Score-Based Bayesian Skill Learning

  • Shengbo Guo
  • Scott Sanner
  • Thore Graepel
  • Wray Buntine
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7523)

Abstract

We extend the Bayesian skill rating system of TrueSkill to accommodate score-based match outcomes. TrueSkill has proven to be a very effective algorithm for matchmaking — the process of pairing competitors based on similar skill-level — in competitive online gaming. However, for the case of two teams/players, TrueSkill only learns from win, lose, or draw outcomes and cannot use additional match outcome information such as scores. To address this deficiency, we propose novel Bayesian graphical models as extensions of TrueSkill that (1) model player’s offence and defence skills separately and (2) model how these offence and defence skills interact to generate score-based match outcomes. We derive efficient (approximate) Bayesian inference methods for inferring latent skills in these new models and evaluate them on three real data sets including Halo 2 XBox Live matches. Empirical evaluations demonstrate that the new score-based models (a) provide more accurate win/loss probability estimates than TrueSkill when training data is limited, (b) provide competitive and often better win/loss classification performance than TrueSkill, and (c) provide reasonable score outcome predictions with an appropriate choice of likelihood — prediction for which TrueSkill was not designed, but which can be useful in many applications.

Keywords

variational inference matchmaking graphical models 

References

  1. 1.
    Abramowitz, M., Stegun, I.A.: Handbook of Mathematical Functions, With Formulas, Graphs, and Mathematical Tables. Dover Publications, New York (1974)Google Scholar
  2. 2.
    Birlutiu, A., Heskes, T.: Expectation Propagation for Rating Players in Sports Competitions. In: Kok, J.N., Koronacki, J., Lopez de Mantaras, R., Matwin, S., Mladenič, D., Skowron, A. (eds.) PKDD 2007. LNCS (LNAI), vol. 4702, pp. 374–381. Springer, Heidelberg (2007)CrossRefGoogle Scholar
  3. 3.
    Dangauthier, P., Herbrich, R., Minka, T., Graepel, T.: Trueskill through time: Revisiting the history of chess. In: NIPS, pp. 337–344. MIT Press, Cambridge (2008)Google Scholar
  4. 4.
    Elo, A.E.: The rating of chess players: past and present. Arco Publishing, New York (1978)Google Scholar
  5. 5.
    Herbrich, R., Minka, T., Graepel, T.: TrueskillTM: A Bayesian skill rating system. In: NIPS, pp. 569–576 (2006)Google Scholar
  6. 6.
    Karlis, D., Ntzoufras, I.: Bayesian modelling of football outcomes: using the skellam’s distribution for the goal difference. IMA Journal of Management Mathematics 20(2), 133–145 (2009)MATHCrossRefGoogle Scholar
  7. 7.
    Kschischang, F.R., Frey, B.J., Loeliger, H.-A.: Factor graphs and the sum-product algorithm. IEEE Transactions on Information Theory 47(2), 498–519 (2001)MathSciNetMATHCrossRefGoogle Scholar
  8. 8.
    Minka, T.: Expectation propagation for approximate bayesian inference. In: UAI, pp. 362–369. Morgan Kaufmann (2001)Google Scholar
  9. 9.
    Moroney, M.J.: Facts from figures, 3rd edn. Penguin Press Science (1956)Google Scholar
  10. 10.
    Skellam, J.G.: The frequency distribution of the difference between two Poisson variates belonging to different populations. Journal of the Royal Statistical Society: Series A 109(3), 296 (1946)MathSciNetCrossRefGoogle Scholar
  11. 11.
    Glickman, M.E., Stern, H.S.: A state-space model for football league scores. Journal of the American Statistical Association 93(441), 25–35 (1998)MATHCrossRefGoogle Scholar
  12. 12.
    Beal, M.J., Ghahramani, Z.: The Variational Bayesian EM Algorithm for Incomplete Data: with Application to Scoring Graphical Model Structures. In: Proceedings of the Seventh Valencia International Meeting, pp. 453–464 (2002)Google Scholar
  13. 13.
    Karlis, D., Ntzoufras, I.: Bayesian modelling of football outcomes: using the Skellam’s distribution for the goal difference. IMA Journal of Management Mathematics 20(2), 133–145 (2009)MATHCrossRefGoogle Scholar
  14. 14.
    Karlis, D., Ntzoufras, I.: Analysis of Sports Data by Using Bivariate Poisson Models. Journal of the Royal Statistical Society: Series D 52(3), 381–393 (2003)MathSciNetCrossRefGoogle Scholar
  15. 15.
    Moroney, M.J.: Facts from figures, 3rd edn. Penguin Press Science (1956)Google Scholar
  16. 16.
    Dixon, M.J., Coles, S.G.: Modelling Association Football Scores and Inefficiencies in the Football Betting Market. Journal of the Royal Statistical Society: Series C 46(2), 265–280 (1997)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Shengbo Guo
    • 1
  • Scott Sanner
    • 2
  • Thore Graepel
    • 3
  • Wray Buntine
    • 2
  1. 1.Xerox Research Centre EuropeFrance
  2. 2.NICTA and the Australian National UniversityAustralia
  3. 3.Microsoft Research CambridgeUK

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