Rating Table Tennis Players

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# Rating Table Tennis Players - PowerPoint PPT Presentation

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

An application of Bayesian inference

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

Lee Bahlman 2045

Dell Sweeris 2080

Todd Sweeris

Example

Lee Bahlman (2045)

Dell Sweeris (2080)

If Lee wins

Bahlman (2055)

Sweeris (2070)

If Dell wins

Bahlman (2038)

Sweeris (2087)

Complications
• Unrated Players
• Underrated or Overrated Players
Processing a Tournament
• Rate unrated players
• Second Pass - Adjust Ratings
• The “fifty point change” rule
• Third Pass - Compute Final Ratings
• Using the table of points
Problems

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

Problems

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

Human Intervention Necessary

Manipulable

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
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)
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
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
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

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