how to convert match score to ELO difference
Moderators: bob, hgm, Harvey Williamson
Forum rules
This textbox is used to restore diagrams posted with the [d] tag before the upgrade.
This textbox is used to restore diagrams posted with the [d] tag before the upgrade.
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 winlossdraw is 250200550, what ELO difference between A and B does that indicate?
Re: how to convert match score to ELO difference
Here's a table : http://www.pradu.us/old/Nov27_2008/Buzz/elotable.htmljack512 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 winlossdraw is 250200550, what ELO difference between A and B does that indicate?
And a formula : https://en.wikipedia.org/wiki/Elo_ratin ... nce_rating
(250200)/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.

 Posts: 10243
 Joined: Wed Mar 08, 2006 7:57 pm
 Location: Redmond, WA USA
 Contact:
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
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
Taking ideas is not a vice, it is a virtue. We have another word for this. It is called learning.
But sharing ideas is an even greater virtue. We have another word for this. It is called teaching.
But sharing ideas is an even greater virtue. We have another word for this. It is called teaching.
 Ajedrecista
 Posts: 1405
 Joined: Wed Jul 13, 2011 7:04 pm
 Location: Madrid, Spain.
 Contact:
Re: How to convert match score to Elo difference?
Hello John:
You can also use the ratio points/games:
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.

In your example:
Regards from Spain.
Ajedrecista.
I would use the standard formula, already pointed by Dann. I will explain it a little more: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 winlossdraw is 250200550, what ELO difference between A and B does that indicate?
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
Code: Select all
µ = points/games
(Elo difference) = 400*log10[µ/(1  µ)]
0 < µ < 1 as above
(Elo difference) = [400/ln(10)]*ln[µ/(1  µ)] = [400/ln(10)]*logit(µ)
(Elo difference) ~ 173.7178*logit(µ)
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
(Elo difference) = 400*log10[525/(1000  525)] = 400*log10(525/475) ~ 17.39 Elo
Ajedrecista.