Mathematics and Sports

A mathematical model for scoring athletic performances

2023-04-17T18:43:12+00:00

We present an application of our recently proposed scoring method to running performances. To this end we use the performances corresponding to the elite level, as given by the World Athletics scoring tables, in order to calibrate the high-end (max-score) of our scoring formula. For the lower end (null-score) we start from the prescription put forward by one of the authors (G.P.), stated epigrammatically as ``walking is not running'' and obtain an estimate of the corresponding performances. The result is a set of parameters, calculated once and for all, which allow, given the distance and the registered time, to obtain the scoring for the performance for distances ranging from sprints to ultramarathons (for both sexes and adjusted for the age of the runner).

The Improvement in NCAA Division 1 Basketball Free Throw Accuracy Since 1987, and the Counter-Productive Increased Reliance on Three-Point Shots

2023-11-02T18:43:51+00:00

We examine two diametrically opposite levels of action on a basketball court to address incorrect concepts about both. When a free throw is taken, all action stops. The fouled player steps unopposed to the free throw line to shoot at the open basket. A specific player may have flaws in technique, but consistent improvement across many games for many players at first consideration seems unlikely. A plot of yearly free throw shooting accuracy from 1987 through 2022 tells a different story. At the opposite end of the basketball activity spectrum is the three-point shot. Since 1987 when the top division of US college basketball created the opportunity to score three points for shots taken outside of an arc, we see much effort being taken to shoot increasing numbers of three-point shots, given the obvious advantage of scoring three points instead of two. Of course, a team with accurate three-point shooters should exploit that option. Late in a game when a team is behind, again, the three-point shot should be exploited. However, we ask if it is good practice as a rule for teams to become infatuated with shooting that shot. We will display significant flaws with that strategy.

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

2023-10-02T17:21:47+00:00

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.