Elo math

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Elo math

Postby xinix » 05 Sep 2008, 08:07

Hi all,

although I'm not really mathematicly challenged, I'm can't really figure this one out. I'll first explain, then try to make sense.

At our chessclub, the children play in 4 (rising strength) groups (pawn,knight,rook,king) of about 16. I have wriiten new software to make the pairings, keep te scores etc, since the old program was written in DOS and hardly anybody could work with it.

Normally the children would only play outside their group, if it solves an odd amount in 2 groups.

I also calculate the rating for the children. What I do after every round, is calculate the winning chances for both players, look at the actual score, and add/substract the difference times 32. (k=32, as adviced by FIDE)

What happened with the old software was that the number 3 of the pawn group (lowest) could end up with the same rating as the number 3 of the knight group, while (mostly) you want them to end up with an elo of about the number 3 from the end of the knight group.

Questions:
Is this normal, or was the old program wrong ?
Is this solvable ?

IMO the problem is that the groups behave lindependent, and have too little relation to eachother.
One solution could be to lower the k-factor when someone reaches the toprating of his group. Anybody experience with that ? Is that mathematicly defendable ?

Cheers,

Tony
xinix
 
Posts: 22
Joined: 28 Aug 2008, 21:42

Re: Elo math

Postby Richard Pijl » 15 Sep 2008, 09:53

xinix wrote:I also calculate the rating for the children. What I do after every round, is calculate the winning chances for both players, look at the actual score, and add/substract the difference times 32. (k=32, as adviced by FIDE)

What happened with the old software was that the number 3 of the pawn group (lowest) could end up with the same rating as the number 3 of the knight group, while (mostly) you want them to end up with an elo of about the number 3 from the end of the knight group.

Questions:
Is this normal, or was the old program wrong ?
Is this solvable ?

IMO the problem is that the groups behave lindependent, and have too little relation to eachother.
One solution could be to lower the k-factor when someone reaches the toprating of his group. Anybody experience with that ? Is that mathematicly defendable ?

I suppose you started with a sufficient lower average rating in the lower groups.
You haven't said anything about the rating distribution other than that the top ratings are getting similar, but my guess is that the difference between the highest and lowest rating in the lower groups is larger than in the higher groups. I think this is quite normal. The core of the problem might be that a suitable rating interval for the lowest group is possibly -1000 - 500 while the next group has 500-1000, 1000-1250, 1250-1400 (just making up some numbers here). But giving negative ratings is not very encouraging to the players. So transposing to 1000-2500, 2500-3000, 3000-3250, 3250-3400 may be an idea.
Another thing I observed is that the ratings at the top and bottom of a closed group are almost always exaggerated. Lowering K based on the expected result (i.e. lower K when expected result is very high or very low) should reduce this effect a little, but probably does not remove it.
Another thing you could try is to use a lower K in groups where the difference between the highest and lowest ratings are the biggest, but the disadvantage is that these are probably also the groups where improvement of the players can be 50-100 Elo per week, so this is actually counterproductive.
Richard.
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Richard Pijl
 
Posts: 105
Joined: 26 Sep 2004, 21:09
Location: Minderhout, Belgium

Re: Elo math

Postby Dann Corbit » 15 Sep 2008, 21:02

xinix wrote:Hi all,

although I'm not really mathematicly challenged, I'm can't really figure this one out. I'll first explain, then try to make sense.

At our chessclub, the children play in 4 (rising strength) groups (pawn,knight,rook,king) of about 16. I have wriiten new software to make the pairings, keep te scores etc, since the old program was written in DOS and hardly anybody could work with it.

Normally the children would only play outside their group, if it solves an odd amount in 2 groups.

I also calculate the rating for the children. What I do after every round, is calculate the winning chances for both players, look at the actual score, and add/substract the difference times 32. (k=32, as adviced by FIDE)

What happened with the old software was that the number 3 of the pawn group (lowest) could end up with the same rating as the number 3 of the knight group, while (mostly) you want them to end up with an elo of about the number 3 from the end of the knight group.

Questions:
Is this normal, or was the old program wrong ?
Is this solvable ?

IMO the problem is that the groups behave lindependent, and have too little relation to eachother.
One solution could be to lower the k-factor when someone reaches the toprating of his group. Anybody experience with that ? Is that mathematicly defendable ?

Cheers,

Tony


There are lots of possibilities here. One possibility is that the one who gets a high rating really does have excellent ability. The most likely thing is that the number of games is too small for an accurate assessment.

Really, you won't know much at all until you have 32 games against the class of opponents in a rating pool, and if you have only a few games against people in another group, then one game can swing the results wildly.

For instance, suppose that you have five groups of players who have an average of 40 games played against the members within their own groups. Then, in a cross-pollination tournament, three members of a lower group play four games each against members of a higher group. If one of those in the lower group goes 4-0 what can we tell about it? Is this person a prodigy? Did they just have a good day? Did the opponent from the higher group have a bad day? We don't know. We do know that it will probably raise the Elo of the entire lower group, if we do not consider it provisionally.

I guess your question is really: "Is there a bug in the Elo calculation program?"

I don't think we have enough information to answer that question.
Dann Corbit
 


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