# How is this kind of performance rating calculated?

On this website, I came across three ways of calculating performance rating:

• Performance rating (the proper method)

• Performance rating (FIDE)

• Performance rating (Linear approximation)

I'm familiar with the last two methods, but I was wondering how the first kind of PR is calculated.

Does it use some iterative algorithm? If so, what is it?

I'd be glad for the details of the method involved.

• Why was this question downvoted? Let me know if there is something to be fixed! Dec 26, 2017 at 8:03
• Proper method is meaningless. There are many rating methods with different levels of accuracy for various purposes. Do not know any that call their method linear approximation. Jan 18, 2020 at 0:03

The ELO rating is based on the assumption that the expected score of a player A against an opponent B is:

E_A = 1/ (1 + 10^((R_B - R_A)/400))

where R_B and R_A are the ratings of B and A, respectively.

Now, what could be done is that based on the data you give a rating average is computed and the score (per game) that was obtained is computed, this is plugged in for E_A and R_B, respectively. Then, one solves for R_A. [Given that only the global score is entered, whatever is done should be based on the average.]

In other words the hypothetical rating is computed that would yield an expected score matching the actual score obtained. This is how I would interpret the description on the site.

This does however not match what the site does or there are numerical errors.
Maybe they use a different formula for the expected score.

To get a definite answer you might need to contact the maintainer of the site.

• Thanks, I've accepted your answer. I guess it's best to verify with the maintainer of the site as well. Dec 30, 2017 at 17:40

Well, in many cases FIDE and the 'proper' performance are pretty close to each other or the same. But fide performance is an approximation to a strict mathematical performance. In this case the 'proper' refers to a strict mathematical definition of performance. You can typically see the big differences in some special cases. For instance try to input 1 in the score and 2000 in the rating field. Essentially you have an infinite high performance, since your score is 100% and the calculator also shows infinity. Now Fide has a cut off in cases like this and you will see the performance as 2800. To be honest in cases where somebody scores 100 %, it's in my opinion a bit meningless to calculate performance. There are also a few other areas where the two methods differ a lot , try to input 0 and 2000 and in a strict mathematical since your performance is negative infinity. There are various ways to calculate the mathematical performance, when it's different than 0 or 100%, iterative being one way, but I believe there are other ways to do it

• If you type in 3.5 against 6 opponents with 2000 rating they give 2060, 2057, 2067 respectively.
– quid
Dec 25, 2017 at 19:37
• Yes, because Fide is an approximation and not a true mathematical performance rating Dec 25, 2017 at 19:39
• What is the meaning of your first sentence then. Clearly they are not the same in most cases.
– quid
Dec 25, 2017 at 19:40
• I have rephrased it Dec 25, 2017 at 19:43
• Proper rating is not well defined. All ratings are approximations of past performance. Future performance is not guaranteed as the ad says. Jan 18, 2020 at 0:05