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Performance calculator
Score:
Ratings of the opponents:
Result:
Average rating of the opponents:
Performance rating:
Performance rating (FIDE):
Performance rating (linear):
Instructions
Score
: Here you are expected to type the points gathered. For example, both 1.5 and 1½ should work.
Ratings of the opponents
: Here you should give the ratings of the opponents, separated by spaces.
Calculate
: After completing the previous steps you click this and, assuming you have JavaScript enabled, the results should be shown.
Result
: Player's score and number of games separated by a slash. It's worth checking that this corresponds to your idea of the result. For example, ratings with five digits are simply ignored without any warnings.
Average rating of the opponents
: This is, indeed, the average rating of the opponents.
Performance rating
: Performance rating calculated in a proper fashion, i.e. by finding such a rating that the expected score equals to the actual score. Such a performance rating is used e.g. on this site.
Performance rating (FIDE)
: Performance rating as calculated by FIDE, that is by adding a rating difference based on the percentage score to the average rating of the opponents. Among other things, this is used in calculation of title norms.
Performance rating (linear)
: Performance rating calculated by the linear approximation: average rating of the opponents + 8 * (percentage score - 50). This has been fairly popular in Finland.
As far as I can see, the reason the latter two formulas are used is the ease of calculation. The first one practically requires a computer, the second one is manageable with a calculator and a printout of the rating difference table, and the third one doesn't even need the table. FIDE performances are usually fairly close to the proper ones when the dispersion of opponents' ratings is small. However, the FIDE formula doesn't handle outliers well and a win against a weak opponent may very well even decrease the FIDE performance. The linear formula is near to the FIDE formula when the score is close enough to 50%.
When a player wins or loses all the games, performance rating is undefined. FIDE has solved this by choosing somewhat arbitrarily 800 points as the rating difference of an extreme result, whereas the linear formula gives 400 points. In these cases it would be pretty much equally justifiable to declare any other sufficiently high number as the performance rating. The performance of a maximal score is definitely higher than the performance when half a point has been lost, but that's it.
Juha Kivijärvi