Whole-History Rating: A Bayesian Rating System for Players of Time-Varying Strength

  • Rémi Coulom
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5131)


Whole-History Rating (WHR) is a new method to estimate the time-varying strengths of players involved in paired comparisons. Like many variations of the Elo rating system, the whole-history approach is based on the dynamic Bradley-Terry model. But, instead of using incremental approximations, WHR directly computes the exact maximum a posteriori over the whole rating history of all players. This additional accuracy comes at a higher computational cost than traditional methods, but computation is still fast enough to be easily applied in real time to large-scale game servers (a new game is added in less than 0.001 second). Experiments demonstrate that, in comparison to Elo, Glicko, TrueSkill, and decayed-history algorithms, WHR produces better predictions.


Wiener Process Prediction Rate Rating Algorithm Rating Uncertainty Incremental Algorithm 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Coulom, R.: Bayeselo (2005),
  2. 2.
    Dangauthier, P., Herbrich, R., Minka, T., Graepel, T.: TrueSkill through time: Revisiting the history of chess. In: Platt, J.C., Koller, D., Singer, Y., Roweis, S. (eds.) Advances in Neural Information Processing Systems 20, Vancouver, Canada, MIT Press, Cambridge (2007)Google Scholar
  3. 3.
    Edwards, R.: Edo historical chess ratings (2004),
  4. 4.
    Elo, A.E.: The Rating of Chessplayers, Past and Present. Arco Publishing, New York (1978)Google Scholar
  5. 5.
    Fahrmeir, L., Tutz, G.: Dynamic stochastic models for time-dependent ordered paired comparison systems. Journal of the American Statistical Association 89(428), 1438–1449 (1994)zbMATHCrossRefGoogle Scholar
  6. 6.
    Glickman, M.E.: Paired Comparison Model with Time-Varying Parameters. PhD thesis, Harvard University, Cambridge, Massachusetts (1993)Google Scholar
  7. 7.
    Glickman, M.E.: Parameter estimation in large dynamic paired comparison experiments. Applied Statistics 48(33), 377–394 (1999)zbMATHGoogle Scholar
  8. 8.
    Herbrich, R., Graepel, T.: TrueSkillTM: A Bayesian skill rating system. Technical Report MSR-TR-2006-80, Microsoft Research (2006)Google Scholar
  9. 9.
    Hunter, D.R.: MM algorithms for generalized Bradley-Terry models. The Annals of Statistics 32(1), 384–406 (2004)zbMATHCrossRefMathSciNetGoogle Scholar
  10. 10.
    Rybicki, G.B., Hummer, D.G.: An accelerated lambda iteration method for multilevel radiative transfer. Astronomy and Astrophysics 245(1), 171–181 (1991)Google Scholar
  11. 11.
    Rybicki, G.B., Press, W.H.: Interpolation, realization, and reconstruction of noisy, irregularly sampled data. The Astrophysical Journal 398(1), 169–176 (1992)CrossRefGoogle Scholar
  12. 12.
    Knorr-Held, L.: Dynamic rating of sports teams. The Statistician 49(2), 261–276 (2000)Google Scholar
  13. 13.
    Shubert, W.M.: Details of the KGS rank system (2007),
  14. 14.
    Sonas, J.: Chessmetrics (2005),

Copyright information

© Springer-Verlag Berlin Heidelberg 2008

Authors and Affiliations

  • Rémi Coulom
    • 1
  1. 1.Université Charles de Gaulle, INRIA SEQUEL, CNRS GRAPPALilleFrance

Personalised recommendations