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log5 : ウィキペディア英語版
log5
Log 5 is a formula invented by Bill James to estimate the probability that team A will win a game, based on the true winning percentage of Team A and Team B. It is equivalent to the Bradley-Terry-Luce model used for paired comparisons, the Elo rating system used in chess and the Rasch model used in the analysis of categorical data.
Let p_i be the fraction of games won by team i and also let q_i = 1-p_i be the fraction of games lost by team i. The Log5 estimate for the probability of A defeating B is p_ = \frac.
A few notable properties
*If p_A = 1, Log5 will always give A a 100% chance of victory
*If p_A = 0, Log5 will always give A a 0% chance of victory
*If p_A = p_B, Log5 will always return a 50% chance of victory for either side
*If p_A = 1/2, Log5 will give A a 1-p_B probability of victory.
It may also be conveniently rewritten using the odds ratio〔 as \frac} = \frac\times \frac.
Here as before q_=1-p_.
==References==



抄文引用元・出典: フリー百科事典『 ウィキペディア(Wikipedia)
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