مقایسهٔ روش‌ها

	TrueSkill: رتبه‌بندی مهارت بیزی برای رتبه‌بندی رقابتی	استنتاج بیزی	مدل بردلی-تری	سیستم رتبه‌بندی اِلو (Elo Rating System)
حوزه	تصمیم‌گیری	آمار	تصمیم‌گیری	تصمیم‌گیری
خانواده	Regression model	Bayesian methods	Regression model	Regression model
سال پیدایش	2007	1763	1952	1978
پدیدآور	Ralf Herbrich, Tom Minka & Thore Graepel	Thomas Bayes; Pierre-Simon Laplace	Ralph Bradley & Milton Terry	Arpad Elo
نوع	Probabilistic ranking model	Probabilistic inference paradigm	Probabilistic paired comparison model	Pairwise comparison ranking model
منبع بنیادین	Herbrich, R., Minka, T., & Graepel, T. (2007). TrueSkill: A Bayesian skill rating system. Advances in Neural Information Processing Systems, 19, 569–576.	Bayes, T. (1763). An essay towards solving a problem in the doctrine of chances. Philosophical Transactions of the Royal Society of London, 53, 370–418.	Bradley, R. A., & Terry, M. E. (1952). Rank analysis of incomplete block designs: I. The method of paired comparisons. Biometrika, 39(3/4), 324–345.	Elo, A. E. (1978). The Rating of Chessplayers, Past and Present. Arco Publishing. ISBN: 978-0-668-04721-0
نام‌های دیگر	Bayesian Skill Rating, TrueSkill Ranking System, Gaussian Skill Model, Beceri Derecelendirme Modeli	Bayes inference, Bayesian statistics, Bayesian updating, posterior inference	BT Model, Bradley-Terry-Luce Model, Paired Comparison Model, İkili Karşılaştırma Modeli	Elo Rating System, Elo Chess Rating, Elo Skill Rating, Elo Derecelendirme Sistemi
مرتبط	3	3	3	2
خلاصه	TrueSkill is a Bayesian skill rating system developed by Herbrich, Minka, and Graepel at Microsoft Research and introduced at NeurIPS 2006. It represents each player's skill as a Gaussian distribution parameterized by a mean (estimated skill) and a variance (uncertainty). After each match outcome, the system updates these distributions via approximate message passing, yielding a principled ranking that handles team games, draws, and partial observations in online settings.	Bayesian inference is a statistical paradigm in which probability represents degrees of belief rather than long-run frequencies. It encodes prior knowledge about parameters in a prior distribution, combines that prior with the likelihood of observed data via Bayes' theorem, and produces a posterior distribution that quantifies updated uncertainty. The foundational theorem was published posthumously by Thomas Bayes in 1763 and subsequently systematized by Pierre-Simon Laplace in his 1812 Théorie analytique des probabilités.	The Bradley-Terry model is a probabilistic model for paired comparisons that assigns a latent strength parameter to each item and predicts the probability that one item beats another in a head-to-head contest. Introduced by Ralph A. Bradley and Milton E. Terry in 1952, it provides a principled statistical framework for ranking items from pairwise preference data, including incomplete comparison designs where not every pair is directly observed.	The Elo Rating System is a pairwise comparison-based ranking method developed by Hungarian-American physicist and chess master Arpad Elo and formally published in 1978. Originally designed to assess the relative skill levels of chess players, it assigns each competitor a numerical rating that rises or falls after each encounter based on the expected versus actual outcome. The system assumes that player performance follows a logistic distribution, enabling probabilistic predictions of match results and continuous rating refinement over time.