Related papers: What statistics can tell us about strategy in tenn…
Probabilistic properties of tennis scoring systems are examined and compared with best-of-K systems. A model, where each player has his/her own probability of winning his/her service point and which remains invariant for the duration of the…
We establish a general formula for the distribution of the score in table tennis. We use this formula to derive the probability distribution (and hence the expectation and variance) of the number of rallies necessary to achieve any given…
Tennis, like other games and sports, is governed by rules, including the rules that determine the winner of points, games, sets, and matches. If the two players are equally skilled -- each has the same probability of winning a point when…
Tennis is one of the world's biggest and most popular sports. Multiple researchers have, with limited success, modeled the outcome of matches using probability modelling or machine learning approaches. The approach presented here predicts…
Using methods from the statistical mechanics of disordered systems we analyze the properties of bimatrix games with random payoffs in the limit where the number of pure strategies of each player tends to infinity. We analytically calculate…
In many competitive settings, from education to politics, rules do not reward effort evenly, and thresholds (e.g., grade cutoffs or electoral majorities) make some moments disproportionately important. Success thus depends on efficiently…
Individual sports competitions provide a natural setting for examining the relative importance of talent and luck/chance in achieving success. The belief that success is primarily due to individual abilities and hard work rather than…
Tennis is a popular sport worldwide, boasting millions of fans and numerous national and international tournaments. Like many sports, tennis has benefitted from the popularity of rigorous record-keeping of game and player information, as…
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,…
This paper considers the impact of unforced errors in sport. Although the proposed methods are applicable to various sports, we demonstrate the approach in the context of professional tennis. The value of the approach is that we can provide…
In a classical chess round-robin tournament, each of $n$ players wins, draws, or loses a game against each of the other $n-1$ players. A win rewards a player with 1 points, a draw with 1/2 point, and a loss with 0 points. We are interested…
We consider two-player contests with the possibility of ties and study the effect of different tie-breaking rules on effort. For ratio-form and difference-form contests that admit pure-strategy Nash equilibrium, we find that the effort of…
This paper discusses match result prediction ability of ATP ranking points, which is official ranking points for men's professional tennis players. The structure of overall ATP World Tour and the ranking point attribution system leads that…
Moves in chess games are usually analyzed on a case-by-case basis by professional players, but thanks to the availability of large game databases, we can envision another approach of the game. Here, we indeed adopt a very different point of…
We show that the Brier game of prediction is mixable and find the optimal learning rate and substitution function for it. The resulting prediction algorithm is applied to predict results of football and tennis matches. The theoretical…
In the light of the need to achieve a ranking which is understood by all tennis supporters, the ATP ranking is exposed to constant complaints from players and at the same time exposes new players to be benefited with a good tournament to be…
In the 2023 Wimbledon Gentlemen's final, Carlos Alcaraz defeated Novak Djokovic. This study aims to predict athletes' performance through five key aspects: first, a mul-ti-classification model based on logistic regression was established,…
This paper represents an analysis on the momentum of tennis match. And due to Generalization performance of it, it can be helpful in constructing a system to predict the result of sports game and analyze the performance of player based on…
Matrix games constitute a fundamental problem of game theory and describe a situation of two players with completely conflicting interests. We show how methods from statistical mechanics can be used to investigate the statistical properties…
Ranking athletes by their performance in competitions and tournaments is common in every popular sport and has significant benefits that contribute to both the organization and strategic aspects of competitions. Although rankings are…