Participation rates and maximal performance: A log-linear explanation for group differences, such as Russian and male dominance in chess

Can the superiority of some countries and groups at certain activities be explained solely by the relative sizes of the participating populations? We focus on the expected highest achievement, max, as a function of the participating group's size. For several relevant statistical distributions, max can be shown to be approximately log-linear in sample size, with a slope of about 0.7 SD units. We use this relation (max is log-linear similar to 0.7: MILL7) to examine differences in performance in chess by men and women and by different countries. The expected differences under MILL7 are very close to the observed differences. We also examine the implications of MILL7 for the interpretation of other group differences and discuss its limitations.