{"about":{"site":"https://codewithpapers.app","non_affiliation":"Code with Papers and Syntology are not affiliated with, endorsed by, or sponsored by Papers with Code, Meta, or the pwc-archive mirror.","licence":"CC BY-SA 4.0","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","attribution":"https://codewithpapers.app/attribution","modified":"archive material modified by Syntology; see the attribution page"},"url":"/paper/performance-rating-in-chess-tennis-and-other","title":"Performance rating in chess, tennis, and other contexts","arxiv_id":"2312.12700","date":"2023-12-20","proceeding":null,"authors":["Mehmet S. Ismail"],"abstract":"In this note, I introduce Estimated Performance Rating (PR$^e$), a novel system for evaluating player performance in sports and games. PR$^e$ addresses a key limitation of the Tournament Performance Rating (TPR) system, which is undefined for zero or perfect scores in a series of games. PR$^e$ is defined as the rating that solves an optimization problem related to scoring probability, making it applicable for any performance level. The main theorem establishes that the PR$^e$ of a player is equivalent to the TPR whenever the latter is defined. I then apply this system to historically significant win-streaks in association football, tennis, and chess. Beyond sports, PR$^e$ has broad applicability in domains where Elo ratings are used, from college rankings to the evaluation of large language models.","url_abs":"https://arxiv.org/abs/2312.12700v1","url_pdf":"https://arxiv.org/pdf/2312.12700v1.pdf","source":{"archive":"pwc-archive (Hugging Face), CC BY-SA 4.0","snapshot":"2025-07-28","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","row_kind":"abstracts"},"code_links":[{"paper_slug":"performance-rating-in-chess-tennis-and-other","repo_url":"https://github.com/drmehmetismail/estimated-performance-rating","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":0,"framework":"none","reach":null}],"tasks":[],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"syntology_url":null,"atlas_url":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}