Super groups or fair leagues? Rich-get-richer dynamics can drive capture despite active redistribution in professional basketball

Much of modern society is founded on orchestrating institutions that produce social goods by fostering motivated groups, pitting them against each other, and distributing the fruits of the arms races that ensue. In this paper, we explore how institutions may change over time and, using the example of competitive balance in professional basketball, analyze whether these changes expose institutions to capture by the few or equilibrium among members. Using outcomes of over 60,000 contests from four professional sports leagues, more than 100 years’ worth of seasons, we compute the evolving rate of transitivity violations (A > B, B > C, but C > A) to measure the ability of leagues to maintain parity between teams and support the efficient generation and distribution of innovation. Comparing against a baseline of randomly permuted outcomes, we find that leagues become less competitive over time, suggesting that teams diverge in performance, and reflecting a possible failure of market makers to tame their overpowered teams. Our results suggest that rich-get-richer dynamics are so pernicious that they can even emerge under the watch of a powerful administrator that is motivated to prevent them.