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Rating Table Tennis Players

Rating Table Tennis Players. An application of Bayesian inference. Ratings. The USATT rates all members A rating is an integer between 0 and 3000. Fan Yi Yong 2774. Example. Lee Bahlman 2045 Dell Sweeris 2080. Todd Sweeris. Old System. Example. Lee Bahlman (2045)

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Rating Table Tennis Players

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  1. Rating Table Tennis Players An application of Bayesian inference

  2. Ratings • The USATT rates all members • A rating is an integer between 0 and 3000

  3. Fan Yi Yong 2774

  4. Example Lee Bahlman 2045 Dell Sweeris 2080 Todd Sweeris

  5. Old System

  6. Example Lee Bahlman (2045) Dell Sweeris (2080) If Lee wins Bahlman (2055) Sweeris (2070) If Dell wins Bahlman (2038) Sweeris (2087)

  7. Complications • Unrated Players • Underrated or Overrated Players

  8. Processing a Tournament • First Pass - Assign Initial Ratings • Rate unrated players • Second Pass - Adjust Ratings • The “fifty point change” rule • Third Pass - Compute Final Ratings • Using the table of points

  9. Problems Arbitrary Numbers (table of points, fifty-point rule)

  10. Problems Arbitrary Numbers (table of points, fifty-point rule) Human Intervention Necessary Manipulable

  11. A New Rating System? • USATT commissioned a study • David Marcus (Ph.D., MIT, Statistics) developed a new method • Under review by USATT • May or may not be adopted

  12. Proposed New Method Based on three mathematical ideas • Either player may win a match (probability) • Ratings have some uncertainty (probability) • Tournaments are data to update ratings (statistics)

  13. What is a rating? • Classical statistical model – • a rating is a parameter that is possibly unknown • We need to estimate the parameter • Bayesian model - • our uncertainty about the parameter is reflected in a probability distribution, the probability is subjective probability

  14. What is a rating? • A rating is a probability distribution • The distributions used are discrete versions of the normal distribution • The mass function is nonzero on ratings 0, 10, 20, … , 3590, 3600

  15. Unrated Players

  16. Unrated Players 1400 (450)

  17. Rating Change with Time

  18. Updating Ratings

  19. Example Probability that Lee is rated 2050 and loses Dell Rated 2000 Lee Rated 2050 Probability Lee loses if rated 2050 and Dell rated 2000

  20. Lee’s Rating

  21. Dell’s Rating

  22. Bayes’ Theorem

  23. Updating Ratings • Each player has an initial rating • The results of the tournament are the data • Bayes Theorem is used to update the ratings • Computationally intense - hundreds of players and hundreds of possible ratings per player

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