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BGonline.org Forums
PR of players and probability of winning (Question for those mathematically interested)
Posted By: Henrik Bukkjaer In Response To: PR of players and probability of winning (Question for those mathematically interested) (eXtreme Gammon)
Date: Monday, 5 December 2011, at 10:06 a.m.
The question however, is if things scale right in real life?
Eg. when dElo goes up, will the best player be able to realize his full advantage?
It will probably require him to adjust his game (thus dPR goes down). So at some point, the two (dElo and dPR) will not scale proportional anymore? Some of this can be eliminated if you measure "wrong double-pass", etc. as no-error on the inducing side, but for conservative passes and later doubles, this doesn't work - and especially not for "complex checkerplays" (made to steer into difficult positions, rather than races or more simple games).
Another thing is, if actual play will scale "correctly" with match length. The table you provide, may actually be more or less progressive in real life, between to particular players. Again, this will depend upon both players ability to see themselves as favorites or underdogs, and adjust their game accordingly.
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A funny observation from the numbers, time-wise short matches doesn't prove as useful in letting the stronger player win, as longer matches.
Eg. for a "best of 3" format to 5 points, in your example (6 PR diff), the player taking the worst of it, is at the same percentage as he is in a single 11 point match. Best of 3 to 5 takes a lot longer to play, than eon match to 11, yet the additional time played will not benefit the stronger player.
I've done some simulation on DBgF data, that arrive at the same conclusion, but then again - that was also based on our rating system, which is similar to the one described here (apart from a slightly different balance, in adjusting for long/short matches). /Henrik
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