Recently, Hirsch (2019a) proposed a new variant of the h -index called the h α -index. The h α -index was criticized by Leydesdorff, Bornmann, and Opthof (2019) . One of their most important points is that the index reinforces the Matthew effect in science. The Matthew effect was defined by Merton (1968) as follows: “the Matthew effect consists in the accruing of greater increments of recognition for particular scientific contributions to scientists of considerable repute and the withholding of such recognition from scientists who have not yet made their mark” (p. 58). We follow up on the point about the Matthew effect in the current study by using a recently developed Stata command (h_index) and R package (hindex), which can be used to simulate h -index and h α -index applications in research evaluation. The user can investigate under which conditions h α reinforces the Matthew effect. The results of our study confirm what Leydesdorff et al. (2019) expected: The h α -index reinforces the Matthew effect. This effect can be intensified if strategic behavior of the publishing scientists and cumulative advantage effects are additionally considered in the simulation.