## how to convert match score to ELO difference

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jack512
Posts: 19
Joined: Sat Nov 14, 2015 3:29 pm

### how to convert match score to ELO difference

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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Joined: Thu Mar 09, 2006 8:40 am
Full name: Vincent Lejeune

### Re: how to convert match score to ELO difference

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?
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

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?

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

&#40;Elo difference&#41; = 400*log10&#91;points/&#40;games - points&#41;&#93;

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:

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.

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``````games = 250 + 550 + 200 = 1000