how to convert match score to ELO difference

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jack512
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how to convert match score to ELO difference

Post by jack512 » Fri Mar 10, 2017 3:46 am

Can somebody point me to a reference showing how to convert match scores into ELO differences? E.g. if A and B play a thousand games, and A's win-loss-draw is 250-200-550, what ELO difference between A and B does that indicate?

Vinvin
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Re: how to convert match score to ELO difference

Post by Vinvin » Fri Mar 10, 2017 4:51 am

jack512 wrote:Can somebody point me to a reference showing how to convert match scores into ELO differences? E.g. if A and B play a thousand games, and A's win-loss-draw is 250-200-550, what ELO difference between A and B does that indicate?
Here's a table : http://www.pradu.us/old/Nov27_2008/Buzz/elotable.html
And a formula : https://en.wikipedia.org/wiki/Elo_ratin ... nce_rating

(250-200)/1000*400 = +20 -> Performance of A is 20 Elo over B.
Last edited by Vinvin on Fri Mar 10, 2017 4:56 am, edited 1 time in total.

Dann Corbit
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Re: how to convert match score to ELO difference

Post by Dann Corbit » Fri Mar 10, 2017 4:55 am

http://www.3dkingdoms.com/chess/elo.htm

If you right click on the page and show page source, you can see the underlying code that calculates it.

It gives +17 Elo difference for your 250:200:550 sample
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Ajedrecista
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Re: How to convert match score to Elo difference?

Post by Ajedrecista » Fri Mar 10, 2017 5:02 pm

Hello John:
jack512 wrote:Can somebody point me to a reference showing how to convert match scores into ELO differences? E.g. if A and B play a thousand games, and A's win-loss-draw is 250-200-550, what ELO difference between A and B does that indicate?
I would use the standard formula, already pointed by Dann. I will explain it a little more:

Code: Select all

games = wins + draws + loses
points = wins + draws/2

(Elo difference) = 400*log10[points/(games - points)]

It is valid when 0 < points < games
You can also use the ratio points/games:

Code: Select all

µ = points/games

&#40;Elo difference&#41; = 400*log10&#91;µ/&#40;1 - µ&#41;&#93;

0 < µ < 1 as above

&#40;Elo difference&#41; = &#91;400/ln&#40;10&#41;&#93;*ln&#91;µ/&#40;1 - µ&#41;&#93; = &#91;400/ln&#40;10&#41;&#93;*logit&#40;µ&#41;
&#40;Elo difference&#41; ~ 173.7178*logit&#40;µ&#41;
Just to have a general idea, you can see an image of logit function here:

Image

Then imagine that the horizontal axis is µ and the Elo difference is more less the vertical axis of that image multiplied by 173.7.

------------------------

In your example:

Code: Select all

games = 250 + 550 + 200 = 1000
points = 250 + 550/2 = 250 + 275 = 525

&#40;Elo difference&#41; = 400*log10&#91;525/&#40;1000 - 525&#41;&#93; = 400*log10&#40;525/475&#41; ~ 17.39 Elo
Regards from Spain.

Ajedrecista.

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