The growing work in multi-lingual parsing faces the challenge of fair comparative evaluation and performance analysis across languages and their treebanks. The difficulty lies in teasing apart the properties of treebanks, such as their size or average sentence length, from those of the annotation scheme, and from the linguistic properties of languages. We propose a method to evaluate the effects of word order of a language on dependency parsing performance, while controlling for confounding treebank properties. The method uses artificially-generated treebanks that are minimal permutations of actual treebanks with respect to two word order properties: word order variation and dependency lengths. Based on these artificial data on twelve languages, we show that longer dependencies and higher word order variability degrade parsing performance. Our method also extends to minimal pairs of individual sentences, leading to a finer-grained understanding of parsing errors.