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The seminal Bradley-Terry model exhibits transitivity, i.e., the property that the probabilities of player A beating B and B beating C give the probability of A beating C, with these probabilities determined by a skill parameter for each…

Methodology · Statistics 2025-04-10 Jess Spearing , Jonathan Tawn , David Irons , Tim Paulden

We can construct passing networks when we regard a player as a node and a pass as a link in football games. Thus, we can analyze the networks by using tools developed in network science. Among various metrics characterizing a network,…

Physics and Society · Physics 2021-05-07 Genki Ichinose , Tomohiro Tsuchiya , Shunsuke Watanabe

American football is unique in that offensive and defensive units typically consist of separate players who don't share the field simultaneously, which tempts one to evaluate them independently. However, a team's offensive and defensive…

Applications · Statistics 2025-06-04 Andrey Skripnikov , Sujit Sivadanam

Paired comparison models, such as Bradley-Terry and Thurstone-Mosteller, are commonly used to estimate relative strengths of pairwise compared items in tournament-style data. We discuss estimation of paired comparison models with a ridge…

Methodology · Statistics 2024-10-03 Cristiano Varin , David Firth

Prediction and modelling of competitive sports outcomes has received much recent attention, especially from the Bayesian statistics and machine learning communities. In the real world setting of outcome prediction, the seminal \'{E}l\H{o}…

Machine Learning · Statistics 2017-01-30 Franz J. Király , Zhaozhi Qian

In American football, a pass rush is an attempt by the defensive team to disrupt the offense and prevent the quarterback (QB) from completing a pass. Existing metrics for assessing pass rush performance are either discrete-time quantities…

Applications · Statistics 2023-08-01 Quang Nguyen , Ronald Yurko , Gregory J. Matthews

Tracking data in the NFL is a sequence of spatial-temporal measurements that vary in length depending on the duration of the play. In this paper, we demonstrate how model-based curve clustering of observed player trajectories can be used to…

Applications · Statistics 2020-03-17 Dani Chu , Matthew Reyers , James Thomson , Lucas Wu

Quarterback performance can be difficult to rank, and much effort has been spent in creating new rating systems. However, the input statistics for such ratings are subject to randomness and factors outside the quarterback's control. To…

Other Statistics · Statistics 2019-10-30 Laura A. Albert , John N. Angelis

Most adversarial evaluations of large language model (LLM) safety assess single prompts and report binary pass/fail outcomes, which fails to capture how safety properties evolve under sustained adversarial interaction. We present ADVERSA,…

Cryptography and Security · Computer Science 2026-03-12 Harry Owiredu-Ashley

Defensive coverage schemes in the National Football League (NFL) represent complex tactical patterns requiring coordinated assignments among defenders who must react dynamically to the offense's passing concept. This paper presents a…

Machine Learning · Computer Science 2026-03-30 Kevin Song , Evan Diewald , Ornob Siddiquee , Chris Boomhower , Keegan Abdoo , Mike Band , Amy Lee

Tackling is a fundamental defensive move in American football, with the main purpose of stopping the forward motion of the ball-carrier. However, current tackling metrics are manually recorded outcomes that are inherently flawed due to…

Applications · Statistics 2025-01-08 Quang Nguyen , Ruitong Jiang , Meg Ellingwood , Ronald Yurko

With the development of measurement technology, data on the movements of actual games in various sports can be obtained and used for planning and evaluating the tactics and strategy. Defense in team sports is generally difficult to be…

Artificial Intelligence · Computer Science 2022-05-10 Kosuke Toda , Masakiyo Teranishi , Keisuke Kushiro , Keisuke Fujii

In sports analytics, player tracking data have driven significant advancements in the task of player evaluation. We present a novel generative framework for evaluating the observed frame-by-frame player positioning against a distribution of…

Applications · Statistics 2026-03-24 Quang Nguyen , Ronald Yurko

Change of direction is a key element of player movement in American football, yet there remains a lack of objective approaches for in-game performance evaluation of this athletic trait. Using tracking data, we propose a Bayesian…

Applications · Statistics 2025-07-09 Quang Nguyen , Ronald Yurko

Defensive Pass Interference (DPI) is one of the most impactful penalties in the NFL. DPI is a spot foul, yielding an automatic first down to the team in possession. With such an influence on the game, referees have no room for a mistake. It…

Machine Learning · Computer Science 2022-06-28 Arian Skoki , Jonatan Lerga , Ivan Štajduhar

Reward models are critical for aligning models to follow instructions, and are typically trained following one of two popular paradigms: Bradley-Terry style or Regression style. However, there is a lack of evidence that either approach is…

Machine Learning · Computer Science 2025-03-07 Zhilin Wang , Alexander Bukharin , Olivier Delalleau , Daniel Egert , Gerald Shen , Jiaqi Zeng , Oleksii Kuchaiev , Yi Dong

Existing works have made great progress in improving adversarial robustness, but typically test their method only on data from the same distribution as the training data, i.e. in-distribution (ID) testing. As a result, it is unclear how…

Machine Learning · Computer Science 2024-06-05 Lin Li , Yifei Wang , Chawin Sitawarin , Michael Spratling

This study explores the relationship between the performance of a football team and the topological parameters of temporal passing networks. To achieve this, we propose a method to identify moments of high and low team performance based on…

Physics and Society · Physics 2025-06-13 Andres Chacoma

Evaluation leaderboards such as LMArena play a central role in benchmarking large language models by aggregating pairwise human preferences into model rankings, yet the robustness of these rankings remains poorly understood. We present a…

Machine Learning · Computer Science 2026-05-18 Hosna Oyarhoseini , Jimmy Lin , Amir-Hossein Karimi

Australian Rules Football is a field invasion game where two teams attempt to score the highest points to win. Complex machine learning algorithms have been developed to predict match outcomes post-game, but their lack of interpretability…

Applications · Statistics 2024-05-22 Carlos Rafael Gonzalez Soffner , Manuele Leonelli
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