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## December 16, 2004

### Inflated Ratings

Last year, I wrote my ISU for Data Management on the "Statistical Analysis of Internet Chess" [SAIC]. I studied the correlation between the duration, the number of moves and rating deviation. Here is the bulk of my research:

The classic etime (expected length of the game) is measured by the formula **etime = time + (2/3)*inc**. This formula comes from standard (long) games which last for 40 moves (on average). Under the official rating system (**16 + D/25**), the standard deviation is around 350.

It was decided that blitz games should be rated the same way. This may be convenient, but from a statistical viewpoint, it is a disaster. This is because blitz games are 60 moves long (on average) and hence the classic etime formula does not apply. This results in a greater standard deviation - around 425. That means the ratings are more spread out: standard chess ratings are capped by 2800 - but blitz ratings go well above 3300.

So what if the ratings are inflated? In a perfect rating system, it is expected that when two players play a sufficiently long series of games, their ratings will be approximate their 'true strengths' (relative to the other players). Hence, rating is meant to be a fair game. But in blitz, there is no such balance. That means that some players are more profitable to play then others.

Posted by Oleg Ivrii at December 16, 2004 04:29 PM