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We present an extensive statistical analysis of the results of all sports competitions in five major sports leagues in England and the United States. We characterize the parity among teams by the variance in the winning fraction from…
The Brier Score is a widely-used criterion to assess the quality of probabilistic predictions of binary events. The expectation value of the Brier Score can be decomposed into the sum of three components called reliability, resolution, and…
Following a penalty in rugby union, teams typically choose between attempting a shot at goal or kicking to touch to pursue a try. We develop an Expected Points (EP) framework that quantifies the value of each option as a function of both…
Time-to-event forecasts are essential when decisions depend on event timing. This article develops a framework for evaluating such forecasts when the event has not yet occurred or is not predicted within the forecast horizon. We introduce a…
I introduce a model of predictive scoring. A receiver wants to predict a sender's quality. An intermediary observes multiple features of the sender and aggregates them into a score. Based on the score, the receiver makes a decision. The…
In this paper a new heuristic optimization algorithm has been introduced based on the performance of the major football leagues within each season in EU countries. The algorithm starts with an initial population including three different…
Calibration is a classical notion from the forecasting literature which aims to address the question: how should predicted probabilities be interpreted? In a world where we only get to observe (discrete) outcomes, how should we evaluate a…
Goals are results of pin-point shots and it is a pivotal decision in soccer when, how and where to shoot. The main contribution of this study is two-fold. At first, after showing that there exists high spatial correlation in the data of…
Prediction markets provide an efficient means to assess uncertain quantities from forecasters. Traditional and competitive strictly proper scoring rules have been shown to incentivize players to provide truthful probabilistic forecasts.…
We propose two Bayesian multinomial-Dirichlet models to predict the final outcome of football (soccer) matches and compare them to three well-known models regarding their predictive power. All the models predicted the full-time results of…
Cricket betting is a multi-billion dollar market. Therefore, there is a strong incentive for models that can predict the outcomes of games and beat the odds provided by bookers. The aim of this study was to investigate to what degree it is…
A common assumption when sampling $p$-dimensional observations from $K$ distinct group is the equality of the covariance matrices. In this paper, we propose two penalized $M$-estimation approaches for the estimation of the covariance or…
A popular quantitative approach to evaluating player performance in sports involves comparing an observed outcome to the expected outcome ignoring player involvement, which is estimated using statistical or machine learning methods. In…
Understanding prediction errors and determining how to fix them is critical to building effective predictive systems. In this paper, we delineate four types of prediction errors and demonstrate that these four types characterize all…
Predicting the results of sport matches and competitions is an arising research field, benefiting from the growing amount of available data and the novel data analytics techniques. Excellent forecasts can be achieved by advanced machine…
In many sports, it is commonly believed that the home team has an advantage over the visiting team, known as the home field advantage. Yet its causal effect on team performance is largely unknown. In this paper, we propose a novel causal…
A new formalism for analyzing the progression of cricket game using Stochastic differential equation (SDE) is introduced. This theory enables a quantitative way of representing every team using three key variables which have physical…
We introduce inference methods for score decompositions, which partition scoring functions for predictive assessment into three interpretable components: miscalibration, discrimination, and uncertainty. Our estimation and inference relies…
Paired comparison models, such as Bradley-Terry and Thurstone-Mosteller, are commonly used to estimate relative strengths of pairwise compared items in tournament-style data. We discuss estimation of paired comparison models with a ridge…
Proper scoring rules are methods for encouraging honest assessment of probability distributions. Just like likelihood, a proper scoring rule can be applied to supply an unbiased estimating equation for any statistical model, and the theory…