Volume 18, Issue 1

In this work we develop a new algorithm for rating of teams (or players) in one-on-one games by exploiting the observed difference of the game-points (such as goals), also known as a margin of victory (MOV). Our objective is to obtain the Elo-style algorithm whose operation is simple to implement and to understand intuitively. This is done in three steps: first, we define the probabilistic model between the teams’ skills and the discretized MOV variable: this generalizes the model underpinning the Elo algorithm, where the MOV variable is discretized into three categories (win/loss/draw). Second, with the formal probabilistic model at hand, the optimization required by the maximum likelihood rule is implemented via stochastic gradient; this yields simple online equations for the rating updates which are identical in their general form to those characteristic of the Elo algorithm: the main difference lies in the way the scores and the expected scores are defined. Third, we propose a simple method to estimate the coefficients of the model, and thus define the operation of the algorithm; it is done in a closed form using the historical data so the algorithm is tailored to the sport of interest and the coefficients defining its operation are determined in entirely transparent manner. The alternative, optimization-based strategy to find the coefficients is also presented. We show numerical examples based on the results of the association football of the English Premier League and the American football of the National Football League.

Evaluation of individuals in a team sport setting is inherently difficult. The level of play of one individual is fundamentally tied to the level of play of the teammates. One way to think about evaluation of individuals is to ‘insert’ the posterior distribution of the parameter that measures individual play into an ‘average’ team, and see how the probability of success (or failure) changes. Using a Bayesian hierarchical logistic model, we can estimate both the average contribution to success of various positions, and the individual contribution of all the players in that position. In this paper, we use data from the 2018 World Championships in Volleyball to model both the position played and the players within each position. Using both the posterior distributions for the mean performance of the different positions, and the posterior distributions for the individual players, we can then estimate the change in the number of points scored for a team with a change from an average player to the individual under consideration. We compute both the points scored above average per set (PAAPS) and the points scored above average per 100 touches (PP100) for 168 men and 168 women playing five different positions. Contributions of the various position groups and of individual players within each position are evaluated and compared.

Sports analysis has gained paramount importance for coaches, scouts, and fans. Recently, computer vision researchers have taken on the challenge of collecting the necessary data by proposing several methods of automatic player and ball tracking. Building on the gathered tracking data, data miners are able to perform quantitative analysis on the performance of players and teams. With this survey, our goal is to provide a basic understanding for quantitative data analysts about the process of creating the input data and the characteristics thereof. Thus, we summarize the recent methods of optical tracking by providing a comprehensive taxonomy of conventional and deep learning methods, separately. Moreover, we discuss the preprocessing steps of tracking, the most common challenges in this domain, and the application of tracking data to sports teams. Finally, we compare the methods by their cost and limitations, and conclude the work by highlighting potential future research directions.

The Elo rating system contains a coefficient called the K-factor which governs the amount of change to the updated ratings and is often determined by empirical or heuristic means. Theoretical studies on the K-factor have been sparse and not much is known about the pertinent factors that impact its appropriate values in applications. This paper has two main goals: to present a new formulation of the K-factor that is optimal with respect to the mean-squared-error (MSE) criterion in a round-robin tournament setting and to investigate the effects of the relevant variables, including the number of tournament participants n , on the optimal K-factor (based on the model-averaged MSE). It is found that n and the variability of the deviation between the true rating and the pre-tournament rating have a strong influence on the optimal K-factor. Comparisons between the MSE-optimal K-factor and the K-factors from Elo and from the US Chess Federation as a function of n are also provided. Although the results are applicable to other sports in similar settings, the study focuses on chess and makes use of the rating data and the K-factor values from the chess world.

In 2019, Eliud Kipchoge ran a sub-two hour marathon wearing Nike’s Alphafly shoes. Despite being the fastest marathon time ever recorded, it wasn’t officially recognized as race conditions were tightly controlled to maximize his success. Besides, Kipchoge’s use of Alphafly shoes was controversial, with some experts claiming that they might have provided an unfair competitive advantage. In this work, we assess the potential influence of advanced footwear technology and the likelihood of a sub-two hour marathon in official races, by studying the evolution of running top performances from 2001 to 2019 for long distances ranging from 10 km to marathon. The analysis is performed using extreme value theory, a field of statistics dealing with analysis of rare events. We find a significant evidence of performance-enhancement effect with a 10% increase of the probability that a new world record for marathon-men discipline is set in 2021. However, results suggest that achieving a sub-two hour marathon in an official race in 2021 is still very unlikely, and exceeds 10% probability only by 2025.