
BGonline.org Forums
Linearity
Posted By: Rich Munitz
Date: Thursday, 13 May 2010, at 11:46 p.m.
In Response To: Linearity (Chuck Bower)
The ratio comes from the XG help file. XG does convert roughly linearly between Elo and PR.
However, the XG help does indicate that it is not actually linear because poor performance changes it.
Here is the actual quote from XG help:
" Actually the Elo formula is more complex in order to take into account very bad performance and also performance when you outplay the computer.
The actual formula is result := 1/(1+exp(performance*401.12))*2000+732 "
Perhaps Xavier can explain how he arrived at this formula.
I imagine that it should be possible to derive the relationship experimentally by playing bots of various levels of diminished skill against one another. The Elo difference will emerge based on the actual win/loss ratio, and the difference in error rate can be determined by analysis of the matches played. Clearly such bots do not attempt to consider their relative skill into the equation when making their choices. But presumably a human who does this effectively will win more and have a higher Elo as a result, but also presumably if these calculated "errors" are generating more wins, they should be compensated for with increased actual errors by the opponent producing more losses. In the end, it is the ER difference between the players that we wish to compare with an Elo difference. The absolute numbers should not matter so much.

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