1. Calculating true performance ratings

Your true performance rating (TPR) is the rating at which your expected score against the field met equals your actual score, ie if that was your start rating you would neither gain nor lose points from the event.

Is there a simple way of determining TPR, even in the ELO system, to within say 20 points (or an online calculator that will do it)? Working out performance ratings by the common batched game method leads to inaccurate results if you have a few outliers skewing the ratings. For instance, I'll quite often play an event in which I play an 1100 in round 1 and nobody weaker than 1500 for the rest of the event. Where games are batched and I look up my %age on a lookup table, the outlier drags the average down so far that my crude PR is higher with the win against the outlier dropped.

Apologies if this has been covered before.

2. The solution is Ra in the following equation:

Ea=sum(i=1..n)(1/(1+10^((Rbi-Ra)/400)))

Where Ea is the score achieved, n is the number of games and Rb1, Rb2, ... Rbn are the ratings of the n opponents.

I don't think there is a simple analytical solution. On the other hand, a numerical solution is easy, since Ea is monotonic in Ra. Bisection can probably get you and answer in a few milliseconds.

Hmm... Maybe I will do a calculator in PHP.

3. Originally Posted by pax
Hmm... Maybe I will do a calculator in PHP.

4. Noting the definition, or interpretation of the definition:
Originally Posted by Kevin Bonham
ie if that was your start rating you would neither gain nor lose points from the event.
the TPR would depend on the rating system; TPR(Glicko) and TPR(Elo) are different from each other and from TPRs under other rating systems.

If you are using a rating system that you can easily model in Excel (such as standard Elo) you can use the Goal Seek function to find the starting rating which generates a zero adjustment.

5. Try this:

http://www.paxmans.net/performance_calc.php

Test it out, let me know if there are any bugs. I can include Glicko as well, if people think that would be useful.

6. Originally Posted by Ian Rout
Noting the definition, or interpretation of the definition: the TPR would depend on the rating system; TPR(Glicko) and TPR(Elo) are different from each other and from TPRs under other rating systems.
Yes, this is true, especially under Glicko if you are playing opponents with a wide variation in rating reliability. I am not sure how different Glicko and ELO would be as a result of this in any given case.

Originally Posted by pax
Try this:

http://www.paxmans.net/performance_calc.php

Test it out, let me know if there are any bugs. I can include Glicko as well, if people think that would be useful.
Excellent! Thanks very much for that. Bill sent me an Excel file that works the same way, but with a small amount of manual trial and error to get the final result. I entered my results vs rated opponents in the current HICC Club Champs thus far and got the same figure (2052) in Bill's file and your php link.

One trivial bug found: it accepts negative scores (however a PR of zero is returned in such cases).

7. Originally Posted by Kevin Bonham
One trivial bug found: it accepts negative scores (however a PR of zero is returned in such cases).
Ta. Will fix that.

8. Originally Posted by pax
Try this:

http://www.paxmans.net/performance_calc.php

Test it out, let me know if there are any bugs. I can include Glicko as well, if people think that would be useful.
I tried it, It's quite good. However, it does not account for 350 rule correctly.
Indeed, after I entered the result and got TPR, I bumped ratings of my opponent to TPR-350 and recalculated. TPR should've stayed the same, but it actually went up.

9. Originally Posted by Igor_Goldenberg
I tried it, It's quite good. However, it does not account for 350 rule correctly.
Indeed, after I entered the result and got TPR, I bumped ratings of my opponent to TPR-350 and recalculated. TPR should've stayed the same, but it actually went up.
When calculating true performance ratings there is absolutely no need to use a 350 rule or in fact any sort of xxx rule.

10. Originally Posted by Bill Gletsos
When calculating true performance ratings there is absolutely no need to use a 350 rule or in fact any sort of xxx rule.
TPR is the rating at which you would not lose/gain rating points. Loss/gain of points depend on 350 rule.

11. Originally Posted by Igor_Goldenberg
TPR is the rating at which you would not lose/gain rating points.
Incorrect.
Originally Posted by Igor_Goldenberg
Loss/gain of points depend on 350 rule.
FIDE use a 350 point rule in calculating rating changes but that isnt the same as calculating what a true performance rating is.

FIDE dont even use a 350 rule in calculation of performance ratings in norms.

However even then we are not talking about the flawed method by which FIDE calculate performance ratings where they average the rating of your opponents as part of the calculation.

A true performance rating is the rating at which your expected score equals your actual score. When determining TPR's 350 rules and any other such xxx rules have no place in the calculations and are totally meaningless and in fact distort results.

e.g. a player 2800 plays a 2800 and a 1400 and he scores 0.5 and 1.0 respectively.

His true performance rating is 2800.
His performance using a 350 rule is 2877 which is totally incorrect.
His performance rating using averaging is 2291 which is also totally incorrect.

12. What Bill said

13. Originally Posted by Bill Gletsos
e.g. a player 2800 plays a 2800 and a 1400 and he scores 0.5 and 1.0 respectively.

His true performance rating is 2800.
His performance using a 350 rule is 2877 which is totally incorrect.
His performance rating using averaging is 2291 which is also totally incorrect.
Bill is the nicest person on the bb. How come all these ... complaining all the time??

14. Originally Posted by pax
What Bill said
Agree

15. pax's site is down at the moment.