# "Variance" of Elo rating

What is the quantitative predictive value of Elo rating for tournament performances? (Or, same, what is the natural strength variabitity of an average player, measured in Elo?)

A quantitative version, so to say, of this question, but the answers are unsuitable, although #3 points in the right direction.

The question has some practical value: assume you get 4.0 points where your Elo predicted 3.0 (D=H-E=+1.0) - are these to read as, on some arbitrary confidence level, rather as 3.0 ± 2.0 (you were just lucky) or 3.0 ± 0.5 (you played good)?

First of all, the Elo rating is a snapshot in time, averaged out a bit by past tournaments, and essentially assumed to be a constant measure of strength. We thus should expect that juniors and seniors in average have larger differences D.

Let's look at a (somewhat) random tournament (pre-Corona by suggestion of Brian), German championship 2015, and observe the last column, which measures the difference D of predicted and actual performance. Mean is ~0 (duh), standard deviation s=~13, interval [-32,+21]. I've seen many such columns and it looks pretty "normal" to me.

Thus two natural questions:

1. How large is s for an "average" tournament? (I.e. pick a large number of random tournaments, compute s for each, compute the average of that.) My own estimate is around 20.
2. Of course there are no "average" tournaments anyway - for example, I expect that s will be far higher in a lower Elo tier. Is that correct?
• Are you asking for a confidence or a prediction interval (not the same)? What you provide as an example is not a "variance" mathematically. Aug 1, 2022 at 20:18