Related papers: Modelling intransitivity in pairwise comparisons w…
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…
Competitive tournaments appear in sports, politics, population ecology, and animal behavior. All of these fields have developed methods for rating competitors and ranking them accordingly. A tournament is intransitive if it is not…
The win ratio (WR) is a novel statistic used in randomized controlled trials that can account for hierarchies within event outcomes. In this paper we report and study the long-run non-transitive behavior of the win ratio and the closely…
We propose a novel ranking model that combines the Bradley-Terry-Luce probability model with a nonnegative matrix factorization framework to model and uncover the presence of latent variables that influence the performance of top tennis…
We study a random game in which two players in turn play a fixed number of moves. For each move, there are two possible choices. To each possible outcome of the game we assign a winner in an i.i.d. fashion with a fixed parameter p. In the…
Answering a pair of questions of Conrey, Gabbard, Grant, Liu, and Morrison, we prove that a triplet of dice drawn from the multiset model are intransitive with probability $1/4+o(1)$ and the probability a random pair of dice tie tends…
The use of statistical modeling in baseball has received substantial attention recently in both the media and academic community. We focus on a relatively under-explored topic: the use of statistical models for the analysis of fielding…
Pairwise comparison models have been widely used for utility evaluation and rank aggregation across various fields. The increasing scale of modern problems underscores the need to understand statistical inference in these models when the…
We study a simple example of a sequential game illustrating problems connected with making rational decisions that are universal for social sciences. The set of chooser's optimal decisions that manifest his preferences in case of a constant…
We present a quantitative analysis of throwing ability for major league outfielders and catchers. We use detailed game event data to tabulate success and failure events in outfielder and catcher throwing opportunities. We attribute a run…
Game AI systems need the theory of mind, which is the humanistic ability to infer others' mental models, preferences, and intent. Such systems would enable inferring players' behavior tendencies that contribute to the variations in their…
Positions of chess players in intransitive (rock-paper-scissors) relations are considered. Namely, position A of White is preferable (it should be chosen if choice is possible) to position B of Black, position B of Black is preferable to…
This work considers reasons for and implications of discarding the assumption of transitivity, which (transitivity) is the fundamental postulate in the utility theory of Von Neumann and Morgenstern, the adiabatic accessibility principle of…
The Bradley-Terry-Luce (BTL) model is a classic and very popular statistical approach for eliciting a global ranking among a collection of items using pairwise comparison data. In applications in which the comparison outcomes are observed…
In the sport of cricket, player batting ability is traditionally measured using the batting average. However, the batting average fails to measure both short-term changes in ability that occur during an innings, and long-term changes that…
A key generative principle within social and other complex networks is transitivity, where friends of friends are more likely friends. We propose a new model for highly dense complex networks based on transitivity, called the Iterated Local…
We study biased Maker-Breaker positional games between two players, one of whom is playing randomly against an opponent with an optimal strategy. In this paper we consider the scenario when Maker plays randomly and Breaker is "clever", and…
Stochastic transitivity is central for rank aggregation based on pairwise comparison data. The existing models, including the Thurstone, Bradley-Terry (BT), and nonparametric BT models, adopt a strong notion of stochastic transitivity,…
We examine whether social data can be used to predict how members of Major League Baseball (MLB) and members of the National Basketball Association (NBA) transition between teams during their career. We find that incorporating social data…
In classical statistics, the bias-variance trade-off describes how varying a model's complexity (e.g., number of fit parameters) affects its ability to make accurate predictions. According to this trade-off, optimal performance is achieved…