GOATs and BOATs; or When Might 11/13 be Less Than 6/18?

Abstract

Comparing extraordinary results and determining GOATs (Greatest of All Time) is a favorite discussion topic for sports fans and data analysts alike. The analysts, however, are more likely to recognize that attempts to measure greatness are always sensitive to the metric chosen.  We consider the general questions that arise when those metrics are associated with the “unlikeliness”, or right tail probability, of team success and how much of that success is associated with a single player.  We would love to eventually answer, or at least offer a thoroughly supported opinion, on who is the GOAT of all GOATs across team sports. This paper spells out preliminary steps in how this could be done.  Because it is difficult to compare players of different positions in the same sport, and because we must also compare across not only sports but eras, we narrow our focus to finding the BOAT of all BOATs (Best of All Teammates).  We are interested in who has seen the most success, not necessarily who has contributed the most.  We outline a framework using a specific example comparing Tom Brady and Bill Russell, two popular candidates for BOAT (or GOAT), and discuss in detail the challenges of comparing across sports, in particular how the playoff structure affects the metrics, and we come down, narrowly, on the side of Brady.  We encourage readers, especially students, to join us in considering specific cases and extensions of these ideas and we hope this discussion will be a fruitful source of projects for classes or independent studies in probability, sports analytics, or modeling.