Continuous-time state-space modelling of the hot hand in basketball

We investigate the hot hand phenomenon using data on 110,513 free throws taken in the National Basketball Association (NBA). As free throws occur at unevenly spaced time points within a game, we consider a state-space model formulated in continuous time to investigate serial dependence in players' success probabilities. In particular, the underlying state process can be interpreted as a player's (latent) varying form and is modelled using the Ornstein-Uhlenbeck process. Our results support the existence of the hot hand, but the magnitude of the estimated effect is rather small

A copula-based multivariate hidden Markov model for modelling momentum in football

We investigate the potential occurrence of change points - commonly referred to as "momentum shifts" - in the dynamics of football matches. For that purpose, we model minute-by-minute in-game statistics of Bundesliga matches using hidden Markov models (HMMs). To allow for within-state correlation of the variables considered, we formulate multivariate state-dependent distributions using copulas. For the Bundesliga data considered, we find that the fitted HMMs comprise states which can be interpreted as a team showing different levels of control over a match. Our modelling framework enables inference related to causes of momentum shifts and team tactics, which is of much interest to managers, bookmakers, and sports fans

A copula-based multivariate hidden Markov model for modelling momentum in football

We investigate the potential occurrence of change points—commonly referred to as “momentum shifts”—in the dynamics of football matches. For that purpose, we model minute-by-minute in-game statistics of Bundesliga matches using hidden Markov models (HMMs). To allow for within-state dependence of the variables, we formulate multivariate state-dependent distributions using copulas. For the Bundesliga data considered, we find that the fitted HMMs comprise states which can be interpreted as a team showing different levels of control over a match. Our modelling framework enables inference related to causes of momentum shifts and team tactics, which is of much interest to managers, bookmakers, and sports fans.publishedVersio

Bettors' reaction to match dynamics -- Evidence from in-game betting

It is still largely unclear to what extent bettors update their prior assumptions about the strength and form of competing teams considering the dynamics during the match. This is of interest not only from the psychological perspective, but also as the pricing of live odds ideally should be driven both by the (objective) outcome probabilities and also the bettors' behaviour. Using state-space models (SSMs) to account for the dynamically evolving latent sentiment of the betting market, we analyse a unique high-frequency data set on stakes placed during the match. We find that stakes in the live-betting market are driven both by perceived pre-game strength and by in-game strength, the latter as measured by the Valuing Actions by Estimating Probabilities (VAEP) approach. Both effects vary over the course of the match

The hot hand in professional darts

Ötting M, Langrock R, Deutscher C, Leos-Barajas V. The hot hand in professional darts. Journal of the Royal Statistical Society. Series A. 2020;183(2):565-580.We investigate the hot hand hypothesis in professional darts in a nearly ideal setting with minimal to no interaction between players. Considering almost 1 year of tournament data, corresponding to 167492 dart throws in total, we use state space models to investigate serial dependence in throwing performance. In our models, a latent state process serves as a proxy for a player's underlying form, and we use auto-regressive processes to model how this process evolves over time. Our results regarding the persistence of the latent process indicate a weak hot hand effect, but the evidence is inconclusive

Performance under pressure in skill tasks: An analysis of professional darts

Ötting M, Deutscher C, Schneemann S, Langrock R, Gehrmann S, Scholten H. Performance under pressure in skill tasks: An analysis of professional darts. PLOS ONE. 2020;15(2): e0228870.Understanding and predicting how individuals perform in high-pressure situations is of importance in designing and managing workplaces. We investigate performance under pressure in professional darts as a near-ideal setting with no direct interaction between players and a high number of observations per subject. Analyzing almost one year of tournament data covering 32,274 dart throws, we find no evidence in favor of either choking or excelling under pressure

Predicting play calls in the National Football League using hidden Markov models

Ötting M. Predicting play calls in the National Football League using hidden Markov models. IMA Journal of Management Mathematics. 2021;32(4):535-545.In recent years, data-driven approaches have become a popular tool in a variety of sports to gain an advantage by, for example, analysing potential strategies of opponents. Whereas the availability of play-by-play or player tracking data in sports such as basketball and baseball has led to an increase of sports analytics studies, equivalent data sets for the National Football League (NFL) were not freely available for a long time. In this contribution, we consider a comprehensive play-by-play NFL dataset provided by www.kaggle.com, comprising 289,191 observations in total, to predict play calls in the NFL using hidden Markov models. The resulting out-of-sample prediction accuracy for the 2018 NFL season is 71.6%, which is similar compared to existing studies on play call predictions in the NFL. In practice, such predictions are helpful for NFL teams, especially for defense coordinators, to make adjustments in real time on the field

Sports statistics in the data age: betting fraud detection and performance evaluation

Ötting M. Sports statistics in the data age: betting fraud detection and performance evaluation. Bielefeld: Universität Bielefeld; 2020