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This paper studies how the Elo rating system behaves when the underlying modelling assumptions are not met.
Harris, S. N
1906
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1910
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[author] Milnor, JohnJ. (1965). Topology from the Differentiable Viewpoint. University Press of Virginia
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[author] Firth, DavidD. (2005). Bradley-Terry Models in R. Journal of Statistical Software 12 1–12. 10.18637/jss.v012.i01
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[author] Elo, A. EA. E. (2008). The Rating of Chess Players, Past and Present. Ishi Press International
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[author] Brooks, SteveS. (2011). Handbook of Markov chain Monte Carlo, 1st ed. ed. Chapman & Hall CRC handbooks of modern statistical methods. Taylor & Francis, Boca Raton, Fla
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[author] Jiang, XiaoyeX., Lim, Lek-HengL.-H., Yao, YuanY. and Ye, YinyuY. (2011). Statistical ranking and combinatorial Hodge theory. Mathematical Programming 127 203–244
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[author] Langville, Amy NA. N. and Meyer, CarlC. (2012). Who’s #1? The Science of Rating and Ranking. Princeton University Press, Princeton
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Pieters, W
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[author] Xu, QianqianQ., Huang, QingmingQ., Jiang, TingtingT., Yan, BoweiB., Lin, WeisiW. and Yao, YuanY. (2012). HodgeRank on random graphs for subjective video quality assessment. IEEE Transactions on Multimedia 14 844–857
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[author] Sizemore, Robert KR. K. (2013). Hodgerank: Applying combinatorial Hodge theory to sports ranking
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[author] Tran, Ngoc MaiN. M. (2013). Pairwise ranking: choice of method can produce arbitrarily different rank order. Linear Algebra and its Applications 438 1012–1024
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[author] Tsang, Colin S. C.C. S. C., Ngan, Henry Y. T.H. Y. T. and Pang, Grantham K. H.G. K. H. (2016). Fabric inspection based on the Elo rating method. Pattern Recognition 51 378-394. https://doi.org/10.1016/j.patcog.2015.09.022
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[author] Koczkodaj, Waldemar WW. W., Mikhailov, LudmilL., Redlarski, GrzegorzG., Soltys, MichaelM., Szybowski, JacekJ., Tamazian, GaikG., Wajch, ElizaE. and Yuen, Kevin Kam FungK. K. F. (2016). Important Facts and Observations about Pairwise Comparisons (the special issue edition). Fundamenta Informaticae 144 291–307
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[author] Aldous, DavidD. (2017). Elo Ratings and the Sports Model: A Neglected Topic in Applied Probability? Statistical Science 32 616 – 629. 10.1214/17-STS628
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Balduzzi, D
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[author] Düring, BertramB., Torregrossa, MarcoM. and Wolfram, Marie-ThereseM.-T. (2019). Boltzmann and Fokker–Planck equations modelling the Elo rating system with learning effects. Journal of Nonlinear Science 29 1095–1128
2019
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[author] Szczecinski, LeszekL. and Djebbi, AymenA. (2020). Understanding draws in Elo rating algorithm. Journal of Quantitative Analysis in Sports 16 211–220. doi:10.1515/jqas-2019-0102
[author] Vaughan-Williams, LeightonL., Liu, ChunpingC., Dixon, LeratoL. and Gerrard, HannahH. (2021). How well do Elo-based ratings predict professional tennis matches? Journal of Quantitative Analysis in Sports 17 91–105
2021
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2022
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[author] Yan, XueX., Du, YaliY., Ru, BinxinB., Wang, JunJ., Zhang, HaifengH. and Chen, XuX. (2022). Learning to Identify Top Elo Ratings: A Dueling Bandits Approach In Thirty-Sixth AAAI Conference on Artificial Intelligence, AAAI 6375–6383. AAAI Press
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[author] chess. com (2017). How Many Chess Players Are There In The World? Accessed on 2023-04-24 14:57:39 +0930
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2019
Cited alongside, same era.
[author] Tenkanen, SanteriS. (2019). Rating National Hockey League teams: the predictive power of Elo rating models in ice hockey, Bachelor’s thesis, Aalto University, Espoo Finland Available at https://aaltodoc.aalto.fi/items/d163b9aa-bcdc-4d64-90d0-6efee35a3cf5
2019
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2019
Cited alongside, same era.
[author] Berg, ArthurA. (2020). Statistical Analysis of the Elo Rating System in Chess. CHANCE 33 31–38. 10.1080/09332480.2020.1820249
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Czarnecki, W. M
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[author] Duersch, PeterP., Lambrecht, MarcoM. and Oechssler, JoergJ. (2020). Measuring skill and chance in games. European Economic Review 127. 10.1016/j.euroecorev.2020
2020
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[author] Ingram, MartinM. (2021). How to extend Elo: a Bayesian perspective. Journal of Quantitative Analysis in Sports 17 203–219. doi:10.1515/jqas-2020-0066
2020
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[author] Kovalchik, StephanieS. (2020). Extension of the Elo rating system to margin of victory. International Journal of Forecasting 36 1329-1341. https://doi.org/10.1016/j.ijforecast.2020.01.006
2020
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[author] Glickman, MarkM. (2022). Glicko Ratings:. Accessed on 2023-06-27 15:57:39 +0930
2023
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[author] Hamilton, AdamA. (2023). A Multi-Dimensional Extension of the Elo Rating System. PhD Thesis, University of Adelaide
2023
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[author] Hua, Hsuan-FuH.-F., Chang, Ching-JuC.-J., Lin, Tse-ChingT.-C. and Weng, Ruby Chiu-HsingR. C.-H. (2024). Rating players by Laplace’s approximation and dynamic modeling. International Journal of Forecasting 40 1152-1165. https://doi.org/10.1016/j.ijforecast.2023.10.004
2023
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[author] Lyons, KeithK. (2014). What are the World Football Elo Ratings? Accessed on 2023-05-1 14:57:39 +0930
2023
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[author] Sackmann, JeffJ. (2019). An Introduction to Tennis Elo. Accessed on 2023-05-1 14:57:39 +0930
2023
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[author] Szczecinski, LeszekL. and Tihon, RaphaëlleR. (2023). Simplified Kalman filter for on-line rating: one-fits-all approach. Journal of Quantitative Analysis in Sports 19 295–315
2023
Later among the works it cites.
[author] Bolsinova, MariaM., Gergely, BenceB. and Brinkhuis, MatthieuM. (2024). Keeping Elo alive: Evaluating and improving measurement properties of learning systems based on Eloratings. preprint
2024
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[author] chess. com (2024). Elo Rating System. Accessed on 2024-12-11
2024
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[author] Dumoulin, VincentV., Johnson, Daniel D.D. D., Castro, Pablo SamuelP. S., Larochelle, HugoH. and Dauphin, YannY. (2024). A density estimation perspective on learning from pairwise human preferences
2024
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[author] Gómez-Abejón, GonzaloG. and Rodríguez, J. TinguaroJ. T. (2024). Stochastic Extensions of the Elo Rating System. Applied Sciences 14. 10.3390/app14178023
2024
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