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In many sports, such as soccer, a coach has to decide whether to adopt an “offensive” or a “defensive” approach to a match. This strategic decision depends on the strengths and weaknesses of his team with respect to the opponent, but also on the strategy chosen by the opponent’s coach. The fact that a draw also results in a point, which may be important for the ranking, further complicates this decision, as the coach must assess whether it is better to adopt a defensive team formation in order to obtain a draw, or to aim for victory despite the increased risk of defeat. We study this topic by means of a game-theoretical approach, and we develop an algorithm which allows to compute the optimal strategy. The algorithm tests the stability of the outcome with respect to uncertainty in the estimated win probabilities. Furthermore, our approach can handle in-game events, which may provoke changes in optimal strategy. Finally, our model also allows us to assess the effect of various point systems on the willingness of teams to opt for attacking play. Our method is applied to a case study, based on the match Italy – Costa Rica (World Cup 2014).

In this work, we propose a new hybrid modeling approach for the scores of international soccer matches which combines random forests with Poisson ranking methods . While the random forest is based on the competing teams’ covariate information, the latter method estimates ability parameters on historical match data that adequately reflect the current strength of the teams. We compare the new hybrid random forest model to its separate building blocks as well as to conventional Poisson regression models with regard to their predictive performance on all matches from the four FIFA World Cups 2002–2014. It turns out that by combining the random forest with the team ability parameters from the ranking methods as an additional covariate the predictive power can be improved substantially. Finally, the hybrid random forest is used (in advance of the tournament) to predict the FIFA World Cup 2018. To complete our analysis on the previous World Cup data, the corresponding 64 matches serve as an independent validation data set and we are able to confirm the compelling predictive potential of the hybrid random forest which clearly outperforms all other methods including the betting odds.

Bayesian methods are becoming increasingly popular in sports analytics. Identified advantages of the Bayesian approach include the ability to model complex problems, obtain probabilistic estimates and predictions that account for uncertainty, combine information sources and update learning as new data become available. The volume and variety of data produced in sports activities over recent years and the availability of software packages for Bayesian computation have contributed significantly to this growth. This comprehensive survey reviews and characterizes the latest advances in Bayesian statistics in sports, including methods and applications. We found that a large proportion of these articles focus on modeling/predicting the outcome of sports games and on the development of statistics that provides a better picture of athletes’ performance. We provide a description of some of the advances in basketball, football and baseball. We also summarise the sources of data used for the analysis and the most commonly used software for Bayesian computation. We found a similar number of publications between 2013 and 2018 as compared to those published in the three previous decades, which is an indication of the growing adoption rate of Bayesian methods in sports.

A well-established assumption in tennis is that point outcomes on each player’s serve in a match are independent and identically distributed (iid). With this assumption, it is enough to specify the serve probabilities for both players to derive a wide variety of event distributions, such as the expected winner and number of sets, and number of games. However, models using this assumption, which we will refer to as “point-based”, have typically performed worse than other models in the literature at predicting the match winner. This paper presents a point-based Bayesian hierarchical model for predicting the outcome of tennis matches. The model predicts the probability of winning a point on serve given surface, tournament and match date. Each player is given a serve and return skill which is assumed to follow a Gaussian random walk over time. In addition, each player’s skill varies by surface, and tournaments are given tournament-specific intercepts. When evaluated on the ATP’s 2014 season, the model outperforms other point-based models, predicting match outcomes with greater accuracy (68.8% vs. 66.3%) and lower log loss (0.592 vs. 0.641). The results are competitive with approaches modelling the match outcome directly, demonstrating the forecasting potential of the point-based modelling approach.

We use a Markov decision process to model the value of the sacrifice bunt. Specifically, we consider a nine-inning baseball game with non-identical batters and compute the degree to which sacrificing increases the probability of winning the game. We populate our model using data covering the National League of Major League Baseball, and demonstrate the importance of using the probability of winning the game when analyzing the value of the sacrifice bunt. We show how and why the criterion of maximizing the probability of winning is superior to that of maximizing the expected number of runs scored or the probability of scoring at least one run in the half inning. Our model enables us to investigate situations that are not possible to investigate using earlier models, and find that the sacrifice bunt is more beneficial than previously thought. We also discuss the effect sizes of individual sacrifice bunts, and the effect of model simplifications on runner advancement or ignoring double plays.

Combinatorial/probabilistic models for cross-country dual-meets are proposed. The first model assumes that all runners are equally likely to finish in any possible order. The second model assumes that each team is selected from a large identically distributed population of potential runners and with each potential runner’s ranking determined by the initial draw from the combined population.