Log5 - Alchetron, The Free Social Encyclopedia

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 A , B = p A − p A × p B p A + p B − 2 × p A × p B .

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 p A , B q A , B = p A q A × q B p B .

Here as before q A , B = 1 − p A , B .

References

Log5 Wikipedia

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