Related papers: Evaluating one-shot tournament predictions
The evaluation of probabilistic forecasts plays a central role both in the interpretation and in the use of forecast systems and their development. Probabilistic scores (scoring rules) provide statistical measures to assess the quality of…
With the aid of mathematical modelling (basic tool is the random walk with absorbing barriers) we derive subsequent formulas to study the effect of different versions of possible rules. For different rules the probability of winning a game,…
Feature importance scores are ubiquitous tools for understanding the predictions of machine learning models. However, many popular attribution methods suffer from high instability due to random sampling. Leveraging novel ideas from…
Tournaments are a widely used mechanism to rank alternatives in a noisy environment. This paper investigates a fundamental issue of economics in tournament design: what is the best usage of limited resources, that is, how should the…
Consider a collection of m competing machine learning algorithms. Given their performance on a benchmark of datasets, we would like to identify the best performing algorithm. Specifically, which algorithm is most likely to ``win'' (rank…
Tournament solutions are standard tools for identifying winners based on pairwise comparisons between competing alternatives. The recently studied notion of margin of victory (MoV) offers a general method for refining the winner set of any…
Despite the significance of probabilistic time-series forecasting models, their evaluation metrics often involve intractable integrations. The most widely used metric, the continuous ranked probability score (CRPS), is a strictly proper…
A tournament is an oriented complete graph. The problem of ranking tournaments was firstly investigated by P. Erd\H{o}s and J. W. Moon. By probabilistic methods, the existence of "unrankable" tournaments was proved. On the other hand, they…
The comparison of benchmark error sets is an essential tool for the evaluation of theories in computational chemistry. The standard ranking of methods by their Mean Unsigned Error is unsatisfactory for several reasons linked to the…
We consider the problem of inferring an unknown ranking of $n$ items from a random tournament on $n$ vertices whose edge directions are correlated with the ranking. We establish, in terms of the strength of these correlations, the…
This paper investigates the Tennis Momentum Model (TMM), which aims to enhance the understanding of match dynamics by integrating key factors such as efficiency, historical scoring probabilities, and real-time scoring data. The model is…
Probability forecasts of events are routinely used in climate predictions, in forecasting default probabilities on bank loans or in estimating the probability of a patient's positive response to treatment. Scoring rules have long been used…
Much work in the parimutuel betting literature has discussed estimating event outcome probabilities or developing optimal wagering strategies, particularly for horse race betting. Some betting pools, however, involve betting not just on a…
Cricket is unarguably one of the most popular sports in the world. Predicting the outcome of a cricket match has become a fundamental problem as we are advancing in the field of machine learning. Multiple researchers have tried to predict…
Who are the most significant players in the history of men tennis? Is the official ATP ranking system fair in evaluating players scores? Which players deserved the most contemplation looking at their match records? Which players have never…
In this note, we introduce a novel performance rating system called Performance Rating Equilibrium (PRE). A PRE is a vector of ratings for each player, such that if these ratings were each player's initial rating at the start of a…
Though athletics statistics are abundant, it is a difficult task to quantitatively compare performances from different events of track, field, and road running in a meaningful way. There are several commonly-used methods, but each has its…
We study the effects of randomness on competitions based on an elementary random process in which there is a finite probability that a weaker team upsets a stronger team. We apply this model to sports leagues and sports tournaments, and…
Statistical analysis of extremes can be used to predict the probability of future extreme events, such as large rainfalls or devastating windstorms. The quality of these forecasts can be measured through scoring rules. Locally scale…
Professional team sports provide an excellent domain for studying the dynamics of social competitions. These games are constructed with simple, well-defined rules and payoffs that admit a high-dimensional set of possible actions and…