall, our data set consists of 2,144 interviews, with some players interviewed twice between consecutive games. After concatenating such interviews we are left with 1,337 interviews from 36 different players, and the corresponding game metrics for each interview. The total number of interview-period metric pairs is 5,226.

We next describe our in-game play-by-play data and the pre-game interviews, along with the processing steps we apply to each.

### 3.1 In-Game Play-by-Play

Basketball data are gathered after each play is done. As described in our “basketball dictionary” in Table 1, a play is any of the following events: Shot, Assist, Block, Free Throw, Rebound, Foul, Turnover, Violation, Time-out, Substitution, Jump Ball, and Start and End of Period. We ignore Time-outs, Jump Balls, Substitutions, and Start/End of Period plays as they do not add any information with respect to the metrics that we are monitoring. If a shot was successful, there could be an assist attributed to the passing player. Also, we observe for every foul the affected player and the opponent charged, as well as the player responsible for each shot, miss, free throw, and lost ball. For every shot taken, there are two location variables, indicating the shot’s coordinates on the court, with which we calculate relative distance from the basket (see Figure 1). We use those indicators to produce performance metrics for each period.

Table 1
Descriptions for basketball terms used in our data set. Explanations and rules derived from the official NBA rule book at: https://official.nba.com/rulebook/, and the Basketball Wikipedia page at: https://en.wikipedia.org/wiki/Basketball.
TermDescription
Shot Attempting to score points by throwing the ball through the basket. Each successful shot is worth 3 points if behind the 3 point arc, and 2 otherwise.
Assist Passing the ball to a teammate that eventually scores without first passing the ball to any other player.
Block Altering an attempted shot by touching the ball while still in the air.
Free Throw Unopposed attempts to score by shooting from behind the free throw line. Each successful free throw is worth one point.
Rebound Obtaining the ball after a missed shot attempt.
Foul Attempting to unfairly disadvantage an opponent through certain types of physical contact.
Turnover A loss of possession by a player holding the ball.
(Shot Clock) Violation Failing to shoot the ball before the shot clock expires. Results in a turnover to the opponent team.
Time-out A limited number of clock stoppages requested by a coach or mandated by the referee for a short meeting with the players.
Substitution Replacing one player with another during a match. In basketball, substitutions are permitted only during stoppages of play, but are otherwise unlimited.
Jump Ball A method used to begin or resume the game, where two opposing players attempt to gain control of the ball after an official tosses it into the air between them.
Period NBA games are played in four periods (quarters) of 12 minutes. Overtime periods are 5 minutes in length. The time allowed is actual playing time; the clock is stopped while the play is not active.
TermDescription
Shot Attempting to score points by throwing the ball through the basket. Each successful shot is worth 3 points if behind the 3 point arc, and 2 otherwise.
Assist Passing the ball to a teammate that eventually scores without first passing the ball to any other player.
Block Altering an attempted shot by touching the ball while still in the air.
Free Throw Unopposed attempts to score by shooting from behind the free throw line. Each successful free throw is worth one point.
Rebound Obtaining the ball after a missed shot attempt.
Foul Attempting to unfairly disadvantage an opponent through certain types of physical contact.
Turnover A loss of possession by a player holding the ball.
(Shot Clock) Violation Failing to shoot the ball before the shot clock expires. Results in a turnover to the opponent team.
Time-out A limited number of clock stoppages requested by a coach or mandated by the referee for a short meeting with the players.
Substitution Replacing one player with another during a match. In basketball, substitutions are permitted only during stoppages of play, but are otherwise unlimited.
Jump Ball A method used to begin or resume the game, where two opposing players attempt to gain control of the ball after an official tosses it into the air between them.
Period NBA games are played in four periods (quarters) of 12 minutes. Overtime periods are 5 minutes in length. The time allowed is actual playing time; the clock is stopped while the play is not active.
Figure 1

Shot location of all attempted shots for all the players in our data set. A darker color represents more shots attempted at that location. Black lines represent the structure of one of the two symmetric halves of an NBA basketball court.

Figure 1

Shot location of all attempted shots for all the players in our data set. A darker color represents more shots attempted at that location. Black lines represent the structure of one of the two symmetric halves of an NBA basketball court.

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For each event there are 10 variables indicating the five-player lineup per team, which we use to monitor whether a player is on court at any given play. In a typical NBA game, there are about 450 plays. Because we are only collecting data for key players, they are present on court during the vast majority of the game, totalling an average of 337 plays per player per game, for an average of 83 plays per period. For each period, we aggregate a player’s performance through the following features: Points, Assists, Turnovers, Rebounds, Field goals made and missed, Free throws made and missed, and mean and variance of shot distance from basket, for both successful and unsuccessful attempts. We build on these features to produce metrics that we believe capture the choice of actions made by the player (see Section 4). Table 2 provides each player’s mean and standard deviation values for all performance metrics. The table also provides the average and standard deviation of the metrics across the entire data set, information that we use to explain some of our findings in Section 7 and modeling decisions in Section 4.

Table 2
Performance metric mean and standard deviation (in parentheses) per player in our data set. We report here the actual values of the performance metrics rather than deviations from the mean. For the definition of the performance metrics, see Section 4.
PlayerPFPTSFGRPRSRMSD2MSD3# Plays
Al Horford 2.07 (1.07) 12.5 (6.71) 0.52 (0.18) 0.26 (0.19) 0.22 (0.17) 5.97 (4.74) 6.81 (6.69) 299.14 (57.97)
Andre Iguodala 2.19 (1.44) 10.42 (6.44) 0.6 (0.2) 0.26 (0.27) 0.42 (0.22) 9.56 (8.5) 8.42 (6.6) 315.0 (68.38)
Carmelo Anthony 3.72 (1.27) 22.78 (7.38) 0.41 (0.1) 0.41 (0.26) 0.22 (0.13) 5.67 (3.61) 6.37 (4.12) 354.0 (51.21)
Chauncey Billups 2.84 (1.42) 18.42 (5.64) 0.5 (0.15) 0.23 (0.21) 0.41 (0.15) 13.7 (13.94) 9.54 (6.84) 368.61 (53.57)
Chris Bosh 2.77 (1.56) 15.87 (7.18) 0.52 (0.19) 0.57 (0.34) 0.12 (0.15) 5.45 (3.94) 4.24 (7.25) 312.11 (49.5)
Chris Paul 3.43 (1.17) 19.8 (7.43) 0.51 (0.1) 0.22 (0.15) 0.31 (0.14) 9.81 (5.27) 9.72 (6.45) 341.14 (57.69)
Damian Lillard 2.08 (1.24) 27.42 (8.07) 0.48 (0.1) 0.43 (0.25) 0.39 (0.13) 10.51 (5.73) 9.19 (5.23) 370.9 (39.93)
DeMar DeRozan 2.73 (1.19) 26.0 (10.52) 0.53 (0.09) 0.48 (0.21) 0.08 (0.09) 5.71 (1.58) 2.12 (3.64) 345.45 (30.37)
Derek Fisher 3.13 (1.61) 8.67 (5.04) 0.54 (0.22) 0.26 (0.21) 0.36 (0.22) 13.06 (14.27) 7.46 (8.26) 282.97 (60.32)
Dirk Nowitzki 2.55 (1.52) 24.36 (8.29) 0.49 (0.14) 0.48 (0.22) 0.17 (0.12) 7.02 (3.01) 8.19 (8.4) 359.12 (61.25)
Draymond Green 4.0 (1.38) 13.02 (6.59) 0.54 (0.19) 0.3 (0.18) 0.39 (0.16) 8.49 (9.61) 7.34 (6.75) 359.68 (47.89)
Dwyane Wade 2.88 (1.46) 23.07 (8.09) 0.5 (0.12) 0.4 (0.18) 0.09 (0.09) 4.49 (2.36) 4.25 (6.7) 350.26 (55.72)
James Harden 2.9 (1.58) 23.8 (9.69) 0.47 (0.14) 0.32 (0.19) 0.43 (0.14) 9.5 (6.08) 8.13 (6.01) 351.27 (66.4)
Kawhi Leonard 2.56 (1.69) 13.0 (5.3) 0.47 (0.18) 0.46 (0.32) 0.33 (0.15) 8.51 (6.82) 8.03 (6.08) 277.17 (70.58)
Kevin Durant 2.58 (1.44) 28.34 (6.86) 0.54 (0.11) 0.44 (0.24) 0.29 (0.09) 8.92 (4.13) 9.75 (5.69) 378.85 (52.26)
Kevin Garnett 3.0 (1.31) 14.83 (5.56) 0.54 (0.2) 0.44 (0.33) 0.02 (0.04) 4.7 (2.16) 0.0 (0.0) 318.31 (64.31)
Kevin Love 2.33 (1.34) 15.75 (9.17) 0.44 (0.15) 0.47 (0.27) 0.44 (0.16) 11.0 (7.95) 8.13 (4.79) 281.58 (58.15)
Klay Thompson 2.51 (1.49) 19.34 (8.65) 0.48 (0.11) 0.45 (0.28) 0.48 (0.15) 16.17 (14.97) 8.92 (4.18) 352.96 (58.37)
Kobe Bryant 2.93 (1.59) 28.07 (7.1) 0.48 (0.09) 0.38 (0.2) 0.24 (0.13) 8.21 (4.21) 7.6 (5.91) 373.7 (53.15)
Kyle Lowry 3.33 (1.32) 21.56 (9.9) 0.49 (0.14) 0.3 (0.2) 0.48 (0.17) 14.09 (11.57) 8.94 (3.97) 334.67 (46.15)
Kyrie Irving 2.44 (1.5) 25.2 (8.34) 0.52 (0.11) 0.37 (0.19) 0.28 (0.14) 9.19 (5.8) 11.49 (7.31) 339.68 (70.44)
Lamar Odom 3.92 (1.64) 12.29 (5.19) 0.52 (0.18) 0.4 (0.27) 0.14 (0.14) 3.06 (2.49) 3.94 (7.82) 309.29 (56.57)
LeBron James 2.49 (1.39) 28.75 (8.66) 0.53 (0.12) 0.34 (0.16) 0.22 (0.1) 5.81 (3.27) 8.2 (6.07) 380.43 (56.21)
Manu Ginobili 3.02 (1.24) 14.84 (7.47) 0.5 (0.19) 0.39 (0.24) 0.44 (0.14) 9.6 (7.8) 7.98 (5.76) 276.0 (65.68)
Pau Gasol 2.97 (1.2) 16.54 (5.99) 0.56 (0.14) 0.36 (0.25) 0.01 (0.03) 2.72 (1.88) 0.0 (0.0) 356.95 (70.03)
Paul George 2.58 (1.54) 21.21 (8.2) 0.5 (0.11) 0.39 (0.18) 0.43 (0.11) 11.03 (4.44) 10.88 (5.76) 326.11 (64.57)
Paul Pierce 3.62 (1.5) 19.56 (7.85) 0.52 (0.2) 0.47 (0.24) 0.31 (0.19) 8.2 (5.38) 9.12 (7.56) 351.69 (77.83)
Rajon Rondo 2.74 (1.51) 12.19 (6.53) 0.5 (0.21) 0.23 (0.11) 0.08 (0.09) 3.22 (2.27) 3.97 (8.03) 354.26 (59.83)
Ray Allen 2.56 (1.35) 14.9 (7.28) 0.5 (0.2) 0.45 (0.3) 0.5 (0.17) 13.56 (8.91) 9.26 (6.16) 342.85 (71.59)
Richard Hamilton 3.61 (1.31) 20.83 (6.91) 0.5 (0.16) 0.36 (0.25) 0.07 (0.06) 5.1 (2.57) 2.32 (4.65) 382.09 (61.51)
Russell Westbrook 2.85 (1.51) 24.3 (8.54) 0.45 (0.11) 0.33 (0.14) 0.21 (0.1) 5.16 (3.28) 6.46 (5.86) 363.52 (55.8)
Shaquille O’Neal 3.68 (1.7) 15.79 (6.96) 0.61 (0.22) 0.71 (0.23) 0.0 (0.0) 1.43 (1.08) 0.0 (0.0) 275.37 (89.38)
Stephen Curry 2.48 (1.36) 26.42 (8.42) 0.48 (0.11) 0.37 (0.18) 0.55 (0.11) 18.0 (8.59) 10.67 (4.05) 362.49 (62.61)
Steve Nash 1.73 (1.2) 19.09 (6.38) 0.55 (0.13) 0.25 (0.15) 0.24 (0.12) 8.42 (3.77) 8.93 (7.0) 334.45 (46.15)
Tim Duncan 2.65 (1.31) 18.43 (7.53) 0.51 (0.15) 0.46 (0.28) 0.01 (0.03) 2.55 (1.41) 0.44 (3.27) 324.07 (58.05)
Tony Parker 1.65 (1.14) 18.02 (6.99) 0.52 (0.16) 0.32 (0.19) 0.1 (0.09) 5.27 (3.24) 6.45 (9.09) 317.44 (52.21)

data set Average 2.791 20.214 0.511 0.38 0.265 7.347 6.922 336.77
data set Std. 1.489 9.438 0.153 0.239 0.204 6.054 6.771 66.44
PlayerPFPTSFGRPRSRMSD2MSD3# Plays
Al Horford 2.07 (1.07) 12.5 (6.71) 0.52 (0.18) 0.26 (0.19) 0.22 (0.17) 5.97 (4.74) 6.81 (6.69) 299.14 (57.97)
Andre Iguodala 2.19 (1.44) 10.42 (6.44) 0.6 (0.2) 0.26 (0.27) 0.42 (0.22) 9.56 (8.5) 8.42 (6.6) 315.0 (68.38)
Carmelo Anthony 3.72 (1.27) 22.78 (7.38) 0.41 (0.1) 0.41 (0.26) 0.22 (0.13) 5.67 (3.61) 6.37 (4.12) 354.0 (51.21)
Chauncey Billups 2.84 (1.42) 18.42 (5.64) 0.5 (0.15) 0.23 (0.21) 0.41 (0.15) 13.7 (13.94) 9.54 (6.84) 368.61 (53.57)
Chris Bosh 2.77 (1.56) 15.87 (7.18) 0.52 (0.19) 0.57 (0.34) 0.12 (0.15) 5.45 (3.94) 4.24 (7.25) 312.11 (49.5)
Chris Paul 3.43 (1.17) 19.8 (7.43) 0.51 (0.1) 0.22 (0.15) 0.31 (0.14) 9.81 (5.27) 9.72 (6.45) 341.14 (57.69)
Damian Lillard 2.08 (1.24) 27.42 (8.07) 0.48 (0.1) 0.43 (0.25) 0.39 (0.13) 10.51 (5.73) 9.19 (5.23) 370.9 (39.93)
DeMar DeRozan 2.73 (1.19) 26.0 (10.52) 0.53 (0.09) 0.48 (0.21) 0.08 (0.09) 5.71 (1.58) 2.12 (3.64) 345.45 (30.37)
Derek Fisher 3.13 (1.61) 8.67 (5.04) 0.54 (0.22) 0.26 (0.21) 0.36 (0.22) 13.06 (14.27) 7.46 (8.26) 282.97 (60.32)
Dirk Nowitzki 2.55 (1.52) 24.36 (8.29) 0.49 (0.14) 0.48 (0.22) 0.17 (0.12) 7.02 (3.01) 8.19 (8.4) 359.12 (61.25)
Draymond Green 4.0 (1.38) 13.02 (6.59) 0.54 (0.19) 0.3 (0.18) 0.39 (0.16) 8.49 (9.61) 7.34 (6.75) 359.68 (47.89)
Dwyane Wade 2.88 (1.46) 23.07 (8.09) 0.5 (0.12) 0.4 (0.18) 0.09 (0.09) 4.49 (2.36) 4.25 (6.7) 350.26 (55.72)
James Harden 2.9 (1.58) 23.8 (9.69) 0.47 (0.14) 0.32 (0.19) 0.43 (0.14) 9.5 (6.08) 8.13 (6.01) 351.27 (66.4)
Kawhi Leonard 2.56 (1.69) 13.0 (5.3) 0.47 (0.18) 0.46 (0.32) 0.33 (0.15) 8.51 (6.82) 8.03 (6.08) 277.17 (70.58)
Kevin Durant 2.58 (1.44) 28.34 (6.86) 0.54 (0.11) 0.44 (0.24) 0.29 (0.09) 8.92 (4.13) 9.75 (5.69) 378.85 (52.26)
Kevin Garnett 3.0 (1.31) 14.83 (5.56) 0.54 (0.2) 0.44 (0.33) 0.02 (0.04) 4.7 (2.16) 0.0 (0.0) 318.31 (64.31)
Kevin Love 2.33 (1.34) 15.75 (9.17) 0.44 (0.15) 0.47 (0.27) 0.44 (0.16) 11.0 (7.95) 8.13 (4.79) 281.58 (58.15)
Klay Thompson 2.51 (1.49) 19.34 (8.65) 0.48 (0.11) 0.45 (0.28) 0.48 (0.15) 16.17 (14.97) 8.92 (4.18) 352.96 (58.37)
Kobe Bryant 2.93 (1.59) 28.07 (7.1) 0.48 (0.09) 0.38 (0.2) 0.24 (0.13) 8.21 (4.21) 7.6 (5.91) 373.7 (53.15)
Kyle Lowry 3.33 (1.32) 21.56 (9.9) 0.49 (0.14) 0.3 (0.2) 0.48 (0.17) 14.09 (11.57) 8.94 (3.97) 334.67 (46.15)
Kyrie Irving 2.44 (1.5) 25.2 (8.34) 0.52 (0.11) 0.37 (0.19) 0.28 (0.14) 9.19 (5.8) 11.49 (7.31) 339.68 (70.44)
Lamar Odom 3.92 (1.64) 12.29 (5.19) 0.52 (0.18) 0.4 (0.27) 0.14 (0.14) 3.06 (2.49) 3.94 (7.82) 309.29 (56.57)
LeBron James 2.49 (1.39) 28.75 (8.66) 0.53 (0.12) 0.34 (0.16) 0.22 (0.1) 5.81 (3.27) 8.2 (6.07) 380.43 (56.21)
Manu Ginobili 3.02 (1.24) 14.84 (7.47) 0.5 (0.19) 0.39 (0.24) 0.44 (0.14) 9.6 (7.8) 7.98 (5.76) 276.0 (65.68)
Pau Gasol 2.97 (1.2) 16.54 (5.99) 0.56 (0.14) 0.36 (0.25) 0.01 (0.03) 2.72 (1.88) 0.0 (0.0) 356.95 (70.03)
Paul George 2.58 (1.54) 21.21 (8.2) 0.5 (0.11) 0.39 (0.18) 0.43 (0.11) 11.03 (4.44) 10.88 (5.76) 326.11 (64.57)
Paul Pierce 3.62 (1.5) 19.56 (7.85) 0.52 (0.2) 0.47 (0.24) 0.31 (0.19) 8.2 (5.38) 9.12 (7.56) 351.69 (77.83)
Rajon Rondo 2.74 (1.51) 12.19 (6.53) 0.5 (0.21) 0.23 (0.11) 0.08 (0.09) 3.22 (2.27) 3.97 (8.03) 354.26 (59.83)
Ray Allen 2.56 (1.35) 14.9 (7.28) 0.5 (0.2) 0.45 (0.3) 0.5 (0.17) 13.56 (8.91) 9.26 (6.16) 342.85 (71.59)
Richard Hamilton 3.61 (1.31) 20.83 (6.91) 0.5 (0.16) 0.36 (0.25) 0.07 (0.06) 5.1 (2.57) 2.32 (4.65) 382.09 (61.51)
Russell Westbrook 2.85 (1.51) 24.3 (8.54) 0.45 (0.11) 0.33 (0.14) 0.21 (0.1) 5.16 (3.28) 6.46 (5.86) 363.52 (55.8)
Shaquille O’Neal 3.68 (1.7) 15.79 (6.96) 0.61 (0.22) 0.71 (0.23) 0.0 (0.0) 1.43 (1.08) 0.0 (0.0) 275.37 (89.38)
Stephen Curry 2.48 (1.36) 26.42 (8.42) 0.48 (0.11) 0.37 (0.18) 0.55 (0.11) 18.0 (8.59) 10.67 (4.05) 362.49 (62.61)
Steve Nash 1.73 (1.2) 19.09 (6.38) 0.55 (0.13) 0.25 (0.15) 0.24 (0.12) 8.42 (3.77) 8.93 (7.0) 334.45 (46.15)
Tim Duncan 2.65 (1.31) 18.43 (7.53) 0.51 (0.15) 0.46 (0.28) 0.01 (0.03) 2.55 (1.41) 0.44 (3.27) 324.07 (58.05)
Tony Parker 1.65 (1.14) 18.02 (6.99) 0.52 (0.16) 0.32 (0.19) 0.1 (0.09) 5.27 (3.24) 6.45 (9.09) 317.44 (52.21)

data set Average 2.791 20.214 0.511 0.38 0.265 7.347 6.922 336.77
data set Std. 1.489 9.438 0.153 0.239 0.204 6.054 6.771 66.44

### 3.2 Pre-game Interviews

NBA players are interviewed by the press before and after games, as part of their contract with their team and with the league. The interviews take place on practice day, which is the day before the game, and on-court before, during, and after the game. An NBA season has 82 games per team, for all 30 teams, spread across 6 months, from October to April. Then, the top eight teams from each conference, Eastern and Western, advance to the playoffs, where teams face opponents in a knockout tournament composed of a best-of-seven series. Playoff games gather much more interest, resulting in more interviews, which are more in-depth and with much more on the line for players and fans alike. Our data set is hence composed almost solely from playoff game data.

Interviews are open-ended dialogues between an interviewer and a key player from one of the teams, with the length of the answers depending solely on the players, and the number of questions depending on both sides.6 Questions tend to follow on player responses, in an attempt to gather as much information about the player’s state of mind as possible. For example:

Q: “On Friday you spoke a lot about this new found appreciation you have this postseason for what you’ve been able to accomplish. For most people getting to that new mindset is the result of specific events or just thoughts. I’m wondering what prompted you specifically this off-season to get to this new mindset?”

LEBRON JAMES: “It’s not a new mindset. I think people are taking it a little further than where it should be. Something just—it was a feeling I was after we won in Game 6 in Toronto, and that’s how I was feeling at that moment. I’m back to my usual self.”

The degrees of freedom given result in a significant variance in interview lengths. Sentences vary from as little as a single word to 147, and interviews vary from 4 sentences to 753. Table 3 provides aggregated statistics about the interviews in our data set, as well as the number of interviews, average number of question-answer (Q-A) pairs, average number of sentences, and average number of words for each player.

Table 3
Number of interviews and averages of number of Q-A pairs, sentences, and words in an interview per player in our data set.
Player# of InterviewsAvg. # of Q-A pairsAvg. # of sentencesAvg. # of words
Al Horford 14 6.43 45.29 685.4
Andre Iguodala 26 12.69 111.08 1888.6
Carmelo Anthony 18 14.28 86.78 1075.8
Chauncey Billups 31 12.19 92.81 1545.6
Chris Bosh 47 11.53 97.96 1311.2
Chris Paul 35 12.49 82.66 1165.4
Damian Lillard 12 7.92 69.00 1115.5
DeMar DeRozan 11 14.36 84.91 1259.1
Derek Fisher 39 6.87 54.00 1149.7
Dirk Nowitzki 33 12.15 114.39 1737.7
Draymond Green 59 14.97 140.88 2161.9
Dwyane Wade 72 18.93 173.58 2494.7
James Harden 30 10.73 63.77 858.6
Kawhi Leonard 18 8.50 37.50 462.9
Kevin Durant 67 17.73 138.25 2094.2
Kevin Garnett 29 11.72 92.45 1459.1
Kevin Love 24 11.79 89.54 1508.6
Klay Thompson 53 13.42 112.25 1674.9
Kobe Bryant 44 25.93 142.27 1861.1
Kyle Lowry 14.44 92.67 1321.8
Kyrie Irving 25 16.04 125.00 2377.6
Lamar Odom 24 10.62 61.00 805.2
LeBron James 122 22.60 189.43 2875.5
Manu Ginobili 55 8.84 68.13 1032.8
Pau Gasol 39 11.38 80.41 1281.6
Paul George 19 12.58 88.63 1220.8
Paul Pierce 32 15.28 122.78 1965.2
Rajon Rondo 27 12.04 74.19 1021.8
Ray Allen 39 8.31 63.36 1068.1
Richard Hamilton 23 12.00 63.83 1099.2
Russell Westbrook 40 18.48 108.05 1567.5
Shaquille O’Neal 19 12.63 70.53 1043.8
Stephen Curry 71 17.70 156.92 2762.9
Steve Nash 22 13.50 80.05 1132.0
Tim Duncan 54 13.13 86.26 1380.9
Tony Parker 55 12.75 80.84 1156.3

Data set average 37.14 14.52 110.28 1520.09
Data set standard deviation 22.11 3.53 6.26 568.08
Player# of InterviewsAvg. # of Q-A pairsAvg. # of sentencesAvg. # of words
Al Horford 14 6.43 45.29 685.4
Andre Iguodala 26 12.69 111.08 1888.6
Carmelo Anthony 18 14.28 86.78 1075.8
Chauncey Billups 31 12.19 92.81 1545.6
Chris Bosh 47 11.53 97.96 1311.2
Chris Paul 35 12.49 82.66 1165.4
Damian Lillard 12 7.92 69.00 1115.5
DeMar DeRozan 11 14.36 84.91 1259.1
Derek Fisher 39 6.87 54.00 1149.7
Dirk Nowitzki 33 12.15 114.39 1737.7
Draymond Green 59 14.97 140.88 2161.9
Dwyane Wade 72 18.93 173.58 2494.7
James Harden 30 10.73 63.77 858.6
Kawhi Leonard 18 8.50 37.50 462.9
Kevin Durant 67 17.73 138.25 2094.2
Kevin Garnett 29 11.72 92.45 1459.1
Kevin Love 24 11.79 89.54 1508.6
Klay Thompson 53 13.42 112.25 1674.9
Kobe Bryant 44 25.93 142.27 1861.1
Kyle Lowry 14.44 92.67 1321.8
Kyrie Irving 25 16.04 125.00 2377.6
Lamar Odom 24 10.62 61.00 805.2
LeBron James 122 22.60 189.43 2875.5
Manu Ginobili 55 8.84 68.13 1032.8
Pau Gasol 39 11.38 80.41 1281.6
Paul George 19 12.58 88.63 1220.8
Paul Pierce 32 15.28 122.78 1965.2
Rajon Rondo 27 12.04 74.19 1021.8
Ray Allen 39 8.31 63.36 1068.1
Richard Hamilton 23 12.00 63.83 1099.2
Russell Westbrook 40 18.48 108.05 1567.5
Shaquille O’Neal 19 12.63 70.53 1043.8
Stephen Curry 71 17.70 156.92 2762.9
Steve Nash 22 13.50 80.05 1132.0
Tim Duncan 54 13.13 86.26 1380.9
Tony Parker 55 12.75 80.84 1156.3

Data set average 37.14 14.52 110.28 1520.09
Data set standard deviation 22.11 3.53 6.26 568.08

In order to give further insight, we trained an LDA topic model (Blei, Ng, and Jordan 2003) for each player over all interviews in which he participated, and present the top words of the most prominent topic per player in Table 4. Unsurprisingly, we can see that most topics involve words describing the world of basketball (e.g., game, play, team, championship, win, ball, shot) and the names of other players and teams, yet with careful observation we can spot some words relating to the player’s or team’s performance in a game (e.g., dynamic, sharp, regret, speed, tough, mental, attack, defense, zone). Generally, most topics contain similar words across players, yet some players show interesting deviations from the “standard” topic.7

Table 4
Top 10 words in the most prominent topic for each player. A topic model was trained for each player on all his interviews in the data set.
 Al Horford live angel trip basically beautiful allow attack next week league Andre Iguodala year know lot rakuten see good warrior come play thing Carmelo Anthony game tough year come kobe play court take hand back Chauncey Billups NBA teammate award twyman thank year story maurice chauncey applause Chris Bosh really game know good team come play thing want look Chris Paul know bowl good team really play lot shot time bowling Damian Lillard straight breather buckle bad begin ne steph stage sick show DeMar DeRozan smith suggest tennis talking rival skin sit sick shut shown Derek Fisher game know play good team really feed come thing back Dirk Nowitzki good great team time back game lot first come always Draymond Green game thing team year know good come time really great Dwyane Wade game team play know good year come time last feel James Harden game good know shot play open team time first point Kawhi Leonard gear matter may minute morning normal noticing opposite order padding Kevin Durant play know good game team come thing shot talk want Kevin Garnett know game play thing lot team really day come want Kevin Love game team year play lot know good last ball feel Klay Thompson regret scary sharp sharpness shore shrug smith speed sulk thigh Kobe Bryant game good play night come take really something much talk Kyle Lowry challenge curious deep dynamic complete contender anything cavalier cake bucket Kyrie Irving game play come great time moment tonight team big would Lamar Odom really win year know last happen team good championship would LeBron James know game year team last able time play take thing Manu Ginobili game know tough good play sometimes see thing last happen Pau Gasol zone really know play much game expect tonight obviously sure Paul George know team something feel work want take together well see Paul Pierce team know come play year game talk look really lot Rajon Rondo game great ball team come play rebound win tonight take Ray Allen standing mental marquis orlando operate row problem thread accustom action Richard Hamilton relationship resolve demand record portland phone philly pay nut new Russell Westbrook team play good great thing able game come time different Shaquille O’Neal arena city fun would mistake lot talk back people really Stephen Curry game play good know team kind year really time obviously Steve Nash game really know play team back year well feel win Tim Duncan game play good team time come back lot want really Tony Parker good game play never rebound chance last big defense keep
 Al Horford live angel trip basically beautiful allow attack next week league Andre Iguodala year know lot rakuten see good warrior come play thing Carmelo Anthony game tough year come kobe play court take hand back Chauncey Billups NBA teammate award twyman thank year story maurice chauncey applause Chris Bosh really game know good team come play thing want look Chris Paul know bowl good team really play lot shot time bowling Damian Lillard straight breather buckle bad begin ne steph stage sick show DeMar DeRozan smith suggest tennis talking rival skin sit sick shut shown Derek Fisher game know play good team really feed come thing back Dirk Nowitzki good great team time back game lot first come always Draymond Green game thing team year know good come time really great Dwyane Wade game team play know good year come time last feel James Harden game good know shot play open team time first point Kawhi Leonard gear matter may minute morning normal noticing opposite order padding Kevin Durant play know good game team come thing shot talk want Kevin Garnett know game play thing lot team really day come want Kevin Love game team year play lot know good last ball feel Klay Thompson regret scary sharp sharpness shore shrug smith speed sulk thigh Kobe Bryant game good play night come take really something much talk Kyle Lowry challenge curious deep dynamic complete contender anything cavalier cake bucket Kyrie Irving game play come great time moment tonight team big would Lamar Odom really win year know last happen team good championship would LeBron James know game year team last able time play take thing Manu Ginobili game know tough good play sometimes see thing last happen Pau Gasol zone really know play much game expect tonight obviously sure Paul George know team something feel work want take together well see Paul Pierce team know come play year game talk look really lot Rajon Rondo game great ball team come play rebound win tonight take Ray Allen standing mental marquis orlando operate row problem thread accustom action Richard Hamilton relationship resolve demand record portland phone philly pay nut new Russell Westbrook team play good great thing able game come time different Shaquille O’Neal arena city fun would mistake lot talk back people really Stephen Curry game play good know team kind year really time obviously Steve Nash game really know play team back year well feel win Tim Duncan game play good team time come back lot want really Tony Parker good game play never rebound chance last big defense keep

Our goal in this section is to define metrics that reflect the player’s in-game decisions and actions and formulate prediction tasks based on our definitions. Naturally, the performance of every player in any specific game is strongly affected by global proper- ties such as his skills, and is strongly correlated with his performance in recent games. We hence define binary classification tasks, predicting whether the player is going to perform above or below his mean performance in the defined metrics. Across the data set, we found that the difference between mean and median performance is insignificant and both statistics are highly correlated, hence we consider them as equivalent and focus on deviation from the mean.

Different players have significantly different variances in their performance (see Table 2) across different metrics. This phenomenon is somewhat inherent to basketball players due to the natural variance in player skills, style, and position. Because of these evident variances, we did not attempt to predict the extent of the deviation from the mean, but preferred a binary prediction of the direction of the deviation. Another reason for our focus on binary prediction tasks is that given our rather limited data set size, and imbalance in number of interviews per player (some players were interviewed less than others, see Table 3), we would like our models to be able to learn across players. That is, the training data for each player should contain information collected on all other players, pushing us toward a prediction task that could be calculated for players with a varying number of training examples and substantially different performance distributions.

#### Performance Metrics.

We consider seven performance metrics:
• 1.

FieldGoalsRatio (FGR)

• 2.

MeanShotDistance2Points (MSD2)

• 3.

MeanShotDistance3Points (MSD3)

• 4.

PassRisk (PR)

• 5.

ShotRisk (SR)

• 6.

PersonalFouls (PF)

• 7.

Points (PTS)

We denote with M = {FGR, MSD2, MSD3, PR, SR, PF, PTS} the set of performance metrics. The performance metrics are calculated from the play-by-play data. In the notation below, p stands for a player, t for a period identifier in a specific game, and # is the count operator.8#{event}p,t denotes the number of events of type event for player p in a game period t. We consider the following events:
• •

shot: A successful shot.

• •

miss: An unsuccessful shot.

• •

2pt: A 2-point shot.

• •

3pt: A 3-point shot.

• •

assist: A pass to a player that had a successful shot after receiving the ball and before passing it to any other player.

• •

turnover: An event in which the ball moved to the opponent team due to an action of the player.

• •

pf: A personal foul.

We further use the notations Distp,t for a set containing the distances for all the shots player p took in period t, in which the distance of that shot from the basket is recorded, and ptsp,t for the total number of points in a certain period. Our performance metrics, $mtp$, are defined for a player p in a game period t, in the following way:
$MSDtp=Mean(Distp,t)$
(1)
$PFtp=#{pf}p,t$
(2)
$PTStp=ptsp,t$
(3)
$FGRtp=#{shot}p,t#{shot}p,t+#{miss}p,t$
(4)
$SRtp=#{3pt}p,t(#{miss}p,t+#{shot}p,t)$
(5)
$PRtp=#{turnover}p,t#{assist}p,t+#{turnover}p,t$
(6)
For MSD we consider two variants, MSD2 and MSD3, for the mean distance of 2- and 3-point shots, respectively.

For each metric m we define the player’s mean as:
$m-p=∑t=1Tpmtp|Tp|$
(7)
where Tp is the set of periods in which the player p participated. We further define the per-metric label set Ym as:
$Ym={ytp,m|p∈P,t∈T},ytp,m=1,mtp≥m-p0,otherwise$
(8)
where P is the set of players and T is the set of periods.9

For each player p and period t, we denote with $xtp$ the player’s interview text prior to the game of t, and with $ytp,m$ the label for performance metric m. In addition, lagged performance metrics are denoted with $yt−jp,m$, ∀j ∈ {1, 2, …, k} (k = 3 in our experiments).10 We transform each sample in our data set into interview-metric tuples, such that for a given player p and period t we predict $ytp,m$ given either:

• (a)

$xtp$: for the text-only mode of our models.

• (b)

{$yt−jp,m$|∀j ∈ {1, 2, …, k}, ∀mM}: for the metric only mode.

• (c)

{$xtp$, $yt−jp,m$|∀j ∈ {1, 2, …, k}, ∀mM}: for the joint text and metric mode.

In this article we consider an independent prediction task for each performance metric, but these metrics are likely to be strongly dependent (Vaz de Melo et al. 2012). Also, we look at each player’s actions independently, although there are connections between actions of different players and between different actions of the same player. We briefly discuss observed connections between our models for different tasks and their relation to the similarity between tasks in Section 7. However, as this is the first paper for our task, we do not attempt to model possible interactions between different players or between metrics that often occur in team sports, and leave these to be explored in future work.

### 4.2 Performance Measures and Decision-Making

Our article is about the transmission of language into actions. In practice we try to predict performance metrics that are associated with such actions. Our measures aim to capture different aspects of the in-game actions made by players. FGR is a measure of risk for the shots attempted. SR is also a measure of risk for attempted shots, yet it tries to capture a player’s choice to take riskier shots that are worth more points. MSD2 and MSD3 are measures of the shot location, trying to capture for a given shot type (2/3 points) how far a player is willing to go in order to score. PR considers another offensive aspect, passes, and because it accounts for both turnovers and assists, it captures part of the risk a player is willing to take in his choice of passing. PTS is a more obvious choice; it is the most commonly used metric to observe a player’s offensive performance. PF is related to defensive decisions and is correlated with aggressive behavior.

By carefully observing the data presented in Table 2, we can see that different metrics exhibit different levels of volatility across all players in our data set. More volatile metrics, such as field goals ratio (FGR), shot distance (MSD2/3), and shot risk (SR) are rather static at the player level but differ substantially between players. This volatility in shot-related measures across players could be explained by the natural differences in shot selection between players in different positions. For example, back-court players generally tend to take more 3-point shots than front-court players. Events such as 3-point shots are therefore much sparser in nature for many players, and in many periods they occur at most once if at all. This causes the MSD3 (i.e., Mean Shot Distance for 3-point shots) to be 0 many more times compared with other metrics in our data set. This volatility ultimately makes it harder to distinguish what drives variance in these metrics as opposed to more consistent metrics such as PF (Personal Fouls), PTS (Points), and PR (Pass Risk).

A possible explanation for PF and PTS being more consistent in our data set is that they are considered rather critical performance measures to the overall teams’ performance. Our data set mainly consists of NBA all-stars (who are key players on their teams), interviewed before relatively important playoff games, and thus they are expected by their teams and fans to be more consistent in these critical measures. While players differ substantially in terms of numbers of assists and turnovers, the pass risk (PR) metric accounts for this by looking at the ratio, resulting in a consistent measure across our data set.

Our core learning task is to predict players’ in-game actions from their pre-game interview texts. Interviews are texts that contain a specific form of structured open-ended turn-based dialog between two speakers—the interviewer and the interviewee—which to a certain extent hold opposite goals in the conversation. Generally speaking, an interviewer’s goal is to reveal pieces of exclusive information by giving the player a chance to reflect on his thoughts, actions, and messages. However, the player’s goal is to utilize the opportunity of public speaking to portray his competitive agenda and strengthen his brand, while maintaining a comfortable level of privacy. In-game performance metrics reflect different aspects of a player’s in-game actions, which expose some information about the variance in a player’s actions and performance between different games.

We formulated multiple binary classification tasks in Section 4, and these tasks pose several challenges from natural language processing perspectives:

• •

Time Series: Almost all samples in our data come from events (playoff series) that exhibit a certain form of time-dependence, meaning that subsequent events in the series may impact each other. This aspect requires careful treatment when designing our models and their features.

• •

Remote Supervision Signal: Our labels stem from variables (performance metrics) that are related to the speaker of the text and are only indirectly implied in the text. In this sense, our supervision signal refers to our input signal in an indirect and remote manner. This is in contrast to learning to predict the deviation from the mean based on past performance metrics, where the input and the output are tightly connected. This is also different from tasks such as sentiment analysis where the sentiment of the review is directly encoded in its text.

• •

Textual Structure: Our input consists of interviews, which exhibit a unique textual structure of a dialog between two speakers, with somewhat opposing roles: an interviewer and an interviewee. We are interested in capturing information from these interviews, relevant to labels related only to the interviewee. Yet, it is not trivial to say whether this information appears in the interviewee’s answers alone or what type of context and information the interviewer’s questions provide.

In light of these challenges, we design our models with four main questions in mind:
• 1.

Could classification models utilize pre-game interview text to predict some of the variance in players’ in-game performance at both game and period levels?

• 2.

Could text be combined with past performance metrics to produce better predictions?

• 3.

How could we explicitly model the unique textual structure of interviews in order to facilitate accurate performance prediction?

• 4.

Could DNNs jointly learn a textual representation of their input interview together with a task classifier to help us capture textual signals relevant to future game performance?

To tackle these questions, we chose to design metric-based, text-based, and combined models, and assign the −M, −T, and −TM suffixes to denote them, respectively. Within each set of models, we chose to explore different modeling strategies in an increasing order of complexity and specialization to our task. We next provide a high-level discussion of our models, and then proceed with more specific details.

#### Metric-based models.

We implement two standard autoregressive models, which are commonly used tools in time-series analysis, alongside a BiLSTM (Hochreiter and Schmidhuber 1997) model. Both models make a prediction for the next time step (game/period) given performance metrics from the three previous time steps. These models exhibit the predictive power of performance metrics alone, and serve as baselines for comparison to text-based models.

#### Text-based models.

We design our text-based models to account for different levels of textual structure. We start by implementing a standard bag-of-words text classifier, which represents an interview as counts of unigrams. We continue by implementing a word-level CNN (LeCun and Bengio 1995) model, which represents interviews as a sequence of words in their order of appearance. We then implement a sentence-level BiLSTM model, which represents interviews as a sequence of sentences, where each sentence is represented by the average of its word embeddings. Finally, we chose to implement a BERT (Devlin et al. 2019) model, which accounts for the interview structure by representing interviews as sequences of Q-A pairs. Each pair’s embeddings are learned jointly by utilizing the model’s representations for pairs of sequences, which are based on an attention mechanism (Vaswani et al. 2017) defined over the word-level contextual embeddings of the question and the answer. This serves as an attempt to account for the subtler context a question induces over an answer, and for the role of each speaker in the dialog. These text-based models exhibit the predictive power of text alone in our prediction task.

#### Combined models.

DNNs tranform their input signals into vectors and their computations are hence based on matrix calculations. This shared representation of various input signals makes these models highly suitable to multitask and crossmodal learning, as has been shown in a variety of recent NLP works (e.g., Søgaard and Goldberg 2016; Rosenfeld and Kraus 2018; Malca and Reichart 2018). We therefore implemented variants of our best performing LSTM and BERT text-based models that incorporate textual features from the pre-game interview with performance metrics from the previous three time steps. These models help us quantify the marginal effect of adding textual features in predicting the direction of the deviation from the player’s mean performance, over metric-based models. We next describe each of our models in details.

### 5.1 Metric-Based Autoregressive Models

An autoregressive (AR(k)) model is a representation of a type of a random process. It is a commonly used tool to describe time-varying processes, such as player performance. The AR model assumes that the output variable ($ytp,m$) depends linearly on its own k previous values and on a stochastic term ϵt (the prediction error) (Akaike 1969). We focus on AR(3) to prevent loss of data for players with very few examples (previous games) in our data set:
$ytp,m=c+∑j=13φjyt−jp,m+ϵt$
(9)
We also consider using all lagged metrics as features for predicting a current metric:
$ytp,m=c+∑j=13∑w∈Mφjwyt−jp,w+ϵt$
(10)
That is, we make predictions for a given game t, player p, and metric m, based on performance in the previous k = 3 games, using either the same metric m (Equation (9)) or all metrics in M (Equation (10)).

We used a standard linear regression and a logistic regression. We tested both models for all k values for which we had enough data, and k = 3 was chosen because it performed best in development data experiments. We report results only for the linear regression model, because both models performed similarly.

### 5.2 The BoW and TFIDF Text Classifiers

The bag-of-words (BoW) and term frequency-inverse document frequency (TFIDF) (Salton 1991) models are standard for text classification tasks (Yogatama and Smith 2014), and they therefore serve as our most basic text-based models. We constructed both BoW and TFIDF feature vectors per interview, and have tried using unigrams and bigrams, alone or in combination. We considered random forest (RF) (Liaw and Wiener 2002), support vector machine (SVM) (Cortes and Vapnik 1995), and logistic regression (LR) (Ng and Jordan 2002) classifiers. Whereas BoW provides a straight forward effective way to represent text, it assumes n-gram (in our case we tried n = 1, n = 2, n = 1, 2) independence and therefore does not take the structure of the text into account. TFIDF adjusts for the fact that some words are more frequent in general, but makes the same assumptions. We report results for the RF classifier for both BoW (unigrams) and TFIDF (unigrams + bigrams) feature sets, because these consistently performed better in development data experiments, for BoW and TFIDF respectively. Finally, because these simple models were consistently outperformed by our best text-based DNN models (see Section 7), we did not attempt to incorporate any performance metrics as features into them.

### 5.3 Deep Neural Networks

DNNs have proven effective for many text classification tasks (Kim 2014; Ziser and Reichart 2018). An appealing property of these models is that training a DNN using a supervision signal results not only in a predictive model, but also with a representation of the data in the context of the supervision signal. This is especially intriguing in our case, where the supervision signal is not clearly visible in the text, and is more related to its speaker.

Moreover, the text in our task is structured as a dialog between two speakers, which entails an additional level of contextual dependence between speakers, on top of the internal linguistic structures of the utterances produced by the individual speakers. These factors pose a difficult challenge from a modeling perspective, yet DNNs are known for their architectural flexibility that allows learning a joint representation for more than one sequence (Chen, Bolton, and Manning 2016), and have shown promising performance in different tasks where models attempt to capture nuanced phenomena in text (Peters et al. 2018).

We consider three models that excel on text classification tasks: CNN (Kim 2014), BiLSTM (Hochreiter and Schmidhuber 1997), and BERT (Devlin et al. 2019). In order to obtain a vectorized representation of an interview’s text, we used different text embedding techniques per model, each based on different pre-trained embedding models. Below we describe the various models.

#### 5.3.1 The CNN Model.

##### Motivation.

We implement a standard word-level CNN model for text classification (CNN-T), closely following the implementation described in Kim (2014). This model showed promising results on various text classification tasks such as sentiment classification and stance detection (Kim 2014). By implementing this model we aim to examine the extent to which a standard word-level text classification neural network, which does not explicitly account for any special textual structure except for the order of the words in the text, can capture our performance metrics from text.

##### Model Description.

Interviews are fed into the model as a sequence of words in their order of appearance in the interview. We concatenated the interview’s word embedding vectors into an input matrix, such that embeddings of consequent words appear in consequent matrix columns. Because interviews vary in length, we padded all word matrices to the size of the longest interview in our data set. We then used three 2D convolution layers with max-pooling and a final linear classification layer.

#### 5.3.2 The BiLSTM Models.

##### Motivation.

Our CNN model treats an interview as a single sequence of words, and apart from the fact that the order of words is maintained in the input matrix, it does not model any textual structure. By implementing BiLSTM-based models we aim to directly model the interview as a sequence of sentences, rather than of words. We believe that because interviews involve multiple speakers interacting in the form of questions and answers, where each question and answer are comprised of multiple sentences, a sequential sentence-level model could capture signals that word-level models cannot.

We chose to implement our text-based BiLSTM (LSTM-T) as a sentence-level sequential model, where each sentence is represented by the average of its pre-trained word embeddings (Adi et al. 2016). Because BiLSTM is a general sequential model, it also fits naturally as an alternative time-series model for performance metrics only (LSTM-M), similar to the AR(k) model described in Equation (10). The various model variants allow us to examine the independent effects of text and metrics on our prediction tasks, using the same underlying model. Moreover, we can now examine the effect of combining text and metric features together in a BiLSTM model (LSTM-TM) by concatenating the metric feature vectors used as input to LSTM-M with the final textual vector representation produced by LSTM-T (see Figure 2).

Figure 2

The LSTM-TM model. hn = $hnforward$$hnbackward$, |hn| = |$hnforward$| + |$hnbackward$|. ⊕ denotes the vector concatenation operator.

Figure 2

The LSTM-TM model. hn = $hnforward$$hnbackward$, |hn| = |$hnforward$| + |$hnbackward$|. ⊕ denotes the vector concatenation operator.

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##### Model Description.

We next provide the technical implementation details of each of our BiLSTM-based models.

##### LSTM-T.

The BiLSTM model for text is fed with the sentences of the interview, in their sequential order. Each sentence is represented by the average of its word embeddings. The BiLSTM’s last hidden-state forward and backward vectors are concatenated and fed into two linear layers with dropout and batch normalization, and a final linear classification layer (see the left part of Figure 2).

##### LSTM-M.

The BiLSTM model for metrics, which mimics the AR(k = 3) model of Equation (10), is fed at each time step with the performance metric labels from the last three time steps. We concatenate the last hidden states (forward and backward) and feed the resulting vector as input to a linear classifier. This model is almost identical to LSTM-T, differing only in the input layer.

##### LSTM-TM.

The BiLSTM model, which combines text and metrics, utilizes a similar mechanism as LSTM-T to produce the text vector representation. We then concatenate a vector containing all metrics from the past three time steps, to the text vector. The resulting vector is fed into a binary classifier, similar to the one described for LSTM-T (see Figure 2).

#### 5.3.3 The BERT Models.

##### Motivation.

We are seeking to capture information regarding the player’s pre-game state through the interview text, which comprises a series of consecutive Q-A pairs. In an interview, a player controls only his answers, where his choice of language can be observed in the context of the questions he is asked. Although the player does not have any control over the questions, these can be viewed as a second-order approximation of the player’s state because an interviewer is purposefully phrasing the questions directed at the player. Alternatively, one can view the questions as external information that we cannot attribute to the player based solely on that fact. We choose to proceed with the former approach, to view the questions as a valuable context to the player’s answers.

Since the unique structure of an interview encourages a form of speaker roles and contextual dependence, which may seem similar to other “looser” forms of discourse, in this work we choose to focus our modeling on the local dependencies within each pair of a question and its immediate answer. In future work we plan to further explore the interview structure in our modeling.

##### Interview Representation.

Our CNN model treats an interview as a single sequence of words, and our BiLSTM model treats an interview as a single sequence of sentences where each sentence is represented by the average of its word embeddings. Neither of these models take into account any other characteristics of the interview structure. Although there are CNN and LSTM-based models that aim to capture document structure, for example, hierarchy (Yang et al. 2016), adapting these to capture the subtleties of an interview structure is a non-trivial task.

BERT provides a method for producing a single joint contextual representation for two related text sequences (such as Q-A pairs), which attempts to represent both texts and the relations between them. We found this feature useful for our task and a natural fit for modeling interview structure, as it allowed us to break up each interview to its Q-A pairs, input them in sequence to BERT, and produce a respective sequence of Q-A vectors. We follow a similar method for producing Q-A vectors as described in the BERT paper (Devlin et al. 2019) and provide further details in our model description below.

From a technical perspective, handling texts that greatly vary in length requires some creativity, if we do not want to lose data by truncating long texts to a fixed maximum length. Moreover, it is empirically shown that many recurrent models, for example, LSTM, suffer performance degradation with increasing sequence length (Luong, Pham, and Manning 2015). Our choice of breaking up each interview into its Q-A pairs allows us also to handle shorter sequences at the interview level, as opposed to longer sentence or word level sequences. We let BERT carry out the heavy task of handling the word sequences for each Q-A pair, because it can handle a sequence of up to 512 tokens. We hypothesize that these factors contribute to a more effective interview representation.

##### Model Description.

Interviews are fed into the BERT model as a sequence of Q-A pairs in their order of appearance in the interview. We follow the terminology and methodology presented in the BERT paper (Devlin et al. 2019), which considers the [CLS] token vector from the last hidden layer of the BERT encoder as a representation of an entire input sequence for classification tasks. When a single input is composed of two sequences of text (a Q-A pair in our case), text_A represents the first sequence (a Question in our case) and text_B represents the second sequence (an Answer in our case). Each sequence ends with the special [SEP] token, which represents the end of a single sequence and acts as a separator between the two sequences. For each Q-A pair we produce a Q-A vector, by extracting the vector associated with the special [CLS] token from the last hidden layer of the BERT encoder. This results in a sequence of Q-A vectors per interview (see Figure 3).

Figure 3

The BERT-L-T model. n denotes the number of Q-A pairs in a given interview. Each Q-A pair is fed into BERT to produce a Q-A vector, and the resulting vectors are then fed in sequence to the BiLSTM. hn is generated in the same way as in the LSTM-TM model (see Figure 2).

Figure 3

The BERT-L-T model. n denotes the number of Q-A pairs in a given interview. Each Q-A pair is fed into BERT to produce a Q-A vector, and the resulting vectors are then fed in sequence to the BiLSTM. hn is generated in the same way as in the LSTM-TM model (see Figure 2).

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To produce a single vector representation per interview we implement two alternative models, BiLSTM (BERT-L-T) and Attention (BERT-A-T); both are detailed below. The final interview vector is fed into a linear classification layer activated with a sigmoid function (Finney 1952), to produce a binary prediction. At training, the BiLSTM parameters (BERT-L-T) and the attention parameters (BERT-A-T) are jointly trained with the classifier parameters. In both cases we use a pre-trained BERT model as a source of text representation (BERT feature-based approach [Devlin et al. 2019]11), and do not fine tune its text representation or classification parameters on our data, to avoid heavy computations.

##### BERT-L-T.

A BiLSTM is sequentially fed with the Q-A vectors, and its last hidden states (forward and backward) are concatenated to serve as the interview vector. See Figure 3 for an illustration of the model architecture.

##### BERT-A-T.

A simple attention mechanism (described in Yang et al. 2016) is used over the sequence of Q-A vectors, and produces a pooled vector that serves as the interview representation. See Figure 4 for an illustration of the model architecture. In almost all of our experiments BERT-A-T and BERT-L-T performed similarly, yet the BERT-A-T model proved to be slightly but consistently superior (see Section 7). We hypothesize that the attention mechanism serves as an efficient and effective method of pooling our Q-A vectors, which results in a much lighter model in terms of the number of learned parameters.

Figure 4

The BERT-A-T model. Attention is applied over a sequence of Q-A vectors, which are produced by feeding the interview’s Q-A pairs into BERT. hcontext is randomly initialized and jointly learned with the attention weights during the training process.

Figure 4

The BERT-A-T model. Attention is applied over a sequence of Q-A vectors, which are produced by feeding the interview’s Q-A pairs into BERT. hcontext is randomly initialized and jointly learned with the attention weights during the training process.

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##### BERT-A-TM.

We implemented a variant of the BERT-A-T model, where before the interview vector is fed into the classifier, it is concatenated with all performance metric labels from the last three games. This model lets us explore the combined value of textual and performance metric signals. See Figure 5 for an illustration of the model architecture.

Figure 5

The BERT-A-TM model. We use the same notation as presented in Figure 4.

Figure 5

The BERT-A-TM model. We use the same notation as presented in Figure 4.

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We perform two sets of experiments, differing in the level of metric aggregation: (a) game level; and (b) period level.12 Our period-level task does not distinguish between different periods within a game (that is, the model does not distinguish between, e.g., the second and the third period). In order to solve this task we hence train a classifier on data aggregated at the period level from the various periods in our data set. We experiment with both levels of aggregation in order to explore different aspects of the players’ actions and how they manifest in different parts of the game. Although game-level data is less volatile and can capture more general differences in a player’s performance, it could fail to show behavioral fluctuations that are more subtle, such as “clutch” decisions, momentum performance boosts, or a short series of mistakes. The period-level data can catch those subtleties and tell a more fine-grained story, though it is more sensitive to rare events, such as 3-point shots and fouls.

The differences between these two sub-tasks are demonstrated by the per-metric label distributions (see Table 2). Events such as 3-point shots are sparser in nature—many periods they occur at most once if at all. This causes the MSD of those shots to be 0 and leads to extreme class imbalance, making the classification task considerably more difficult.

Events such as shots in general, as captured by the PTS and FGR metrics, occur more regularly, and thus result in balanced classes at both the game and period levels. Balanced classes are generally desired in binary classification tasks, since imbalanced classes could easily bias models toward the common class in the training data, making it almost impossible for us to determine whether the models captured even the slightest effects from the data. This is especially desired in light of research question #4 presented in Section 5, where we set a goal to understand whether DNNs could learn a textual representation capable of capturing textual signals for our tasks. We would hence like to avoid the potential effects of imbalanced classes, which could inhibit our models from learning such textual representations.

The question of balanced data also stems in our task with respect to the interviewed players, since we do not have an equal number of interviews for all players (see Table 3). This could potentially bias our models toward specific players who are more prevalent in the data set. This could also complicate splitting our data set into training, development, and test sets. For each subset, we would ideally prefer to maintain the same ratio of interviews per player as in the entire data set, in addition to maintaining the same positive to negative classes ratio.

In this study, we chose to utilize a stratified 5-fold cross validation process (see Section 6.3), in order to maintain the positive to negative class ratio across our training, development, and test subsets. We did not attempt to explicitly maintain the ratio of interviews per player, because our aforementioned stratified process yielded subsets that fairly maintained this ratio. In future research, we plan on exploring the effects of different interviews per player ratios, to examine whether certain players exhibit linguistic or performance patterns different from other players, and whether our models could capture such patterns or be biased by them.

### 6.2 Models

We consider the following models (described in further detail in Section 5), and use the −T, −M, and −TM suffixes to denote model variants for textual, metric, and combined features, respectively:

• •

AR(3)-M - a linear autoregressive model that considers the last three time steps of the predicted performance metric.

• •

AR(3)-M* - a linear autoregressive model that considers the last three time steps of all performance metrics.

• •

LSTM-M - a BiLSTM model that considers the last three time steps of all performance metrics.

• •

BoW-RF-T - a Random Forest classifier that utilizes a unigram bag-of-words features set.

• •

TFIDF-RF-T - a Random Forest classifier that utilizes a TFIDF feature set defined over unigrams and bigrams.

• •

CNN-T - a word-level CNN model.

• •

LSTM-T - a sentence-level BiLSTM model.

• •

LSTM-TM - a model similar to LSTM-T, except that the text representation is combined with the last three time steps of all performance metrics, and the result is fed to the classification layer.

• •

BERT-L-T - a model that explicitly accounts for the Q-A structure of the input interviews, with BERT representations and LSTM sequence modeling.

• •

BERT-A-T - a model that explicitly accounts for the Q-A structure of the input interviews, with BERT representations and an attention mechanism.

• •

BERT-A-TM - a model similar to BERT-A-T, except that the text representation is combined with the last three time steps of all performance metrics, and the result is fed to the classification layer.

Recall our four research questions from Section 5. Our experiments are designed to compare between text and metric-based models, demonstrating the predictive power of text-based models in our task. In addition, they are designed to highlight the effects of different modeling strategies, in an increasing order of complexity and specialization to our task. Finally, we compare to the common class (CC) baseline, which assigns to every test set example the most common training label. We chose to add this baseline in order to examine the performance of our models in comparison to a more naive and “data-driven” approach that does not model either text nor past metrics (Sim, Routledge, and Smith 2016).

### 6.3 Cross-Validation

We randomly sampled 20% of our interviews and generated a held-out test set for each performance metric, per game and period tasks, each consisting of interviews and their related performance metrics.13 We then implemented a 5-fold cross validation procedure for each metric label, in each fold randomly sampling 80% of the remaining interviews for training and 20% for development. All our training, development, and test sets are stratified: The ratio of positive and negative examples in each subset is identical to the ratio in the entire data set.14

### 6.4 Implementation Details and Hyperparameters

All models were developed in Python, utilizing different packages per model.

#### Autoregressive Models.

We developed all models utilizing the statsmodels package (Seabold and Perktold 2010).

#### Bag-of-Words Models.

We developed all models with scikit-learn (Pedregosa et al. 2011).

#### 6.4.1 DNN Models.

For all neural network models, we used Dropout (Srivastava et al. 2014) with p = 0.2 and batch normalization for linear layers, ReLU as the activation function for all internal layers, and sigmoid as the activation function for output layers. Training is carried out for 500 epochs with early stopping and a batch size of 8 samples (interviews). Because of the variance in sentence and interview length, we used various batch padding (to the maximum length in batch) and masking techniques. We used binary cross entropy as our loss function, and the ADAM optimization algorithm (Kingma and Ba 2015) with the parameters detailed in Table 5.

Table 5
ParameterValue
Learning Rate 5e−04
Fuzz Factor ϵ 1e−08
Learning rate decay over each update 0.0
ParameterValue
Learning Rate 5e−04
Fuzz Factor ϵ 1e−08
Learning rate decay over each update 0.0
##### The CNN-T Model.

We utilize GloVe word embeddings (Pennington, Socher, and Manning 2014), trained on the 2014 Wikipedia dump + the Gigaword 5 corpus (6B tokens, 400K word types, uncased) where each word vector is of dimension d = 100.15 We developed this model with Keras (Chollet et al. 2015) over TensorFlow (Abadi et al. 2016). The hyperparameter values of the model are given in Table 6.

Table 6
The CNN-T model hyperparameters.
LayerFilter Size
Convolution 1
Convolution 2
Convolution 3
Linear Output
LayerFilter Size
Convolution 1
Convolution 2
Convolution 3
Linear Output
##### The BiLSTM Models.

For our text-based BiLSTM models (LSTM-T and LSTM-TM), we use the same GloVe word embeddings as in the CNN model described earlier. The size of the hidden textual representations at the forward and backward LSTMs is 100. Our LSTM-M model’s hidden state vector size is 7 because we have |M| = 7 metrics. We developed these models with PyTorch (Paszke et al. 2017). The hyperparameter values of the model are given in Table 7.

Table 7
The LSTM-T model hyperparameters.
LayerInput SizeOutput Size
Input (Embedding) |Vocabulary100
LSTMforwardLSTMbackward 100 200
Linear 1 200 100
Linear 2 100 32
Linear Output 32
LayerInput SizeOutput Size
Input (Embedding) |Vocabulary100
LSTMforwardLSTMbackward 100 200
Linear 1 200 100
Linear 2 100 32
Linear Output 32
##### BERT Models.

For our BERT models, we utilize BERT’s pre-trained models as a source of text representation. We experimented with two uncased pre-trained BERT models, both trained on the BookCorpus (800M words) (Zhu et al. 2015) and Wikipedia (2,500M words): BERT-Base (L = 12 layers, H = 768 hidden vector size, A = 12 attention heads, P = 110M parameters) and BERT-Large (L = 24, H = 1,024, A = 16, P = 340M), both publicly available via source code provided by Google Research’s GitHub repository.16 The BERT-Large model slightly outperformed BERT-Base in all of our experiments; hence we report results only for BERT-Large. We developed these models with PyTorch (Paszke et al. 2017), utilizing and modifying source code from HuggingFace’s “PyTorch Pretrained BERT” GitHub repository.17Table 8 details the hyperparamters used for the BERT-L-T model and Table 9 details the hyperparameters used for the BERT-A-T and BERT-A-TM models.

Table 8
The BERT-L-T model hyperparameters. H is the pre-trained BERT model’s hidden vector size (Hbase = 768, Hlarge = 1,024)
LayerInput DimensionsOutput Dimensions
BERT Pretrained Encoder Interview text H × # Q-A pairs
LSTMforwardLSTMbackward H × Max # Q-A pairs in batch 2H
Linear Output 2H
LayerInput DimensionsOutput Dimensions
BERT Pretrained Encoder Interview text H × # Q-A pairs
LSTMforwardLSTMbackward H × Max # Q-A pairs in batch 2H
Linear Output 2H
Table 9
The BERT-A-T model hyperparameters. H is defined as in Table 8.
LayerInput DimensionsOutput Dimensions
BERT Pretrained Encoder Interview text H × # Q-A pairs
Attention H × Max # Q-A pairs in batch H
Linear Output H
LayerInput DimensionsOutput Dimensions
BERT Pretrained Encoder Interview text H × # Q-A pairs
Attention H × Max # Q-A pairs in batch H
Linear Output H

We further experiment with our BERT models, by continuing the Language Model pre-training process for both the BERT-base and BERT-large uncased pre-trained models, on the interviews from our data set. Our goal in this experiment is to evaluate whether further pre-training of BERT on interview data would yield text representations that better capture features relevant to the basketball domain and hopefully improve prediction performance on our tasks.

We utilized the standard Masked Language Model (MLM) and Next Sentence Prediction (NSP) pre-training objectives of BERT (see Devlin et al. 2019). We ran the pre-training process for 1 and 3 epochs on the interview texts at the sentence level (to accommodate the NSP task), and tuned all BERT layers in this process. After completing the pre-training process, we used the new pre-trained BERT models as part of new variants of BERT-A-T and BERT-A-TM, and evaluate their performance on all seven tasks for both the game and the period levels. We denote these models as BERT-EPT-A-T and BERT-EPT-A-TM, respectively, where EPT stands for “extended pre-training.” Our results indicate that the BERT models with extended pre-training are less effective than the standard BERT models that are not pre-trained on interview text. We hence report our results with the standard BERT models and analyze the extended pre-training process in Section 7.

Examining and analyzing our results, we wish to address the four research questions posed in Section 5. That is, we wish to assess the interviews’ predictive power without and alongside past metrics (questions #1 and #2, respectively), the benefit of modeling the interviews’ textual structure (question #3), and the ability of DNNs to learn a textual representation relevant for predicting future performance metrics (question #4).

#### Overview.

The results are presented in Table 10 (top: game level, bottom: period level). First, they suggest that pre-game interviews have predictive power with respect to performance metrics on both game and period-level tasks (question #1). This is evident by observing that text-based (−T) models generally performed better than the most CC baseline and metric-based (−M) models. Performance for all BERT-based and LSTM-based models is superior to CC and metric-based models at the game level, yet at the period-level results are rather mixed. Second, they suggest that combining pre-game interviews with past performance metrics yields better performing models (question #2). This can be seen in the performance gain of our combined (−TM) models over their respective text-based models, and the overall best performance of the BERT-A-TM model in most tasks. Third, they support the use of structure-aware DNNs for these prediction tasks (question #3). This can be seen by the general performance gain of text-based models as their modeling complexity of textual structure rises, especially in game-level tasks. Furthermore, our DNN models generally outperformed non-neural models, suggesting that DNNs are able to learn a textual representation suitable to our tasks (question #4). We shall examine the results in further detail below, in light of our four research questions.

Table 10
Game-level (top) and period-level (bottom) accuracy on a 0–100 scale. Best accuracy on each performance metric is highlighted in bold. CC stands for the most common class baseline. Models that involve text perform best in all game-level tasks and in three of seven period-level tasks.
ModelPFPTSFGRPRSRMSD2MSD3
CC 50.4 52.4 50.9 52.8 57.3 55.3 58.9

AR(3)-M 43.7 49.6 48.9 51.9 57.3 53.7 59
AR(3)-M* 48.1 54.9 51.5 47.8 57.5 55.3 56.3
LSTM-M 50.1 50.5 48.2 48.8 58.2 56.9 55.9

BoW-RF-T 50.8 50.8 51.1 53.7 57.8 54.9 59.3
TFIDF-RF-T 51.5 53.7 53.3 53.3 57.6 58.0 57.6
CNN-T 51.9 54.9 50.4 48.5 57.5 53.7 57.8
LSTM-T 56.7 58.2 55.7 58.2 55.2 55.8 58.2
BERT-L-T 54.9 55.6 55.6 57.5 59.5 57.8 60.5
BERT-A-T 57.5 60.1 58.7 58.6 63.4 61.9 60.8

LSTM-TM 57.5 58.2 55.5 57.7 61.6 59.7 55.8
BERT-A-TM 59.3 60.7 60.5 60.1 61.2 59.7 60.8

ModelPFPTSFGRPRSRMSD2MSD3
CC 52.2 54.1 51.5 64.8 64.3 64 75.1

AR(3)-M 52.6 53.6 48.8 65 64.9 65.7 75.9
AR(3)-M* 53.3 54.2 51.7 65 63.2 65.7 75.9
LSTM-M 50.1 51.5 50.3 62.7 62.4 62.3 74.2

BoW-RF-T 52.3 52.5 49.3 60 61.6 58.2 67.1
TFIDF-RF-T 50.2 53.9 50.3 63.1 63.5 63.7 74.5
CNN-T 51.6 53.3 49.4 59.2 62.5 57 68.1
LSTM-T 51.6 53.7 52.3 64.1 64.9 63.1 74
BERT-L-T 53.2 56 53.6 63.8 63.6 64.3 74.5
BERT-A-T 55.6 53.7 52.3 64.3 63.7 64.2 75.1

LSTM-TM 52.3 58.3 56.6 63.6 63.4 63.4 74.2
BERT-A-TM 56.3 58.5 57.8 64.1 64.7 64.9 74.7
ModelPFPTSFGRPRSRMSD2MSD3
CC 50.4 52.4 50.9 52.8 57.3 55.3 58.9

AR(3)-M 43.7 49.6 48.9 51.9 57.3 53.7 59
AR(3)-M* 48.1 54.9 51.5 47.8 57.5 55.3 56.3
LSTM-M 50.1 50.5 48.2 48.8 58.2 56.9 55.9

BoW-RF-T 50.8 50.8 51.1 53.7 57.8 54.9 59.3
TFIDF-RF-T 51.5 53.7 53.3 53.3 57.6 58.0 57.6
CNN-T 51.9 54.9 50.4 48.5 57.5 53.7 57.8
LSTM-T 56.7 58.2 55.7 58.2 55.2 55.8 58.2
BERT-L-T 54.9 55.6 55.6 57.5 59.5 57.8 60.5
BERT-A-T 57.5 60.1 58.7 58.6 63.4 61.9 60.8

LSTM-TM 57.5 58.2 55.5 57.7 61.6 59.7 55.8
BERT-A-TM 59.3 60.7 60.5 60.1 61.2 59.7 60.8

ModelPFPTSFGRPRSRMSD2MSD3
CC 52.2 54.1 51.5 64.8 64.3 64 75.1

AR(3)-M 52.6 53.6 48.8 65 64.9 65.7 75.9
AR(3)-M* 53.3 54.2 51.7 65 63.2 65.7 75.9
LSTM-M 50.1 51.5 50.3 62.7 62.4 62.3 74.2

BoW-RF-T 52.3 52.5 49.3 60 61.6 58.2 67.1
TFIDF-RF-T 50.2 53.9 50.3 63.1 63.5 63.7 74.5
CNN-T 51.6 53.3 49.4 59.2 62.5 57 68.1
LSTM-T 51.6 53.7 52.3 64.1 64.9 63.1 74
BERT-L-T 53.2 56 53.6 63.8 63.6 64.3 74.5
BERT-A-T 55.6 53.7 52.3 64.3 63.7 64.2 75.1

LSTM-TM 52.3 58.3 56.6 63.6 63.4 63.4 74.2
BERT-A-TM 56.3 58.5 57.8 64.1 64.7 64.9 74.7

#### The Predictive Power of Interviews.

Game-level BERT-A-T, our top performing text-based model, outperforms the CC baseline and all metric-based models, in all seven tasks, with improvements over the CC baseline ranging up to an added accuracy of: 7.1% on personal fouls (PF), 7.7% on points (PTS), 7.8% on field goal ratio (FGR), 5.8% on pass risk (PR), 6.1% on shot risk (SR), 6.6% on mean 2-point shot distance (MSD2), and 1.9% on mean 3-point shot distance (MSD3). Game-level LSTM-T outperforms the most CC baseline and all metric-based models in five of the seven tasks.

For four period-level tasks, PR, SR, MSD2, and MSD3, the CC baseline and metric-based models outperform text-based and combined models. We hypothesize that this is because at many periods the participation of many of the players is limited, which results in a below-average performance. For all tasks at the game level, as well as for PF, PTS, and FGR at the period level, this is much less frequent and the text is then much more informative.

Interestingly, for most game-level tasks, metric-based models (that rely only on performance metric information) are not able to predict much better than a coin flip or the most CC baseline. Only in three cases does a metric-based model outperform these baselines by more than 1%: game-level PTS, period-level PF, and period-level MSD2. These results emphasize the achievement of text-based prediction that succeeds where standard approaches fail.

#### The Predictive Power of Text and Performance Metric Combination.

BERT-A-TM outperforms BERT-A-T, its text-only counterpart (which outperforms all other models across all seven game-level tasks), in four out of seven game-level tasks (PF, PTS, FGR, and PR are on par for MSD3) and in five out of seven period-level tasks. Game-level BERT-A-TM performs particularly well on the personal fouls (PF) and pass risk (PR) tasks, outperforming the most common class baseline (CC) by 8.9% and 7.3%, respectively. Interestingly, both metrics tend to be similar across players (see Table 2). Deviations from the mean in these metrics reflect an increased or decreased level of aggressiveness (PF for defensive and PR for offensive decisions), suggesting that this quality is somewhat more visible in the language shown in the interviews.

More volatile metrics, such as field goals ratio (FGR), shot distance (MSD2/3), and shot risk (SR) are rather static at the player level but differ substantially between players (see Table 2). This makes it harder to distinguish what drives variance in those metrics. Our results on those tasks are not as strong as those of the PF, PTS, and PR tasks, but besides MSD3 we still observe significant improvement for most text-based (−T) and combined models (−TM) over the alternative models (see game-level results in Table 10).

A closer look into the data reveals a potential explanation for the superiority of BERT-A-TM on period-level PF, PTS, and FGR: Because these performance metrics are less volatile between periods, it is useful for BERT-A-T to use past performance metrics to better predict current player performance, compared with the text-only alternative.18 Adding performance metric information is hence particularly useful in these setups.

The game-level LSTM-TM model substantially outperforms the LSTM-T model, its text-only counterpart, on SR and MSD2, but the two models perform similarly on the other tasks, with the exception of MDS3, where LSTM-T outperforms LSTM-TM. Period-level LSTM-TM outperforms LSTM-T on PF, PTS, and FGR, yet LSTM-T outperforms LSTM-TM on SR. Overall, combining text and metrics with the LSTM-based models proves to be valuable in some of the tasks, but certainly not in all of them. Given the comparison between BERT-A-TM and BERT-A-T, and between LSTM-TM and LSTM-T, we can conclude that BERT better captures the combination between text and past performance metrics compared with LSTM.

We also look at the variation in our models’ performance across all five folds, to test for their robustness. For this, we calculated the standard deviation of our models across all folds and have found that in all seven game-level tasks and seven period-level tasks, the average standard deviations of BERT-A-T and BERT-A-TM were lower than the average standard deviations of each of the non-neural models (BoW-RF-T, TFIDF-RF-T, and the AR models). On average, the standard deviation of the BERT-A-T and BERT-A-TM models is 1% (absolute, i.e., 1 accuracy point), a fifth of the standard deviation of the TFIDF-RF-T, the best-performing non-neural model. Some non-neural models are less noisy than TFIDF-RF-T, but have a standard deviation of at least 1.5% and are still much noisier than the BERT-A-T and BERT-A-TM models.

To summarize, BERT-A-TM is our overall best performing model, outperforming all other models in a total of 8 (5 game-level and 3 period-level tasks) out of 14 tasks. In all seven game-level prediction tasks and in three of the period-level tasks (in total 10 out of 14 tasks), it is a BERT-A model that performs best. In eight of these cases it is BERT-A-TM and only in two is it BERT-A-T. This clearly indicates the added value of the textual signal on top of the signal in past metrics.

#### The Value of DNN Modeling: Textual Structure and Representation Learning.

With regard to our third and fourth questions, Table 10 reveals a general performance gain when using text-based DNN models, as they capture more intricate aspects of the interview structure. Notably, at both the game- and the period-level the text-based BERT-A-T model outperforms the TFIDF-RF-T non-neural text-based model (in seven of seven game-level comparisons and in six of seven period-level comparisons). Moreover, it is clear from the table that overall the text-based BERT-A-T model outperforms the text-based LSTM-T model, which in turn outperforms the text-based CNN-T model. This leads to two conclusions. First, it suggests that DNNs are able to learn a textual representation suitable for our tasks, which might be needed due to the remote nature of the supervision signal, as discussed in Section 5 (question #4). Second, it suggests that modeling the textual structure of interviews is valuable for our tasks (question #3).

In particular, modeling an interview on a Q-A level better captures the interview structure compared with simpler word or sentence-level modeling. In addition, we hypothesize that the attention mechanism handles sequences of jointly represented Q-A pairs better than more rigid sequential models such as LSTMs. This observation is further supported by the better performance of the attention-based BERT-A-T model compared to BERT-L-T, which uses an LSTM instead of attention on top of the BERT representations (BERT-A-T performs better in seven of seven game-level tasks, and both models perform similarly on the period-level tasks). These observations clearly demonstrate the benefits of modeling an interview’s textual structure, in an increasing level of complexity and nuance with respect to the unique characteristics of interviews.

#### Extended BERT Pre-training.

When examining the BERT-EPT-A-T and BERT-EPT-A-TM models, we observe a slight yet consistent degradation in prediction performance through- out almost all tasks, in comparison with both the BERT-A-T and the BERT-A-TM models. There is an average accuracy degradation of 0.6% over all tasks: 0.7% on the game level, and on the period level the results are mostly on par, with the exception of PTS, FGR, and SR metrics where BERT-EPT-A-TM is somewhat better. Moreover, we observe an increase in overall result variance when comparing our BERT-EPT-A models (average standard deviation of 1.8%) to the BERT-A models (average standard deviation of 1%). This suggests that the extended pre-training process yields less stable models. We hypothesize that continuing the pre-training process might lead to BERT overfitting on our data, at the cost of “forgetting” valuable features from its original pre-trained representations. This could be explained by the following observations:

• 1.

Our data set size is orders of magnitude smaller (about 2M words in total) compared wih the BookCorpus (800M words) and Wikipedia (2,500M words) data sets on which BERT was originally pre-trained.

• 2.

Our pre-trained models that ran for one epoch outperformed our pre-trained models that ran for three epochs, by an average of 0.2%. This suggests that longer pre-training would slightly increase the “forgetting” effect and harm prediction performance.

• 3.

The NSP task might be inadequate for interview text, because it does not allow for capturing the unique structures present in interviews, such as the dependence between speakers’ utterances, which are usually composed of multiple sentences each.

In light of our experimental results, and specifically our observation on the possible limitations of the NSP task for interview processing, we believe that investigating the process of pre-training BERT for interview text is an interesting direction for future work. For example, one idea is to replace the standard NSP task with a similar task, designed for Q-A pairs, with the goal of predicting whether a given Q and A are a real pair in an interview. In future work, we would like to further explore different possible pre-training methods that might be better-suited for interviews, by designing them to capture the unique structures present in interviews and the roles of the participating speakers.

#### Per-Player Model Performance.

In the analysis so far we have adhered to results on aggregated performance, without observing differences between players. To provide an analysis of the model’s performance per player, we present in Figure 6 the relative performance of the BERT-A-T model at the game level, for each player and for each task. We shall use the definitions below to explain the figure structure: Let BERT-A-T’s accuracy score for a given metric mM, over all examples in the test set Itest, be defined as:
$ACCm=∑i∈Itest1{ŷim=yim}|Itest|$
(11)
where $ŷim$ denotes the label predicted by BERT-A-T and $yim$ denotes the true label for example i. Let BERT-A-T’s accuracy score for a given metric mM and a player pP, over the subset of all test set examples $Itestp$ in which player p participates, be defined as:
$ACCp,m=∑i∈Itestp1{ŷim=yim}|Itestp|$
(12)
Each point in Figure 6 is defined as the difference between ACCp,m and ACCm:
$ΔACCp,m=ACCp,m−ACCm$
(13)
We use this difference measure to facilitate the visualization of BERT-A-T’s relative performance in terms of accuracy for all players in all tasks, on a single graph.
Figure 6

BERT-A-T prediction accuracy per player, relative to its accuracy for all players, for each prediction task. Each point in the graph is defined by Equation (13).

Figure 6

BERT-A-T prediction accuracy per player, relative to its accuracy for all players, for each prediction task. Each point in the graph is defined by Equation (13).

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Observing this figure, some interesting patterns arise. First, model performance in SR prediction is significantly better for front-court players (e.g., Tim Duncan, Shaquille O’Neal, and Pau Gasol), who make significantly fewer attempts to shoot behind the 3-point arc, in a manner that could be quite predictable.19 Second, the performance of BERT-A-T is significantly lower in predicting the distance of the 3-point shots taken by those players (the average of this distance is captured by the MSD3 metric). This could be the result of the infrequent nature of these types of shots by these players. Comparatively, performance of back-court players, such as Kyle Lowry, Manu Ginobili, and Steve Nash, who frequently attempt 3-point shots, are better predicted by our BERT-A-T model.

Thus far we have shown the predictive power of our models, but we would also like to get an insight as to what in the text is indicative of the player’s actions and decisions. Relying on the sports psychology and analytics literature, we would like to test the efficacy of theories such as IZOF (Hanin 1997) and its successors (see discussion of such theories in Sections 1 and 2). That is, we would like to observe whether the success of our models in predicting players’ actions is related to the players’ hypothesized “emotional state” as reflected in the text.

The rise of deep learning models, such as those we use here, has produced substantially better prediction models for a plethora of tasks, most notably for those that rely on unstructured data (Peters et al. 2018; Devlin et al. 2019). This improved predictive power, however, has come at the expense of model explainability and understandability. Understanding predictions made by DNNs is notoriously difficult, as their layered structure, which is coupled with nonlinear activations, does not allow for tracing and reasoning over the effect of each input feature on the model’s output. In the case of text-based models this problem is amplified, as features are usually composed of adjacent sequences of words, and not abstract linguistic concepts that might exist in the text and push the model toward specific predictions.

Following the meteoric rise of such models, there have been many attempts to build tools that allow for model explanation and interpretation (Ribeiro, Singh, and Guestrin 2016; Lundberg and Lee 2017). However, such tools often rely on local perturbations or shallow correlations. They are ill-suited for text-based models and for reasoning on higher-level concepts, such as our players’ states. When attempting to reason about abstract concepts such as “emotional state,” it is not clear how to highlight the effects of different features on the predictions a model makes, when its input features are word sequences. To be able to estimate such effects we need to represent the models’ output in a space where we can reason about high level concepts. Specifically, we decided to represent such concepts as interview topics.

### 8.1 LDA Topic Modeling for DNN Interpretation

Following this reasoning, we qualitatively interpret the predictions of our models using latent Dirichlet allocation (LDA) (Blei, Ng, and Jordan 2003). Importantly, we do not perform predictions with LDA, but instead use the topics it induces in order to interpret the results of our DNN models. To the best of our knowledge, the idea of interpreting the predictions of DNNs in text classification tasks using LDA topics has not been proposed previously. LDA models the interviews as mixtures of topics, where each topic is a probability distribution over the vocabulary. Our goal in this analysis is to find the topics that are most associated with the predictions our DNN models make in each of the seven performance classification tasks. Our reasoning is that LDA-based topics may provide a latent space suited for intuitive reasoning about the predictions of DNN models, allowing enough dimensions for observing differences in higher-level concepts, while keeping it relatively compact for proper analysis.

Interpreting a supervised DNN prediction model utilizing an auxilliary unsupervised LDA model, which itself learns a latent representation of the data, raises a question about the predictive power of the LDA model in the original prediction task. Suppose the LDA topics prove to hold the same predictive power as the DNN or they are perfectly correlated with the DNN’s predictions; then the LDA model could serve as an interpretable alternative to the uninterpretable DNN. This is not the usual case with most DNN prediction models, which generally outperform LDA-based counterparts in most text-based prediction tasks. Therefore, we are interested in finding LDA topics that correlate with the DNN predictions, keeping in mind that we need to quantify this correlation in order to understand how well the topics explain the DNN predictions. We chose to perform two types of analyses:

• •

Associating a specific topic with the positive predictions of the analyzed classifier, for each prediction task (see Table 11 and Figure 7). This yields a rather informative and intuitive analysis, which sheds light on what a prediction model managed to consistently capture in the text. Yet, the selection of a single topic might limit the interpretation to a single specific aspect and miss other aspects.

• •

Analyzing the correlations between all LDA topics and the predictions of the analyzed classifier, for each performance task (see Figure 8). This analysis is complementary to the previous one: it is multidimensional and hence gives a higher-level view rather than delving into the details of one explaining topic.

We describe each analysis in further detail below.

Table 11
The 10 most likely words according to the topic with the largest probability difference between positive and negative BERT-A-T predictions, zm+. We refer to these as the positive class topics. Results are presented at the game level, for each prediction task.
PFPTSFGRPRSRMSD2MSD3
Aggressive Fun Year Try Shot Get Game
Defensively Star Team Offensively Miss Shot Last
Guard See Season Physical Make Ball Night
Adjustment Great Championship Intensity Three Make Make
Transition Think Think Pace Field Defense Series
Roll Time Career Attack Credit Think Win
Turnover Good Work Paint Confident Able Little
Paint Enjoy Great Lane Opportunity Try Think
Defensive Fan Win Communication Look Run Better
Offense Basketball Experience Space Ball Go Loss
PFPTSFGRPRSRMSD2MSD3
Aggressive Fun Year Try Shot Get Game
Defensively Star Team Offensively Miss Shot Last
Guard See Season Physical Make Ball Night
Adjustment Great Championship Intensity Three Make Make
Transition Think Think Pace Field Defense Series
Roll Time Career Attack Credit Think Win
Turnover Good Work Paint Confident Able Little
Paint Enjoy Great Lane Opportunity Try Think
Defensive Fan Win Communication Look Run Better
Offense Basketball Experience Space Ball Go Loss
Figure 7

BERT-A-T’s averaged positive class prediction confidence ($p^$($yim$ = 1)) as a function of the positive class topic probability ($θzm+i$) assigned to each interview. The computation of f($θzm+i$; j) is described by Equation (16).

Figure 7

BERT-A-T’s averaged positive class prediction confidence ($p^$($yim$ = 1)) as a function of the positive class topic probability ($θzm+i$) assigned to each interview. The computation of f($θzm+i$; j) is described by Equation (16).

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Figure 8

Correlation heat-maps of LDA topic probability ($θzmi$) and the DNN positive prediction confidence ($p^$($yim$ = 1)) ((a) LSTM-T; (b) BERT-A-T), for each prediction task.

Figure 8

Correlation heat-maps of LDA topic probability ($θzmi$) and the DNN positive prediction confidence ($p^$($yim$ = 1)) ((a) LSTM-T; (b) BERT-A-T), for each prediction task.

Close modal

### 8.2 Associating Topics with Classifier Predictions

We train a topic model20 and optimize the number of topics on our entire training set Itrain for maximal coherence (Lau, Newman, and Baldwin 2014), resulting in a set Z of 36 topics. Then, for each label we split the test set Itest into positively and negatively classified interviews, according to the BERT-A-T predictions, our best performing text-based model. We note that, because we are interested in interpreting our model’s predictions, we perform the split according to the model predictions and not according to the gold standard.

Following this split, we then search for the topic that is on average most associated with the model’s positive predictions (i.e., the topic with the largest probability difference between positive and negative model predictions). We denote the topic distribution (mixture) of an interview i with θi (as defined in Blei, Ng, and Jordan [2003]), and p(zi) = $θzi$ as the probabilities of words in interview i to be generated by topic z. Intuitively, $θzi$ can be thought of as the degree to which topic z is referred to in interview i (Blei, Ng, and Jordan 2002). The computations for both positive and negative topics are described in Equations (14) and (15).
$PositiveClassTopicm=zm+=argmaxz∈Z{∑i∈Itestŷim⋅θzi}$
(14)
$NegativeClassTopicm=zm−=argmaxz∈Z{∑i∈Itest−ŷim⋅θzi}$
(15)
where:
$ŷim=1,p^(yim=1)≥0.5−1,p^(yim=1)<0.5$
and $p^$($yim$ = 1) is the positive class probability according to the DNN.21 We then investigate the zm+ topic, which we denote as the positive class topic, to observe what our model has learned. From now on we shall refer to $p^$($yim$ = 1) as the DNN’s positive class prediction confidence and to $θzm+i$ as the positive class topic probability.

Following Sievert and Shirley (2014),22 we print out the words that are most associated with the zm+ topic according to their estimated term frequency within the selected topic. The top words belonging to those topics, for the game-level BERT-A-T classifiers, are presented in Table 11.

As can be seen in the table, the positive class topics seem intuitively related to the label, capturing not merely naive sentiment or emotion, but more refined, task-related words. For positive personal fouls (PF) predictions, the model picks up concepts related to aggressive and defensive play. The topic for points (PTS) suggests it is most positively correlated with joyfulness, implying that the model has learned to associate a positive sentiment with more points. The field goal ratio (FGR) topic conveys game importance and long-term thinking, implying a learned link between a player’s performance and the game’s significance. Pass risk (PR) and shot risk (SR) positive topics show a connection to players willingness to take more risk, as they are associated with words such as “try” and “confident,” respectively. Finally, the mean shot distances metrics, MSD2 and MSD3, seem unrelated to their topics, which is unsurprising at least for MSD3 that BERT-A-T does not predict well (see results in Table 10).

In Figure 7 we plot f($θzm+i$; j), the averaged BERT-A-T positive prediction confidence $p^$($yim$ = 1), as a function of $θzm+i$, the probability of the positive class topic zm+ in the interviews, for each metric m. We compute each point in the plot, by calculating f($θzm+i$; j) for each interval jJ = {0.1, 0.2, …, 1} as defined:
$f(θzm+i;j)=∑i∈Itestjp^(yim=1)|Itestj|,Itestj={i|i∈Itest,θzm+i∈(j−0.1,j]}$
(16)

We calculate this for visualization purposes: for each positive class topic probability ($θzm+i$) interval of size 0.1, we compute the average BERT-A-T positive prediction confidence ($p^$($yim$ = 1)) over all interviews with $θzm+i$ falling in the interval. As demonstrated in Figure 7, we observe that the probability assigned to positive topics ($θzm+i$) from Table 11 increases monotonously with BERT-A-T’s averaged positive predicted probability (confidence) for deviation above the player’s mean performance ($p^$($yim$ = 1)), in six out of the seven tasks (SR being the exception).

### 8.3 Topic Correlation with LSTM-T and BERT-A-T

We finally investigate the predictions of our two best-performing text-based models, LSTM-T and BERT-A-T, in terms of the LDA topics. Because LDA is trained on free text and does not observe the predictions of any DNN model, its topics can be used to analyze two different DNNs: LSTM-T and BERT-A-T in this case.

The heat-maps in Figure 8 present the correlations for each metric m, between $θzmi$, the probability of each topic zZ, and $p^$($yim$ = 1), the DNN’s positive prediction confidence, for both LSTM-T and BERT-A-T. Observing the results, it is clear that BERT-A-T’s predictions are more correlated with the LDA topics, compared with the LSTM-T (darker colors indicate higher correlations). Looking closer at the heat-maps, we notice some interesting patterns.

First, SR and MSD2 seem to exhibit opposing topic correlation patterns when examining the BERT-A-T model’s predictions (bottom figure). This implies that topics associated with a higher probability of taking more 3-point shots are also associated with 2-point shots that are closer to the rim. The correlation exhibited by the BERT-A-T model could be explained by the growing tendency of players to take more 3-point shots at the expense of long-range 2-point shots, a phenomenon widely observed in recent years in the NBA.23 This phenomenon also serves as an example of attempting to maximize the expected payoff (Von Neumann and Morgenstern 1944). If shot-takers are in a situation in which they are unable to minimize their risk (i.e., they cannot take a 2-point shot close to the rim and must take a shot further out), they choose to increase their risk for a higher payoff and take a longer-range 3-point shot.

Second, we also note that topic 23, which is associated with PR for BERT-A-T, is also positively correlated with PF for both BERT-A-T and LSTM-T. PR’s positive topic exhibits top-words such as “Physical” and “Intensity” (as can be seen in Table 11), and PF’s positive topic exhibits top-words such as “Aggressive,” “Defensively,” and “Guard.” This suggests that topic 23 captures some aspects of the concept of physical intensity and aggressiveness on both offense (PR) and defense (PF), and moreover that the DNNs capture this as well, to a certain extent.

Finally, the BERT-A-T classifiers for SR and FGR are generally correlated with similar topics. Particularly, it seems that both classifiers are positively correlated with topics that are highly associated with shot-related words.24 Although this may seem counter-intuitive, notice that the corresponding LSTM-T classifiers do not show this correlation and they also perform significantly worse on those tasks (as seen in Table 10). Overall, we can see that our topic analysis enables a level of intuitive reasoning, which serves as a new tool for providing insights on both the data and the properties of the prediction models (DNNs).

We explored the task of predicting the relative performance of NBA players based on their pre-game interviews, building on the extensive computational work on performance prediction in sports analytics and on text classification in NLP. We hypothesized that these interviews hold valuable information regarding the players’ current state and that this information could shed light on their in-game actions and performance.

To facilitate such a study, we collected a data set consisting of pre- and post-game interviews alongside in-game performance metrics from the game following the interviews, for 36 prominent NBA players. Most of the games in our data set are part of a playoff series where the stakes are typically higher, player and team performance or outcomes are harder to predict, and key players are expected to take on bigger roles, in comparison to regular season games.

Based on standard basketball in-game performance metrics, we introduced seven decision related metrics, each aiming to examine a different aspect of a player’s in-game actions and performance. We formulated binary text classification tasks, attempting to predict a player’s deviation from his mean performance in each metric, to examine whether pre- and post-game interview texts hold predictive power of the player’s in-game actions. We formulated four research questions, trying to assert: (1) if text classification models could utilize pre-game interviews for predicting performance, (2) if text could be combined with past performance metrics for better predictions, (3) if text classification models gain from modeling an interview’s textual structure, and (4) if DNNs could jointly learn a textual representation together with the task classifier, in a way that improves prediction accuracy over standard bag-of-words features.

We demonstrated that deep neural networks, mainly BERT and to some extent LSTM, are capable of using interview-based signals to predict players’ performance indicators. Moreover, we showed that our text-based models perform better than commonly used autoregressive metrics-based models, and that models that combine the two signals yield even better predictions. Also, we have shown that all game-level metrics and most period-level metrics can be predicted, to varying degrees.

In conducting this research, we were not interested only in predictive power, but also in understanding the phenomena at hand. Hence, it was important for us to be able to understand the predictions of the model. However, DNN interpretation is challenging, which hurts our ability to understand our models’ predictions in terms of difference in language usage.

Thus, in order to interpret our DNN models in terms of linguistic concepts, we presented an LDA-based method. Our idea is based on examining topics that are on average most associated with the predictions of the model. In this analysis, we found that in six of seven cases our best performing text-only model, BERT-A-T, is most associated with topics that are intuitively related to each prediction task, revealing that the model has successfully learned task specific representations.

In particular, in this work we have attempted to set the stage for future exploration on several axes. First, much more research can be done on prediction models in scenarios where the signal is not stated directly in the text, in contrast to better-explored cases such as sentiment classification and intent detection. Moreover, the connection between language and decision making can also be further explored, specifically in real-world rather than lab conditions. Models for predicting behavior using language could be useful in strategic settings such as multiplayer games, and can also be useful in medical settings, where predicting the patient’s current state, which may not be explicitly discussed in the text, could have life-saving implications.

We consider our task a domain specific instance of a more general question: How should language be used as a predictive signal for actions in real-world scenarios. We hope that our discussion, observations, and algorithms, as well as data set and code, will facilitate future work by the community.

In future work we will consider more advanced time-series analysis tools along with the text, and better incorporate the interview’s structure into our model. Our experiments have shown that incorporating the Q-A structure of the interview does improve the predictions, but this is only a first step in this direction, and more work can be done on this frontier. Also, we will aim to learn various performance metrics jointly, and to model the interactions between the actions of different players. This will hopefully yield better, more interpretable models for understanding the connection between language and actions.

Another interesting direction is taking into account the development of players’ performance over time. It could be that measuring players across fewer seasons could lead to better estimates, as players change along their careers. On average players are represented in our data set for six seasons, which corresponds to their prime in terms of average performance. That is, we are generally capturing players at their peak performance, where quality tends to remain more consistent. In the future, given sufficient data per player, it would be interesting to integrate the time factor into our models.

Finally, another interesting theoretical question that arises is the extent to which language can really tell us about decisions that are made in later situations. It would be interesting to investigate and model these connections, and perhaps develop a theoretical bound for the predictive power that language could have in such situations.

1

2

Building on this literature, we use this concept of “emotional state” freely here and note that although some similarities exist, it is not directly mapped to the psychological literature.

3

There are novel attempts to estimate players’ partial effect on the game (Gramacy, Taddy, and Tian 2017), which constitute estimating the difference they make on final game outcomes. However, in this research we decided to focus on metrics that can be attributed to specific types of decisions and not to overall game outcomes.

4

There are four periods in a basketball game, not including overtime. We do not deal with overtime performance as it might be less affected by the player pre-game state, and more by the happenings in the four game periods.

5

See Section 3.2 for an explanation on NBA playoffs.

6

The most famous short response, by football player Marshawn Lynch, can be seen at: https://www.youtube.com/watch?v=G1kvwXsZtU8.

7

The LDA model is used here for data exploration purposes only, specifically, to show the general topic distribution per player in our data set.

8

In the game data set, t denotes a specific game.

9

Because $mtp$ is hardly ever equal to $m-p$, the meaning of $ytp,m$ = 0 is almost always a negative deviation from the mean.

10

Lagged performance metrics refer to the same metric for the same player in the previous periods.

11

12

Recall that each game is composed of 4 periods.

13

Recall that in our period-level task we do not distinguish between the different periods within a game.

14

We achieved this by utilizing the StratifiedShuffleSplit and StratifiedKFoldCV utility methods from scikit-learn, using a random seed of 212.

18

All three performance metrics have an average standard deviation of 0.7 at the period level, substantially below the other four performance metrics, which exhibit an average standard deviation of 1.4.

19

Court structure, including the location of the 3-point arc, is presented in Figure 1.

20

Using the gensim library (Řehůřek and Sojka 2010).

21

For our DNNs to produce class probabilities, we use a binary Cross-Entropy loss function (Goodfellow, Bengio, and Courville 2016); see Section 6.4.1.

22

Note that this work addresses topic model visualization, rather than neural network interpretation.

23

See the substitutionality of long-range 2-point shots and 3-point shots in: http://www.nbaminer.com/shot-distances/.

24

We chose not to present all topics and their corresponding top-words as most are not informative and do not add information that helps us answer our research questions.

,
Martín
,
Paul
Barham
,
Jianmin
Chen
,
Zhifeng
Chen
,
Andy
Davis
,
Jeffrey
Dean
,
Matthieu
Devin
,
Sanjay
Ghemawat
,
Geoffrey
Irving
,
Michael
Isard
,
Manjunath
Kudlur
,
Josh
Levenberg
,
Rajat
Monga
,
Sherry
Moore
,
Derek G.
Murray
,
Benoit
Steiner
,
Paul
Tucker
,
Vijay
Vasudevan
,
Pete
Warden
,
Martin
Wicke
, and
Xiaoqiang
Zheng
.
2016
.
Tensorflow: A system for large-scale machine learning
. In
Proceedings of the 12th USENIX Conference on Operating Systems Design and Implementation, OSDI’16
, pages
265
283
,
USENIX Association
,
Savannah, GA
.
,
Yossi
,
Einat
Kermany
,
Yonatan
,
Ofer
Lavi
, and
Yoav
Goldberg
.
2016
.
Fine-grained analysis of sentence embeddings using auxiliary prediction tasks
.
arXiv preprint arXiv:1608.04207
.
Akaike
,
Hirotugu
.
1969
.
Fitting autoregressive models for prediction
.
Annals of the institute of Statistical Mathematics
,
21
(
1
):
243
247
.
Angrist
,
Joshua D.
and
Jörn-Steffen
Pischke
.
2008
.
Mostly Harmless Econometrics: An Empiricist’s Companion
.
Princeton University Press
.
Bar-Eli
,
Michael
and
Noam
Tractinsky
.
2000
.
Criticality of game situations and decision making in basketball: An application of performance crisis perspective
.
Psychology of Sport and Exercise
,
1
(
1
):
27
39
.
Berger
,
James O
.
1985
.
Statistical Decision Theory and Bayesian Analysis
.
.
Bickerton
,
Derek
.
1995
.
Language and Human Behavior
.
University of Washington Press
.
Blei
,
David M.
,
Andrew Y.
Ng
, and
Michael I.
Jordan
.
2002
.
Latent Dirichlet allocation
. In
Dietterich
,
T. G.
,
S.
Becker
, and
Z.
Ghahramani
, editors,
Advances in Neural Information Processing Systems 14
,
MIT Press
, pages
601
608
.
Blei
,
David M
,
Andrew Y.
Ng
, and
Michael I.
Jordan
.
2003
.
Latent Dirichlet allocation
.
Journal of Machine Learning Research
,
3
(
Jan
):
993
1022
.
Cervone
,
Dan
,
Alexander
D’Amour
,
Luke
Bornn
, and
Kirk
Goldsberry
.
2014
.
Pointwise: Predicting points and valuing decisions in real time with NBA optical tracking data
. In
Proceedings of the 8th MIT Sloan Sports Analytics Conference
,
volume 28
, page
3
,
Boston, MA
.
Cervone
,
Daniel
,
Alex
D’Amour
,
Luke
Bornn
, and
Kirk
Goldsberry
.
2016
.
A multiresolution stochastic process model for predicting basketball possession outcomes
.
Journal of the American Statistical Association
,
111
(
514
):
585
599
.
Chen
,
Danqi
,
Jason
Bolton
, and
Christopher D.
Manning
.
2016
.
. In
Proceedings of the 54th Annual Meeting of the Association for Computational Linguistics (Volume 1: Long Papers)
, pages
2358
2367
,
Berlin
.
Chollet
,
François
et al
2015
.
Keras
. https://keras.io.
Coate
,
Patrick
.
2012
.
A basic structural framework of NBA offense
. In
Proceedings of the MIT Sloan Sports Analytics Conference
, pages
1
7
,
Boston, MA
.
Cortes
,
Corinna
and
Vapnik
.
1995
.
Support-vector networks
.
Machine Learning
,
20
(
3
):
273
297
.
Danescu-Niculescu-Mizil
,
Cristian
,
Moritz
Sudhof
,
Dan
Jurafsky
,
Jure
Leskovec
, and
Christopher
Potts
.
2013
.
A computational approach to politeness with application to social factors
. In
Proceedings of the 51st Annual Meeting of the Association for Computational Linguistics (Volume 1: Long Papers)
,
volume 1
, pages
250
259
,
Sofia
.
Devlin
,
Jacob
,
Ming-Wei
Chang
,
Kenton
Lee
, and
Kristina
Toutanova
.
2019
.
BERT: Pre-training of deep bidirectional transformers for language understanding
. In
Proceedings of the 2019 Conference of the North American Chapter of the Association for Computational Linguistics: Human Language Technologies, Volume 1 (Long and Short Papers)
, pages
4171
4186
,
Minneapolis, MN
.
Einhorn
,
Hillel J.
and
Robin M.
Hogarth
.
1981
.
Behavioral decision theory: Processes of judgement and choice
.
Annual Review of Psychology
,
32
(
1
):
53
88
.
Erev
,
Ido
and
Alvin E.
Roth
.
1998
.
Predicting how people play games: Reinforcement learning in experimental games with unique, mixed strategy equilibria
.
American Economic Review
,
88
(
4
):
848
881
.
Fasold
,
Ralph W.
and
Elisabeth
Stephens
.
1990
.
The Sociolinguistics of Language
.
Blackwell Oxford
.
Field
,
Anjalie
,
Doron
Kliger
,
Shuly
Wintner
,
Jennifer
Pan
,
Dan
Jurafsky
, and
Yulia
Tsvetkov
.
2018
.
Framing and agenda- setting in Russian news: A computational analysis of intricate political strategies
. In
Proceedings of the 2018 Conference on Empirical Methods in Natural Language Processing
, pages
3570
3580
,
Brussels
.
Finney
,
David John
.
1952
.
Probit Analysis: A Statistical Treatment of the Sigmoid Response Curve
.
Cambridge University Press
,
Cambridge
.
Ganguly
,
Sujoy
and
Nathan
Frank
.
2018
.
The problem with win probability
. In
Proceedings of the 12th MIT Sloan Sports Analytics Conference
, pages
1
10
,
Boston, MA
.
Gilboa
,
Itzhak
.
2009
.
Theory of Decision Under Uncertainty
,
volume 1
.
Cambridge University Press
.
Goldman
,
Matt
and
Justin M.
Rao
.
2011
.
Allocative and dynamic efficiency in NBA decision making
. In
Proceedings of the MIT Sloan Sports Analytics Conference
, pages
4
5
,
Boston, MA
.
Goldwasser
,
Dan
and
Hal
Daumé III
.
2014
.
“ I object!” Modeling latent pragmatic effects in courtroom dialogues
. In
Proceedings of the 14th Conference of the European Chapter of the Association for Computational Linguistics
, pages
655
663
,
Gothenburg
.
Goodfellow
,
Ian
,
Yoshua
Bengio
, and
Aaron
Courville
.
2016
.
Deep Learning
.
MIT Press
. http://www.deeplearningbook.org.
Gramacy
,
Robert B.
,
Matt
, and
Sen
Tian
.
2017
.
Hockey player performance via regularized logistic regression
.
Handbook of Statistical Methods and Analyses in Sports
.
Chapman and Hall/CRC
, pages
303
322
.
Hanin
,
Yuri L.
1997
.
Emotions and athletic performance: Individual zones of optimal functioning model
.
European Yearbook of Sport Psychology
,
1
:
29
72
.
Hanin
,
Yuri L.
2007
.
Emotions in sport: Current issues and perspectives
.
Handbook of Sport Psychology
,
3
(
3158
):
22
41
.
Hartford
,
Jason S.
,
James R.
Wright
, and
Kevin
Leyton-Brown
.
2016
.
Deep learning for predicting human strategic behavior
. In
Advances in Neural Information Processing Systems
, pages
2424
2432
,
Barcelona
.
Hochreiter
,
Sepp
and
Jürgen
Schmidhuber
.
1997
.
Long short-term memory
.
Neural Computation
,
9
(
8
):
1735
1780
.
Kahneman
,
Daniel
and
Amos
Tversky
.
1979
.
Prospect theory: An analysis of decision under risk
.
Econometrica
,
47
(
2
):
263
292
.
Kaya
,
.
2014
.
Decision making by coaches and athletes in sport
.
Procedia-Social and Behavioral Sciences
,
152
:
333
338
.
Kim
,
Yoon
.
2014
.
Convolutional neural networks for sentence classification
. In
Proceedings of the 2014 Conference on Empirical Methods in Natural Language Processing (EMNLP)
, pages
1746
1751
,
Doha, Qatar
.
Kingma
,
Diederik P.
and
Jimmy
Ba
.
2015
.
Adam: A method for stochastic optimization
. In
Bengio
,
Yoshua
and
Yann
LeCun
, editors.
3rd International Conference on Learning Representations, ICLR 2015
, pages
1
13
,
San Diego, CA
.
Kogan
,
Shimon
,
Dimitry
Levin
,
Bryan R.
Routledge
,
Jacob S.
Sagi
, and
Noah A.
Smith
.
2009
.
Predicting risk from financial reports with regression
. In
Proceedings of Human Language Technologies: The 2009 Annual Conference of the North American Chapter of the Association for Computational Linguistics
, pages
272
280
,
Boulder, CO
.
Kvam
,
Paul
and
Joel S.
Sokol
.
2006
.
A logistic regression/Markov chain model for NCAA basketball
. In
Naval Research Logistics (NrL)
,
53
(
8
):
788
803
.
Lamas
,
Leonardo
,
Felipe
Santana
,
Matthew
Heiner
,
Carlos
Ugrinowitsch
, and
Gilbert
Fellingham
.
2015
.
Modeling the offensive-defensive interaction and resulting outcomes in basketball
.
PloS ONE
,
10
(
12
):
1
15
.
Lau
,
Jey Han
,
David
Newman
, and
Timothy
Baldwin
.
2014
.
Machine reading tea leaves: Automatically evaluating topic coherence and topic model quality
. In
Proceedings of the 14th Conference of the European Chapter of the Association for Computational Linguistics
, pages
530
539
,
Gothenburg
.
Lazarus
,
Richard S
.
2000
.
How emotions influence performance in competitive sports
.
The Sport Psychologist
,
14
(
3
):
229
252
.
LeCun
,
Yann
and
Yoshua
Bengio
.
1995
.
Convolutional networks for images, speech, and time series
.
The Handbook of Brain Theory and Neural Networks
,
3361
(
10
):
1995
.
LeCun
,
Yann
,
Léon
Bottou
,
Yoshua
Bengio
, and
Patrick
Haffner
.
1998
.
Gradient-based learning applied to document recognition
.
Proceedings of the IEEE
,
86
(
11
):
2278
2324
.
Liaw
,
Andy
and
Matthew
Wiener
.
2002
.
Classification and regression by randomforest
.
R News
,
2
(
3
):
18
22
.
Lundberg
,
Scott M.
and
Su-In
Lee
.
2017
.
A unified approach to interpreting model predictions
. In
I.
Guyon
,
U. V.
Luxburg
,
S.
Bengio
,
H.
Wallach
,
R.
Fergus
,
S.
Vishwanathan
, and
R.
Garnett
, editors,
Advances in Neural Information Processing Systems 30
.
Curran Associates, Inc.
, pages
4765
4774
.
Luong
,
Thang
,
Hieu
Pham
, and
Christopher D.
Manning
.
2015
.
Effective approaches to attention-based neural machine translation
. In
Proceedings of the 2015 Conference on Empirical Methods in Natural Language Processing
, pages
1412
1421
,
Lisbon
.
Malca
,
Rivka
and
Roi
Reichart
.
2018
.
Neural transition based parsing of web queries: An entity based approach
. In
Proceedings of the 2018 Conference on Empirical Methods in Natural Language Processing
, pages
2700
2710
,
Brussels
.
McFarlane
,
Patrick
.
2018
.
Evaluating NBA end-of-game decision-making
.
Journal of Sports Analytics
,
5
(
1
):
1
6
.
Vaz de Melo
,
Pedro O. S.
,
Virgilio A. F.
Almeida
,
Antonio A. F.
Loureiro
, and
Christos
Faloutsos
.
2012
.
Forecasting in the NBA and other team sports: Network effects in action
.
ACM Transactions on Knowledge Discovery from Data (TKDD)
,
6
(
3
):
1
27
.
Ng
,
Andrew Y.
and
Michael I.
Jordan
.
2002
.
On discriminative vs. generative classifiers: A comparison of logistic regression and naive Bayes
. In
Advances in Neural Information Processing Systems
, pages
841
848
,
Vancouver
.
Niculae
,
,
Srijan
Kumar
,
Jordan
Boyd-Graber
, and
Cristian
Danescu-Niculescu-Mizil
.
2015
.
Linguistic harbingers of betrayal: A case study on an online strategy game
. In
Proceedings of the 53rd Annual Meeting of the Association for Computational Linguistics and the 7th International Joint Conference on Natural Language Processing (Volume 1: Long Papers)
, pages
1650
1659
,
Beijing
.
Pang
,
Bo
,
Lillian
Lee
, and
Shivakumar
Vaithyanathan
.
2002
.
Thumbs up?: Sentiment classification using machine learning techniques
. In
Proceedings of the ACL-02 Conference on Empirical Methods in Natural Language Processing-Volume 10
, pages
79
86
,
.
Paszke
,
,
Sam
Gross
,
Soumith
Chintala
,
Gregory
Chanan
,
Edward
Yang
,
Zachary
DeVito
,
Zeming
Lin
,
Alban
Desmaison
,
Luca
Antiga
, and
Lerer
.
2017
.
Automatic differentiation in PyTorch
. In
NIPS-W
, pages
1
4
,
Long Beach, CA
.
Pedregosa
,
Fabian
,
Gaël
Varoquaux
,
Alexandre
Gramfort
,
Vincent
Michel
,
Bertrand
Thirion
,
Olivier
Grisel
,
Mathieu
Blondel
,
Peter
Prettenhofer
,
Ron
Weiss
,
Vincent
Dubourg
,
Jake
Vanderplas
,
Alexandre
Passos
,
David
Cournapeau
,
Matthieu
Brucher
,
Matthieu
Perrot
, and
Édouard
Duchesnay
.
2011
.
Scikit-learn: Machine learning in Python
.
Journal of Machine Learning Research
,
12
:
2825
2830
.
Pennington
,
Jeffrey
,
Richard
Socher
, and
Christopher
Manning
.
2014
.
GloVe: Global vectors for word representation
. In
Proceedings of the 2014 Conference on Empirical Methods in Natural Language Processing (EMNLP)
, pages
1532
1543
,
Doha
.
Peters
,
Matthew E.
,
Mark
Neumann
,
Mohit
Iyyer
,
Matt
Gardner
,
Christopher
Clark
,
Kenton
Lee
, and
Luke
Zettlemoyer
.
2018
.
Deep contextualized word representations
. In
Proceedings of NAACL
, pages
2227
2237
,
New Orleans, LA
.
Plonsky
,
Ori
,
Ido
Erev
,
Tamir
Hazan
, and
Moshe
Tennenholtz
.
2017
.
Psychological forest: Predicting human behavior
. In
Proceedings of AAAI
, pages
656
662
,
San Francisco, CA
.
Řehůřek
,
and
Petr
Sojka
.
2010
.
Software framework for topic modelling with large corpora
. In
Proceedings of the LREC 2010 Workshop on New Challenges for NLP Frameworks
, pages
45
50
,
ELRA
,
Valletta
. http://is.muni.cz/publication/884893/en.
Ribeiro
,
Marco Tulio
,
Sameer
Singh
, and
Carlos
Guestrin
.
2016
.
Why should I trust you?: Explaining the predictions of any classifier
. In
Proceedings of the 22nd ACM SIGKDD International Conference on Knowledge Discovery and Data Mining
, pages
1135
1144
,
San Francisco, CA
.
Rosenfeld
,
Ariel
and
Sarit
Kraus
.
2018
.
Predicting human decision-making: From prediction to action
.
Synthesis Lectures on Artificial Intelligence and Machine Learning
,
12
(
1
):
1
150
.
Rosenfeld
,
Ariel
and
Sarit
Kraus
.
2018
.
Bridging languages through images with deep partial canonical correlation analysis
. In
Proceedings of the 56th Annual Meeting of the Association for Computational Linguistics (Volume 1: Long Papers)
, pages
910
921
,
Melbourne
.
Salton
,
Gerard
.
1991
.
Developments in automatic text retrieval
.
Science
,
253
(
5023
):
974
980
.
Sampaio
,
Jaime
,
Tim
McGarry
,
Julio
Calleja-González
,
Sergio Jiménez
Sáiz
,
Xavi
Schelling i del Alcázar
, and
Mindaugas
Balciunas
.
2015
.
Exploring game performance in the national basketball association using player tracking data
.
Plos ONE
,
10
(
7
):
1
14
.
Sandholtz
,
Nathan
and
Luke
Bornn
.
2018
.
Replaying the NBA
. In
Proceedings of the 12th MIT Sloan Sports Analytics Conference
, pages
1
13
,
Boston, MA
.
Seabold
,
Skipper
and
Josef
Perktold
.
2010
.
Statsmodels: Econometric and statistical modeling with Python
. In
9th Python in Science Conference
, pages
92
96
,
Austin, TX
.
Sievert
,
Carson
and
Kenneth
Shirley
.
2014
.
LDAvis: A method for visualizing and interpreting topics
. In
Proceedings of the Workshop on Interactive Language Learning, Visualization, and Interfaces
, pages
63
70
,
Baltimore, MD
.
Sim
,
Yanchuan
,
Bryan
Routledge
, and
Noah A.
Smith
.
2016
.
Friends with motives: Using text to infer influence on SCOTUS
. In
Proceedings of the 2016 Conference on Empirical Methods in Natural Language Processing
, pages
1724
1733
,
Austin, TX
.
Søgaard
,
Anders
and
Yoav
Goldberg
.
2016
.
. In
Proceedings of the 54th Annual Meeting of the Association for Computational Linguistics (Volume 2: Short Papers)
, pages
231
235
,
Berlin
.
Srivastava
,
Nitish
,
Geoffrey
Hinton
,
Alex
Krizhevsky
,
Ilya
Sutskever
, and
Ruslan
Salakhutdinov
.
2014
.
Dropout: A simple way to prevent neural networks from overfitting
.
Journal of Machine Learning Research
,
15
(
1
):
1929
1958
.
Uphill
,
Mark
,
Ryan
Groom
, and
Marc
Jones
.
2014
.
The influence of in-game emotions on basketball performance
.
European Journal of Sport Science
,
14
(
1
):
76
83
.
Vaswani
,
Ashish
,
Noam
Shazeer
,
Niki
Parmar
,
Jakob
Uszkoreit
,
Llion
Jones
,
Aidan N.
Gomez
,
Łukasz
Kaiser
, and
Illia
Polosukhin
.
2017
.
Attention is all you need
. In
Advances in Neural Information Processing Systems
, pages
5998
6008
,
Long Beach, CA
.
Von Neumann
,
John
and
Oskar
Morgenstern
.
1944
.
Theory of Games and Economic Behavior
.
Princeton University Press
.
Wang
,
Jiaxuan
,
Ian
Fox
,
Jonathan
Skaza
,
Nick
Linck
,
Satinder
Singh
, and
Jenna
Wiens
.
2018
.
The advantage of doubling: A deep reinforcement learning approach to studying the double team in the NBA
. In
Proceedings of the 12th MIT Sloan Sports Analytics Conference
, pages
1
12
,
Boston, MA
.
Wardhaugh
,
Ronald
.
2011
.
An Introduction to Sociolinguistics
,
volume 28
.
John Wiley & Sons
.
Wright
,
James R.
and
Kevin
Leyton-Brown
2010
.
Beyond equilibrium: Predicting human behaviour in normal form games
. In
Proceedings of AAAI
, pages
901
907
,
Atlanta, GA
.
Xu
,
Chenyan
,
Yang
Yu
, and
Chun-Keung
Hoi
.
2015
.
Hidden in-game intelligence in NBA players’ tweets
.
Communications of the ACM
,
58
(
11
):
80
89
.
Yang
,
Zichao
,
Diyi
Yang
,
Chris
Dyer
,
Xiaodong
He
,
Alex
Smola
, and
Eduard
Hovy
.
2016
.
Hierarchical attention networks for document classification
. In
Proceedings of the 2016 Conference of the North American Chapter of the Association for Computational Linguistics: Human Language Technologies
, pages
1480
1489
,
San Diego, CA
.
Yogatama
,
Dani
and
Noah
Smith
.
2014
.
Making the most of bag of words: Sentence regularization with alternating direction method of multipliers
. In
International Conference on Machine Learning
, pages
656
664
,
Beijing
.
Zhu
,
Yukun
,
Ryan
Kiros
,
Rich
Zemel
,
Ruslan
Salakhutdinov
,
Raquel
Urtasun
,
Antonio
Torralba
, and
Sanja
Fidler
.
2015
.
Aligning books and movies: Towards story-like visual explanations by watching movies and reading books
. In
IEEE International Conference on Computer Vision (ICCV)
, pages
19
27
,
Santiago
.
Ziser
,
Yftah
and
Roi
Reichart
.
2018
.
Pivot based language modeling for improved neural domain adaptation
. In
Proceedings of the 2018 Conference of the North American Chapter of the Association for Computational Linguistics: Human Language Technologies, Volume 1 (Long Papers)
, pages
1241
1251
,
New Orleans, LA
.

## Author notes

*

Authors contributed equally.

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