Volume 19, Issue 1

We present a mathematical modeling framework for roster construction of a Major League Soccer (MLS) expansion team. The model seeks to construct the best squad feasible under league salary rules, while balancing present value, potential value, and future cap flexibility. Player acquisition decisions, as well as allocation of salary, targeted allocation money ( TAM ), general allocation money ( GAM ), and designated player slots, are determined simultaneously by a mixed-integer programming model. We demonstrate the model’s functionality in constructing a hypothetical expansion roster and propose a number of extensions.

The COVID-19 pandemic forced almost all professional and amateur sports to be played without attending crowds. Thus, it induced a large-scale natural experiment on the impact of social pressure on decision making and behavior in sports fields. Using a data set of 1027 rugby union matches from 11 tournaments in 10 countries, we find that home teams have won less matches and their point difference decreased during the pandemic, shedding light on the impact of crowd attendance on the home advantage of sports teams.

The ATP finals is the concluding tournament of the tennis season since its initiation over 50 years ago. It features the 8 best players of that year and is often considered to be the most prestigious event in the sport other than the 4 grand slams. Unlike any other professional tennis tournament, it includes a round-robin stage where all players in a group compete against each other, making it a unique testbed for examining performance under forgiving conditions, where losing does not immediately result in elimination. Analysis of the distribution of final group standings in the ATP Finals for singles from 1972 to 2021 reveals a surprising pattern, where one of the possible and seemingly likely outcomes almost never materializes. The present study uses a model-free, optimization approach to account for this distinctive phenomenon by calculating what match winning probabilities between players in a group can lead to the observed distribution. Results show that the only way to explain the empirical findings is through a “paradoxical” balance of power where the best player in a group shows a vulnerability against the weakest player. We discuss the possible mechanisms underlying this result and their implications for match prediction, bettors, and tournament organization.

This paper examines how the Kelly criterion, a strategy for maximizing the expected log-growth of capital through informed betting, can be applied to non-mutually exclusive bets. These are bets where there is no one-to-one correspondence between the bets and the possible outcomes of the game. This type of situation is common in horse racing, where multiple types of bets are available for a single race. The paper begins by providing a theoretical overview of the Kelly betting strategy and then discusses how it can be extended to non-mutually exclusive bets. A new formulation of the fractional Kelly strategy, which involves betting a fixed fraction of the amount suggested by the Kelly criterion, is also presented for this type of scenario.

Adjusted plus-minus (APM) can sometimes lack common sense. This happens, for instance, when mediocre players move into the top ten, and superstars fall out of the top 100. These occasional outliers hurt the credibility of APM, and mask the benefits, such as increased prediction accuracy. We address this problem with a new method, called Augmented APM. Augmented APM incorporates external player ratings into APM methodology. The purpose of the external rating system is to capture common sense player value. Augmented APM maintains the benefits of APM, and improves credibility by leveraging external ratings that pass the eye test. The key technical idea is recasting APM into a Bayesian framework and using external ratings in the prior distribution. This paper instantiates the Augmented APM method by applying it to soccer. APM methods have not had a substantial impact on soccer, because soccer matches are low scoring, with a low number of substitutions. For external ratings, we use the video game FIFA, which provides subjective evaluations from thousands of scouts, coaches, and season ticket holders. Our paper shows that Augmented APM predicts match outcomes better than (1) APM, and (2) FIFA ratings. We also show that Augmented APM de-correlates players on the same team, which helps for players that play most of their minutes together. Although our results are specific to soccer and FIFA ratings, Augmented APM is a principled method to combine subjective and objective ratings into a single system.