Sonas on ratings

[Roger de Coverly]

Here's the latest http://www.chessbase.com/newsdetail.asp?newsid=7114

We've seen the graphs before , Howard Grist waved them in front of us in justification of the re-base of the ECF system. I think Sonas is trying to say that the statistical distribution underlying the Elo formula doesn't properly reflect the reality of results. He's promising some material on K-factors as well.

So he's presenting ideas that the ECF grading team rejected in their calculation revamp.

So if the actual results don't reflect those predicted from the combination of the theory and previous ratings
does this mean?
(a) the ratings are wrong ( which is what the ECF grading team concluded)
(b) the underlying distribution isn't as assumed.

[E Michael White]

Its a common misconception that grades should allow accurate prediction of results or even map past performance closely.

To show one of the difficulties its only necessary to consider the effect of the different numbers of players in different bands. Eg. there are probably more players rated 140 - 145 than in the group 150-155, showing that In matches between these two groups the 150-155 players are more likely to have played multiple games. The result of a random new pairing will then be out of step with historic performance. A random new pairing assumes each player plays only one game so the wrong conditional probablilites are being used.

While this doesnt make much difference, maybe 1-2%, national grading systems have been rehashed for less !

[Brian Valentine]

Its a common misconception that grades should allow accurate prediction of results or even map past performance closely

While correct, I think that the fundamental problem is: precise current strength (aka rating, grade -even if performance could be summarised by one parameter) cannot be calculated from (a few) past results.

[Sean Hewitt]

Here's the latest http://www.chessbase.com/newsdetail.asp?newsid=7114

We've seen the graphs before , Howard Grist waved them in front of us in justification of the re-base of the ECF system. I think Sonas is trying to say that the statistical distribution underlying the Elo formula doesn't properly reflect the reality of results. He's promising some material on K-factors as well.

So he's presenting ideas that the ECF grading team rejected in their calculation revamp.

So if the actual results don't reflect those predicted from the combination of the theory and previous ratings
does this mean?
(a) the ratings are wrong ( which is what the ECF grading team concluded)
(b) the underlying distribution isn't as assumed.

Sonas's results (assuming them to be correct, and I have no reason to doubt his analysis) shows that the distribution for Elo ratings is wrong. This is perfectly possible and is fairly simple to correct.

However, given that ECF grades do not use Elo probability tables (ECF works on mean averages instead), this tells us nothing about the ECF grading system.

[Roger de Coverly]

However, given that ECF grades do not use Elo probability tables (ECF works on mean averages instead), this tells us nothing about the ECF grading system.

For most practical purposes the ECF method is a linear approximation to the Elo tables. A difference of 200 Elo points is 76% in Elo and a difference of 25 ECF points is 75% under the linear approximation. The methods diverge at the extremities. For example the 90% mark is 40 ECF points but 350 Elo ones.

In his earlier work for the USCF, Elo assumed a Normal distribution for his tables which was much less linear. 200 Points was 69% for example. This did cause ratings drift and was abandoned for the current assumed distribution. Does anyone recall when?

For performance measurements, the official Elo approach is to back solve for the rating that would have a theoretical performance equal to the actual. For calculations in the centre, where the performance is near 50%, the approach of adding up the Elo ratings, adding 400* excess of wins over losses and dividing by the game count gives similar results.

So I would relate the ECF method to the Elo method as follows
(a) calculate the performance over a rating period (of at least 30 games where possible) for each player using the linear approximation.
(b) use the performance in (a) as the start rating for the next period.

(a) is equivalent to the approach in Elo systems of calculating an initial rating over a minimum of 9 games.

The archives of magazines would have articles where Elo and Clarke compared their systems and noted their similarities.