“Log5”的意思、由来-开放百科全书

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Log5

释义

References

Log 5 is a formula invented by Bill James^[1] 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.^[2]

Let be the fraction of games won by team and also let be the fraction of games lost by team .

The Log5 estimate for the probability of A defeating B is .

A few notable properties exist:

If , Log5 will always give A a 100% chance of victory.
If , Log5 will always give A a 0% chance of victory.
If , Log5 will always return a 50% chance of victory for either team.
If , Log5 will give A a probability of victory.

It may also be conveniently rewritten using the odds ratio^[2] as

Here as before .

References

1. ^{{cite news|title=Chancesis: The Origins of Log5 |url=http://www.chancesis.com/2010/10/03/the-origins-of-log5/ |accessdate=2013-03-07 |deadurl=yes |archiveurl=https://web.archive.org/web/20120412130735/http://www.chancesis.com/2010/10/03/the-origins-of-log5/ |archivedate=April 12, 2012 }}
2. ^¹{{cite news|title=Baseball, Chess, Psychology and Pychometrics: Everyone Uses the Same Damn Rating System|url=http://angrystatistician.blogspot.com/2013/03/baseball-chess-psychology-and.html|accessdate=2013-12-29}}

4 : Bill James|Baseball terminology|Baseball statistics|Sports records and statistics

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