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PR of players and probability of winning (Question for those mathematically interested)

Posted By: eXtreme Gammon
Date: Thursday, 1 December 2011, at 2:39 p.m.

In Response To: PR of players and probability of winning (Question for those mathematically interested) (Max Levenstein)


The formula used in all bg program is the one than Larry Kaufman created. The formula is

  • P=1/(1+10^(dElo/2000*sqrt(N)))

    Where

  • P is the probability of player 1 to win
  • dElo is Elo2-Elo1
  • N is the match length

    For instance if a player is playing someone 200 Elo point stronger in a 3 point match P =
    1/(1+POWER(10,200/2000*SQRT(3)))=40.16%

    Jake Jacobs mentioned that the formula was designed so that a 400 difference meant that the stronger player will win 10 out of 11 25 point matches

    The relation between Elo and PR has been discussed on Bgonline. My own experiments and the general consensus is that Elo=Constant-33*PR where the constant depend on the site. That means that dElo=33*dPR (independent of the site)

    (for Snowie ER dElo=31.5*dER)


    We can rewrite the probability formula as
    P=1/(1+10^(dPR*33/2000*sqrt(N)))

    For a player playing someone 6 PR stronger (delo=198) here is the winning chances per match length

     ML        chances
     

     1        44% 

     3        40% 

     5        38% 

     11       32% 

     25       24%


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