Scoring probability

A rating is a number intended to estimate a player's competitive strength. Scoring probability, identified as PD in the FIDE regulations, converts the difference between two ratings into an expected score. It does not predict one particular game. It summarizes what the system expects across many comparable games, counting 1 point for a win, 0.5 for a draw and 0 for a loss.

When the ratings are almost equal, the table gives each player about 0.50. For a difference of 92 to 98 points, it gives 0.63 to the higher-rated player and 0.37 to the lower-rated player. The two values add to 1 because they describe how the single available point is expected to be divided on average.

To update a rating, PD is subtracted from the actual score in each game. Beating the expectation produces a positive amount; falling short produces a negative one. The total for the rating period is then multiplied by a development coefficient called K, which controls how quickly the rating can move. The same expected-score idea also supports calculations such as Perfect Tournament Performance.