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In wake of the Covid-19 pandemic, 2019-2020 soccer seasons across the world were postponed and eventually made up during the summer months of 2020. Researchers from a variety of disciplines jumped at the opportunity to compare the…
It is common to be interested in rankings or order relationships among entities. In complex settings where one does not directly measure a univariate statistic upon which to base ranks, such inferences typically rely on statistical models…
Behavioral experiments on the Ultimatum Game have shown that we human beings have remarkable preference in fair play, contradicting the predictions by the game theory. Most of the existing models seeking for explanations, however, strictly…
Inspired by the flashing ratchet, Parrondo's game presents an apparently paradoxical situation. Parrondo's game consists of two individual games, game A and game B. Game A is a slightly losing coin-tossing game. Game B has two coins, with…
Standard measures of batting performance such as a batting average and an on-base percentage can be decomposed into component rates such as strikeout rates and home run rates. The likelihood of hitting data for a group of players can be…
Player performance prediction is a serious problem in every sport since it brings valuable future information for managers to make important decisions. In baseball industries, there already existed variable prediction systems and many types…
In this paper, we present a new model for ranking sports teams. Our model uses all scoring data from all games to produce a functional rating by the method of least squares. The functional rating can be interpreted as a teams average point…
We study a modification of the so-called Parrondo's paradox where a large number of individuals choose the game they want to play by voting. We show that it can be better for the players to vote randomly than to vote according to their own…
This paper discusses the gambling contest introduced in Seel & Strack (Gambling in contests, Discussion Paper Series of SFB/TR 15 Governance and the Efficiency of Economic Systems 375, Mar 2012.) and considers the impact of adding a penalty…
For the last ten years, almost every theoretical result concerning the expected run time of a randomized search heuristic used drift theory, making it the arguably most important tool in this domain. Its success is due to its ease of use…
Player ONE chooses a meager set and player TWO, a nowhere dense set per inning. They play $\omega$ many innings. ONE's consecutive choices must form a (weakly) increasing sequence. TWO wins if the union of the chosen nowhere dense sets…
In set theory without the axiom of regularity, we consider a game in which two players choose in turn an element of a given set, an element of this element, etc.; a player wins if its adversary cannot make any next move. Sets that are…
Scouting is a major part of talent acquisition for any professional sports team. In the National Hockey League (NHL), the market for scouting is set by the NHLs Central Scouting Service which develops a ranking of draft eligible players. In…
This paper proposes a multiple-membership generalized linear mixed model for ranking college football teams using only their win/loss records. The model results in an intractable, high-dimensional integral due to the random effects…
Treatment effect estimands based on win statistics, including the win ratio, win odds, and win difference are increasingly popular targets for summarizing endpoints in clinical trials. Such win estimands offer an intuitive approach for…
Humans often make decisions which maximize an internal utility function. For example, humans often maximize their expected reward when gambling and this is considered as a "rational" decision. However, humans tend to change their betting…
Recent work has considered natural variations of the multi-armed bandit problem, where the reward distribution of each arm is a special function of the time passed since its last pulling. In this direction, a simple (yet widely applicable)…
Pruning is a well-established technique for removing unnecessary structure from neural networks after training to improve the performance of inference. Several recent results have explored the possibility of pruning at initialization time…
Intransitive player dominance, where player A beats B, B beats C, but C beats A, is common in competitive tennis. Yet, there are few known attempts to incorporate it within forecasting methods. We address this problem with a graph neural…
It is known that a player in a noncooperative game can benefit by publicly restricting his possible moves before play begins. We show that, more generally, a player may benefit by publicly committing to pay an external party an amount that…