Rating Table Tennis Players - PowerPoint PPT Presentation

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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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Rating table tennis players l.jpg

Rating Table Tennis Players

An application of Bayesian inference


Ratings l.jpg

Ratings

  • The USATT rates all members

  • A rating is an integer between 0 and 3000


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Fan Yi Yong 2774


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Example

Lee Bahlman 2045

Dell Sweeris 2080

Todd Sweeris


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Old System


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Example

Lee Bahlman (2045)

Dell Sweeris (2080)

If Lee wins

Bahlman (2055)

Sweeris (2070)

If Dell wins

Bahlman (2038)

Sweeris (2087)


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Complications

  • Unrated Players

  • Underrated or Overrated Players


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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


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Problems

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


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Problems

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

Human Intervention Necessary

Manipulable


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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


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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)


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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


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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


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Unrated Players


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Unrated Players 1400 (450)


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Rating Change with Time


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Updating Ratings


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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


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Lee’s Rating


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Dell’s Rating


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Bayes’ Theorem


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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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