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Elo rating, widely used for skill assessment across diverse domains ranging from competitive games to large language models, is often understood as an incremental update algorithm for estimating a stationary Bradley-Terry (BT) model.…
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…
Chess championships are often organised as a Swiss-system tournament, causing great challenges in ranking the participants due to the different strength of schedules and possible circular triads. The paper suggests that pairwise comparison…
Real-world competitive games, such as chess, go, or StarCraft II, rely on Elo models to measure the strength of their players. Since these games are not fully transitive, using Elo implicitly assumes they have a strong transitive component…
Accurately estimating human skill levels is crucial for designing effective human-AI interactions so that AI can provide appropriate challenges or guidance. In games where AI players have beaten top human professionals, strength estimation…
We consider a general class of round-robin tournament models of equally strong players. In these models, each of the $n$ players competes against every other player exactly once. For each match between two players, the outcome is a value…
Ranking the participants of a tournament has applications in voting, paired comparisons analysis, sports and other domains. In this paper we introduce bipartite tournaments, which model situations in which two different kinds of entity…
We introduce a new measure to capture fairness of a schedule in a single round robin (SRR) tournament when participants are ranked by strength. To prevent distortion of the outcome of an SRR tournament as well as to guarantee equal…
League of Legends (LoL) is the most widely played multiplayer online battle arena (MOBA) game in the world. An important aspect of LoL is competitive ranked play, which utilizes a skill-based matchmaking system to form fair teams. However,…
Ranking a vector of alternatives on the basis of a series of paired comparisons is a relevant topic in many instances. A popular example is ranking contestants in sport tournaments. To this purpose, paired comparison models such as the…
Matchmaking systems are vital for creating fair matches in online multiplayer games, which directly affects players' satisfactions and game experience. Most of the matchmaking systems largely rely on precise estimation of players' game…
In Natural Language Processing (NLP), the Elo rating system, originally designed for ranking players in dynamic games such as chess, is increasingly being used to evaluate Large Language Models (LLMs) through "A vs B" paired comparisons.…
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…
Strategy iteration is a technique frequently used for two-player games in order to determine the winner or compute payoffs, but to the best of our knowledge no general framework for strategy iteration has been considered. Inspired by…
A tournament is a method to decide the winner in a competition, and describes the overall sequence in which matches between the players are held. While deciding a worthy winner is the primary goal of a tournament, a close second is to…
Large language models perform surprisingly well on many zero-shot classification tasks, but are difficult to fairly compare to supervised classifiers due to the lack of a modifiable decision boundary. In this work, we propose and evaluate a…
A valuation for a player in a game in extensive form is an assignment of numeric values to the players moves. The valuation reflects the desirability moves. We assume a myopic player, who chooses a move with the highest valuation.…
Rating strategies in a game is an important area of research in game theory and artificial intelligence, and can be applied to any real-world competitive or cooperative setting. Traditionally, only transitive dependencies between strategies…
Game Theory concepts have been successfully applied in a wide variety of domains over the past decade. Sports and games are one of the popular areas of game theory application owing to its merits and benefits in solving complex scenarios.…
In this manuscript, we concentrate on a specific type of covariates, which we call statistically enhanced, for modeling tennis matches for men at Grand slam tournaments. Our goal is to assess whether these enhanced covariates have the…