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We study the coupling of bouncing-ball modes to chaotic modes in two-dimensional billiards with two parallel boundary segments. Analytically, we predict the corresponding decay rates using the fictitious integrable system approach.…
This paper aims to explore the impact of tournament design on the incentives of the contestants. We develop a simulation framework to quantify the potential gain and loss from attacking based on changes in the probability of reaching the…
Last-iterate convergence of learning dynamics in games has attracted significant recent attention. In two-player zero-sum games with bandit feedback, where only the loss of the selected action pair is observed, Fiegel et al. (2025) show a…
In this paper, we present betting strategy of a football game using probability theory. We know all betting houses offer slightly unfair odds towards the player. Here we discuss a simple way to figure out which betting house is offering…
In a balls-in-bins process with feedback, balls are sequentially thrown into bins so that the probability that a bin with n balls obtains the next ball is proportional to f(n) for some function f. A commonly studied case where there are two…
In economy, markets are denoted as efficient when it is impossible to systematically generate profits which outperform the average. In the past years, the concept has been tested in other domains such as the growing sports betting market.…
We study the computation contests where players compete for searching a solution to a given problem with a winner-take-all reward. The search processes are independent across the players and the search speeds of players are proportional to…
We present an algorithm for learning the intrinsic value of a batted ball in baseball. This work addresses the fundamental problem of separating the value of a batted ball at contact from factors such as the defense, weather, and ballpark…
If the final position of a team is already secured independently of the outcomes of the remaining games in a round-robin tournament, it might play with little enthusiasm. This is detrimental to attendance and can inspire collusion and…
Inefficient markets allow investors to consistently outperform the market. To demonstrate that inefficiencies exist in sports betting markets, we created a betting algorithm that generates above market returns for the NFL, NBA, NCAAF,…
Boxing has a long-standing problem with biased judging, impacting both professional and Olympic bouts. "Robberies", where boxers are widely seen as being denied rightful victories, threaten to drive fans and athletes away from the sport. To…
Player selection is one the most important tasks for any sport and cricket is no exception. The performance of the players depends on various factors such as the opposition team, the venue, his current form etc. The team management, the…
Baseball is one of the few sports in which each team plays a game nearly everyday. For instance, in the baseball league in South Korea, namely the KBO (Korea Baseball Organization) league, every team has a game everyday except for Mondays.…
This paper aims to reduce randomness in football by analysing the role of lineups in final scores using machine learning prediction models we have developed. Football clubs invest millions of dollars on lineups and knowing how individual…
While PageRank has been extensively used to rank sport tournament participants (teams or individuals), its superiority over simpler ranking methods has been never clearly demonstrated. We use sports results from 18 major leagues to…
Bill James' Pythagorean formula has for decades done an excellent job estimating a baseball team's winning percentage from very little data: if the average runs scored and allowed are denoted respectively by ${\rm RS}$ and ${\rm RA}$, there…
Neural network pruning techniques can reduce the parameter counts of trained networks by over 90%, decreasing storage requirements and improving computational performance of inference without compromising accuracy. However, contemporary…
We report a new result on lotteries --- that a well-funded syndicate has a purely mechanical strategy to achieve expected returns of 10\% to 25\% in an equiprobable lottery with no take and no carryover pool. We prove that an optimal…
Causal inference has become an accepted analytic framework in settings where experimentation is impossible, which is frequently the case in sports analytics, particularly for studying in-game tactics. However, subtle differences in…
We study a stochastic process that mimics single-game elimination tournaments. In our model, the outcome of each match is stochastic: the weaker player wins with upset probability q<=1/2, and the stronger player wins with probability 1-q.…