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The success rate of a basketball shot may be higher at locations where a player makes more shots. For a marked spatial point process, this means that the mark and the intensity are associated. We propose a Bayesian joint model for the mark and the intensity of marked point processes, where the intensity is incorporated in the mark model as a covariate. Inferences are done with a Markov chain Monte Carlo algorithm. Two Bayesian model comparison criteria, the Deviance Information Criterion and the Logarithm of the Pseudo-Marginal Likelihood, were used to assess the model. The performances of the proposed methods were examined in extensive simulation studies. The proposed methods were applied to the shot charts of four players (Curry, Harden, Durant, and James) in the 2017–2018 regular season of the National Basketball Association to analyze their shot intensity in the field and the field goal percentage in detail. Application to the top 50 most frequent shooters in the season suggests that the field goal percentage and the shot intensity are positively associated for a majority of the players. The fitted parameters were used as inputs in a secondary analysis to cluster the players into different groups.

This paper examines the performance of five different measures for forecasting men’s and women’s professional tennis matches. We use data derived from every match played at the 2018 and 2019 Wimbledon tennis championships, the 2019 French Open, the 2019 US Open, and the 2020 Australian Open. We look at the betting odds, the official tennis rankings, the standard Elo ratings, surface-specific Elo ratings, and weighted composites of these ratings, including and excluding the betting odds. The performance indicators used are prediction accuracy, calibration, model discrimination, Brier score, and expected return. We find that the betting odds perform relatively well across these tournaments, while standard Elo (especially for women’s tennis) and surface-adjusted Elo (especially for men’s tennis) also perform well on a range of indicators. For all but the hard-court surfaces, a forecasting model which incorporates the betting odds tends also to perform well on some indicators. We find that the official ranking system proved to be a relatively poor measure of likely performance compared to betting odds and Elo-related methods. Our results add weight to the case for a wider use of Elo-based approaches within sports forecasting, as well as arguably within the player rankings methodologies.

Spatial point processes have been successfully used to model the relative efficiency of shot locations for each player in professional basketball games. Those analyses were possible because each player makes enough baskets to reliably fit a point process model. Goals in hockey are rare enough that a point process cannot be fit to each player’s goal locations, so novel techniques are needed to obtain measures of shot efficiency for each player. A Log-Gaussian Cox Process (LGCP) is used to model all shot locations, including goals, of each NHL player who took at least 500 shots during the 2011–2018 seasons. Each player’s LGCP surface is treated as an image and these images are then used in an unsupervised statistical learning algorithm that decomposes the pictures into a linear combination of spatial basis functions. The coefficients of these basis functions are shown to be a very useful tool to compare players. To incorporate goals, the locations of all shots that resulted in a goal are treated as a “perfect player” and used in the same algorithm (goals are further split into perfect forwards, perfect centres and perfect defence). These perfect players are compared to other players as a measure of shot efficiency. This analysis provides a map of common shooting locations, identifies regions with the most goals relative to the number of shots and demonstrates how each player’s shot location differs from scoring locations.

We introduce a simple and natural iterative version of the well-known and widely studied Markov rating method. We show that this iterative Markov method converges to the usual global Markov rating, and shares a close relationship with the well-known Elo rating. Together with recent results on the relationship between the global Markov method and the maximum likelihood estimate of the rating vector in the Bradley–Terry (BT) model, we connect and explore the global and iterative Markov, Elo, and Bradley–Terry ratings on real and simulated data.

Trail running is an endurance sport in which athletes face severe physical challenges. Due to the growing number of participants, the organization of limited staff, equipment, and medical support in these races now plays a key role. Monitoring runner’s performance is a difficult task that requires knowledge of the terrain and of the runner’s ability. In the past, choices were solely based on the organizers’ experience without reliance on data. However, this approach is neither scalable nor transferable. Instead, we propose a firm statistical methodology to perform this task, both before and during the race. Our proposed framework, Trail Running Assessment of Performance (TRAP), studies (1) the assessment of the runner’s ability to reach the next checkpoint, (2) the prediction of the runner’s expected passage time at the next checkpoint, and (3) corresponding prediction intervals for the passage time. We apply our methodology, using the race history of runners from the International Trail Running Association (ITRA) along with checkpoint and terrain-level information, to the “holy grail” of ultra-trail running, the Ultra-Trail du Mont-Blanc (UTMB) race, demonstrating the predictive power of our methodology.

In this paper, we investigate the correlation between the main physical characteristics of eight variants of football and hockey (such as field size, goal size, player velocity, ball velocity, player density, and game duration) and the resulting average numbers of goals scored per game. To do so, the Pi-theorem in physics is extended to sport science and a non-dimensional parameter of interest is defined. It is based on the ratio between the duration of the game and the order of magnitude of the time needed to cross the midfield, which depends on the average velocity of the ball and the players, the player density and the size of the goals. An excellent correlation is found between the proposed parameter and the average number of goals scored per game during recent international competitions. Using the derived correlation, the effect of any modification of the main characteristics of football and hockey (and their variants) on the scoring pace can be assessed. For instance, it can be predicted that decreasing the length of football fields by 20 m would raise the average number of goals scored to 3.6 (±0.6) per game, versus the 2.6 goals scored during the most recent men’s World Cup.