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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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## PowerPoint Slideshow about 'Rating Table Tennis Players' - richard_edik

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### Rating Table Tennis Players

An application of Bayesian inference

• The USATT rates all members

• A rating is an integer between 0 and 3000

Lee Bahlman 2045

Dell Sweeris 2080

Todd Sweeris

Lee Bahlman (2045)

Dell Sweeris (2080)

If Lee wins

Bahlman (2055)

Sweeris (2070)

If Dell wins

Bahlman (2038)

Sweeris (2087)

• Unrated Players

• Underrated or Overrated Players

• Rate unrated players

• Second Pass - Adjust Ratings

• The “fifty point change” rule

• Third Pass - Compute Final Ratings

• Using the table of points

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

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

Human Intervention Necessary

Manipulable

• USATT commissioned a study

• David Marcus (Ph.D., MIT, Statistics) developed a new method

• Under review by USATT

• May or may not be adopted

Based on three mathematical ideas

• Either player may win a match (probability)

• Ratings have some uncertainty (probability)

• Tournaments are data to update ratings (statistics)

• 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

• 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

Unrated Players 1400 (450)

Probability that Lee is rated 2050 and loses

Dell Rated 2000

Lee Rated 2050

Probability Lee loses if rated 2050 and Dell rated 2000

• 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