user13565: 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.

user15068: 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 

user12255: 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. 

13565: <p>On <a href="http://chess.kivij.info/performance_calculator.shtml" rel="nofollow noreferrer">this website</a>, I came across three ways of calculating performance rating:</p>

<ul>
<li><p><strong>Performance rating (the proper method)</strong></p></li>
<li><p><strong>Performance rating (FIDE)</strong></p></li>
<li><p><strong>Performance rating (Linear approximation)</strong></p></li>
</ul>

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

<p>Does it use some iterative algorithm? If so, what is it?</p>

<p>I'd be glad for the details of the method involved.</p>
 15068: <p>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 </p>
 12255: <p>The ELO rating is based on the assumption that the expected score of a player A against an opponent B is:</p>

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

<p>where R_B and R_A are the ratings of B and A, respectively. </p>

<p>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.]</p>

<p>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. </p>

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

<p>To get a definite answer you might need to contact the maintainer of the site. </p>
