arXiv subjects

Marius Ötting

Publications and source records attributed to Marius Ötting.

13 recordsLinked to original sources

arXiv2024

PEP: a tackle value measuring the prevention of expected points

Traditional assessments of tackling in American Football often only consider the number of tackles made, without adequately accounting for their context and importance for the game. Aiming for improvement, we develop a metric that quantifies the value of a tackle in terms of the prevented expected points (PEP). Specifically, we compare the real end-of-play yard line of tackles with the predicted yard line given the hypothetical situation that the tackle had been missed. For this, we use high-resolution tracking data, that capture the position and velocity of players, and a random forest to account for uncertainty and multi-modality in yard-line prediction. Moreover, we acknowledge the difference in the importance of tackles by assigning an expected points value to each individual tree prediction of the random forest. Finally, to relate the value of tackles to a player's ability to tackle, we fit a suitable mixed-effect model to the PEP values. Our approach contributes to a deeper understanding of defensive performances in American football and offers valuable insights for coaches and analysts.

stat.AP↗

arXiv2023

Extending the Dixon and Coles model: an application to women's football data

The prevalent model by Dixon and Coles (1997) extends the double Poisson model where two independent Poisson distributions model the number of goals scored by each team by moving probabilities between the scores 0-0, 0-1, 1-0, and 1-1. We show that this is a special case of a multiplicative model known as the Sarmanov family. Based on this family, we create more suitable models by moving probabilities between scores and employing other discrete distributions. We apply the new models to women's football scores, which exhibit some characteristics different than that of men's football.

stat.ME↗

arXiv2022

Gambling on Momentum

Sports betting markets are proven real-world laboratories to test theories of asset pricing anomalies and risky behaviour. Using a high-frequency dataset provided directly by a major bookmaker, containing the odds and amounts staked throughout German Bundesliga football matches, we test for evidence of momentum in the betting and pricing behaviour after equalising goals. We find that bettors see value in teams that have the apparent momentum, staking about 40% more on them than teams that just conceded an equaliser. Still, there is no evidence that such perceived momentum matters on average for match outcomes or is associated with the bookmaker offering favourable odds. We also confirm that betting on the apparent momentum would lead to substantial losses for bettors.

econ.GN↗

arXiv2022

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.

stat.AP↗

arXiv2022

The reaction to news in live betting

Sports betting markets have grown very rapidly recently, with the total European gambling market worth 98.6 billion euro in 2019. Considering a high-resolution (1 Hz) data set provided by a large European bookmaker, we investigate the effect of news on the dynamics of live betting. In particular, we consider stakes placed in a live betting market during football matches. Accounting for the general market activity level within a state-space modelling framework, we focus on the market's response to events such as goals (i.e. major news), but also to the general situation within a match such as the uncertainty about the outcome. Our results indicate that markets might overreact to recent news, confirming cognitive biases known from psychology and behavioural economics.

physics.soc-ph↗

arXiv2020

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.

stat.AP↗

arXiv2020

Maximum approximate likelihood estimation of general continuous-time state-space models

Continuous-time state-space models (SSMs) are flexible tools for analysing irregularly sampled sequential observations that are driven by an underlying state process. Corresponding applications typically involve restrictive assumptions concerning linearity and Gaussianity to facilitate inference on the model parameters via the Kalman filter. In this contribution, we provide a general continuous-time SSM framework, allowing both the observation and the state process to be non-linear and non-Gaussian. Statistical inference is carried out by maximum approximate likelihood estimation, where multiple numerical integration within the likelihood evaluation is performed via a fine discretisation of the state process. The corresponding reframing of the SSM as a continuous-time hidden Markov model, with structured state transitions, enables us to apply the associated efficient algorithms for parameter estimation and state decoding. We illustrate the modelling approach in a case study using data from a longitudinal study on delinquent behaviour of adolescents in Germany, revealing temporal persistence in the deviation of an individual's delinquency level from the population mean.

stat.ME↗

arXiv2020

Bookmakers' mispricing of the disappeared home advantage in the German Bundesliga after the COVID-19 break

The outbreak of COVID-19 in March 2020 led to a shutdown of economic activities in Europe. This included the sports sector, since public gatherings were prohibited. The German Bundesliga was among the first sport leagues realising a restart without spectators. Several recent studies suggest that the home advantage of teams was eroded for the remaining matches. Our paper analyses the reaction by bookmakers to the disappearance of such home advantage. We show that bookmakers had problems to adjust the betting odds in accordance to the disappeared home advantage, opening opportunities for profitable betting strategies.

econ.GN↗

arXiv2020

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.

stat.AP↗

arXiv2020

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

In recent years, data-driven approaches have become a popular tool in a variety of sports to gain an advantage by, e.g., 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 datasets 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 71.5%, which is substantially higher compared to similar studies on play call predictions in the NFL.

stat.AP↗

arXiv2019

A regularized hidden Markov model for analyzing the 'hot shoe' in football

Although academic research on the 'hot hand' effect (in particular, in sports, especially in basketball) has been going on for more than 30 years, it still remains a central question in different areas of research whether such an effect exists. In this contribution, we investigate the potential occurrence of a 'hot shoe' effect for the performance of penalty takers in football based on data from the German Bundesliga. For this purpose, we consider hidden Markov models (HMMs) to model the (latent) forms of players. To further account for individual heterogeneity of the penalty taker as well as the opponent's goalkeeper, player-specific abilities are incorporated in the model formulation together with a LASSO penalty. Our results suggest states which can be tied to different forms of players, thus providing evidence for the hot shoe effect, and shed some light on exceptionally well-performing goalkeepers, which are of potential interest to managers and sports fans.

stat.AP↗

arXiv2018

Very Highly Skilled Individuals Do Not Choke Under Pressure: Evidence from Professional Darts

Understanding and predicting how individuals perform in high-pressure situations is of importance in designing and managing workplaces, but also in other areas of society such as disaster management or professional sports. For simple effort tasks, an increase in the pressure experienced by an individual, e.g. due to incentive schemes in a workplace, will increase the effort put into the task and hence in most cases also the performance. For the more complex and usually harder to capture case of skill tasks, there exists a substantial body of literature that fairly consistently reports a choking phenomenon under pressure. However, we argue that many of the corresponding studies have crucial limitations, such as neglected interaction effects or insufficient numbers of observations to allow within-individual analysis. Here, 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. We analyze almost one year of tournament data covering 23,192 dart throws, hence a data set that is very much larger than those used in most previous studies. Contrary to what would be expected given the evidence in favor of a choking phenomenon, we find strong evidence for an overall improved performance under pressure, for nearly all 83 players in the sample. These results could have important consequences for our understanding of how highly skilled individuals deal with high-pressure situations.

stat.AP↗

arXiv2018

The Hot Hand in Professional Darts

We investigate the hot hand hypothesis in professional darts in a near-ideal setting with minimal to no interaction between players. Considering almost one year of tournament data, corresponding to 167,492 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 ability, and we use autoregressive processes to model how this process evolves over time. We find a strong but short-lived serial dependence in the latent state process, thus providing evidence for the existence of the hot hand.

stat.AP↗