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ELO

Posted By: Bob Koca
Date: Wednesday, 16 December 2009, at 8:16 p.m.

In Response To: ELO (Rich Munitz)

"a 1700 player might at any moment in time have an Elo rating between say 1600 and 1800. But on average, players will be above their true rating as often as they will be below and with enough of a sample, this should balance out"

I think that the higher rated someone is the more likely it is that they are overrated. As Rich points out the ratings vary. Think of the top rated player for example. Is it more likely that he is underrated and is even more dominant than the ratings suggest or that he is underrated and perhaps the one of the 5 or so best players who just happened to have a recent lucky streak? This effect leads me to think that matches with a ratings diff of 200 will on average be slightly less than 200 true difference.

Even if the balancing out works there is still a tiny problem in that the ratings formula is not linear. Thus, the ELO differences being correct on average does not mean the formula is correct on average. Calculations indicate this is probably not big enough to worry about though. For example the average favorite win chance for a 100 diff and a 300 diff is only about .15% less than the favorite win chance for a 200 ratings diff.

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