Volume 11, Issue 4

A finite mixture latent trajectory model is developed to study the performance and strategy of runners in a 24-h long ultra running race. The model facilitates clustering of runners based on their speed and propensity to rest and thus reveals the strategies used in the race. Inference for the adopted latent trajectory model is achieved using an expectation-maximization algorithm. Fitting the model to data from the 2013 World Championships reveals three clearly separated clusters of runners who exhibit different strategies throughout the race. The strategies show that runners can be grouped in terms of their average moving speed and their propensity to rest during the race. The effect of age and gender on the probability of belonging to each cluster is also investigated.

Abstract: The predictive performance of various team metrics is compared in the context of 105 best-of-seven national hockey league (NHL) playoff series that took place between 2008 and 2014 inclusively. This analysis provides renewed support for traditional box score statistics such as goal differential, especially in the form of Pythagorean expectations. A parsimonious relevance vector machine (RVM) learning approach is compared with the more common support vector machine (SVM) algorithm. Despite the potential of the RVM approach, the SVM algorithm proved to be superior in the context of hockey playoffs. The probabilistic SVM results are used to derive playoff performance expectations for NHL teams and identify playoff under-achievers and over-achievers. The results suggest that the Arizona Coyotes and the Carolina Hurricanes can both be considered Round 2 over-achievers while the Nashville Predators would be Round 2 under-achievers, even after accounting for several observable team performance metrics and playoff predictors. The Vancouver Canucks came the closest to qualify as Stanley Cup Finals under-achievers after they lost against the Boston Bruins in 2011. Overall, the results tend to support the idea that the NHL fields extremely competitive playoff teams, that chance or other intangible factors play a significant role in NHL playoff outcomes and that playoff upsets will continue to occur regularly.

Prior studies of referee behavior focus on identifying a bias in when certain calls are made [Kovash, Kenneth, & Levitt, Steven (2009). “Professionals do not play minimax: evidence from Major League Baseball and the National Football League (No. w15347).” National Bureau of Economic Research; Rosen, Peter A. and Rick L. Wilson. 2007. “An Analysis of the Defense First Strategy in College Football Overtime Games.” Journal of Quantitative Analysis in Sports 3(2):1–17; Alamar, Benjamin. 2010. “Measuring Risk in NFL Playcalling.” Journal of Quantitative Analysis in Sports 6:11.]. We extend this research by evaluating the consistency of specific discretionary penalties in professional football. In doing so, all NFL plays from 2002 to 2012 are considered, isolating the occurrence of holding and pass interference calls. Even after accounting for game and play specific variables, including team characteristics, type of play, and the game’s score, we find the likelihood of both penalty types follows a quadratic trend, low at the beginning and ends of the game, but high in the middle. We suggest that these penalties are uniquely called with higher levels of discretion, in an attempt by referees to imply fairness in the flow of the game.

Ski jumping is a Winter Olympic sport where the athletes try to fly as far as possible with the best possible style on a ski jumping hill. The best athletes may achieve distances around 100 m on the smallest hills and up to 251.5 m (the world record) on a flying hill. The length of a ski jump is affected by the gate from which the jumpers start, where higher gates give higher speed and therefore longer jumps. Wind conditions are also important, head winds tend to give longer jumps and tail winds tend to give shorter jumps. To ensure relatively fair conditions during competitions, a system including gate and wind compensations was introduced from January 2010. If the conditions change considerably during a round, the jury can change the gate number to avoid too long or too short jumps, and the athlete is then given a compensation (positive or negative). Furthermore, the athletes are given a compensation for the wind conditions during their jump. In this paper, the fairness of this compensation system is investigated by an analysis of the results from 80 ski jumping competitions for men arranged in the World Cup, World Championships and Olympics in the 2011/2012, 2012/2013 and 2013/2014 seasons. The analysis is based on a mixed model. I found that the present compensation for gate number is reasonably fair, but with a tendency for 10% over-compensation. On the other hand, I estimate that the present compensation factor for head winds should be increased by 48% (95% CI 40–57%) and for tail winds by 22% (95% CI 16–30%) to fully compensate for wind conditions.