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Tournament Performance Calculator and Methodology 2018-19

English Youth Grand Prix – Performance Calculator 2018-19

The tournament performance rating (TPR) is a common measure in international chess.  A tournament performance grade (TPG) is essentially a TPR calculation using FIDE ratings that correspond to ECF grades.  The conversion is made using the formula FIDE Rating = ECF Grade x 7.5 + 700.  This calculator may be used to predict your score in the English Youth Grand Prix; however, the official scores are calculated by the National Grading Team.

Performance Calculator’s Method

Definition: The TPR is the theoretical FIDE rating a person would need, such that their expected score based on that rating would match their actual score in the tournament.

The expected score is calculated using the FIDE Scoring Probability Table contained in Section 8.1 of the FIDE Rating Regulations effective from 1 July 2017. The probability of a win is calculated from the FIDE table, on an opponent-by-opponent basis, then added together to obtain the expected score for the tournament.

The method involves trying out various theoretical FIDE ratings, determining the expected tournament score using each rating, until one rating is found where the expected score matches the actual tournament score.

Example: Find the TPR of a player who scores 3.5/5, playing against opponents rated 1500, 1600, 1700, 1800 and 1900.

Start with an arbitrary theoretical FIDE rating of 1600. Using this value, the following expectancy values are obtained for each game.

 Theoretical FIDE rating Opponent Rating Rating difference Expectancy from FIDE table (Probability of a win) 1600 1500 100 0.64 1600 1600 0 0.50 1600 1700 -100 0.36 1600 1800 -200 0.24 1600 1900 -300 0.15 Expected Score: 1.89

The expected score based on a theoretical FIDE rating of 1600 is 1.89, which is less than the actual score of 3.5. The next trial is therefore conducted using a higher theoretical FIDE rating. A value of 1700 yields an expected score of 2.5; 1800 yields a value of 3.11. A theoretical FIDE rating of 1868 yields an expected score of 3.5, matching the actual score. The TPR is 1868.

This method is independent of the player’s own FIDE rating. It gives the true TPR even when one or more of the opponents are rated significantly greater or less than all the other opponents.

The TPG is calculated by converting all ECF grades into corresponding FIDE ratings using: FIDE Rating = ECF Grade x 7.5 + 700, and then applying the method described above. The calculated TPR is then converted into a TPG using: ECF Grade = (FIDE Rating – 700) / 7.5.

Perfect or zero scores

With this methodology, it is not possible to calculate a TPG for a 100% score, because no matter how high the theoretical FIDE rating is, the expected score is always less than 100%. Similarly, there is no theoretical TPG for a zero score.

The solution adopted in practice is to assume no TPG for a zero score and to calculate the TPG for a perfect score by making a notional deduction of 0.2 from the perfect score. This ensures that a TPG for a player with a perfect score is higher than the TPG for another player against the same opponents who does not achieve a perfect score.

If an opponent does not have an ECF grade (category A – E) but has a FIDE rating then their FIDE rating will be used in the calculation.

Results against opponents who do not have an ECF grade (category A – E) or a FIDE rating are ignored.

Minimum number of rounds against ECF graded or FIDE rated opponents

A minimum of four games against opponents with an ECF grade (category A – E) or a FIDE rating are required for a TPG to be calculated. This minimum number of games applies for each section played within a tournament.