Band 12, Heft 4

In sports, there is a constant effort to improve metrics that assess player ability, but there has been almost no effort to quantify and compare existing metrics. Any individual making a management, coaching, or gambling decision is quickly overwhelmed with hundreds of statistics. We address this problem by proposing a set of “meta-metrics”, which can be used to identify the metrics that provide the most unique and reliable information for decision-makers. Specifically, we develop methods to evaluate metrics based on three criteria: (1) stability: does the metric measure the same thing over time (2) discrimination: does the metric differentiate between players and (3) independence: does the metric provide new information? Our methods are easy to implement and widely applicable so they should be of interest to the broader sports community. We demonstrate our methods in analyses of both NBA and NHL metrics. Our results indicate the most reliable metrics and highlight how they should be used by sports analysts. The meta-metrics also provide useful insights about how to best construct new metrics that provide independent and reliable information about athletes.

This paper employs a Skellam process to represent real-time betting odds for English Premier League (EPL) soccer games. Given a matrix of market odds on all possible score outcomes, we estimate the expected scoring rates for each team. The expected scoring rates then define the implied volatility of an EPL game. As events in the game evolve, we re-estimate the expected scoring rates and our implied volatility measure to provide a dynamic representation of the market’s expectation of the game outcome. Using a dataset of 1520 EPL games from 2012–2016, we show how our model calibrates well to the game outcome. We illustrate our methodology on real-time market odds data for a game between Everton and West Ham in the 2015–2016 season. We show how the implied volatility for the outcome evolves as goals, red cards, and corner kicks occur. Finally, we conclude with directions for future research.

Handicap systems are used in many sports to improve competitive balance and equalize the match-win probability between opponents of differing ability. Recognizing the absence of such a system in tennis, we develop a novel optimization-based handicap system for tennis using a Markov Decision Process (MDP) model. In our handicap system, the weaker player is given β “free points” or “credits” at the start of the match, which he can use before the start of any point during the match to win the point outright. The MDP model determines two key features of the handicap system: (1) Fairness: the minimum value of β required to equalize the match-win probability, and (2) Achievability: the optimal policy governing usage of the β credits to achieve the desired match-win probability. We test the sensitivity of the handicap values to the model’s input parameters. Finally, we apply the model to real match data to estimate professional handicaps.