Average Perfect Tournament Performance of Opponents

Average Perfect Tournament Performance of Opponents, abbreviated APPO, is an individual rating-based tie-break defined by FIDE, the International Chess Federation. A rating is a numerical estimate of competitive strength. APPO does not merely use each opponent's published rating. It uses a value calculated from what that opponent achieved in the tournament.

First, a Perfect Tournament Performance, or PTP, is calculated for every opponent. PTP is the lowest whole-number rating for which FIDE's scoring probabilities would give that player an expected score at least as high as the score actually achieved against the full field. A zero score has a special rule: PTP is set 800 points below the lowest-rated opponent.

The PTP values of opponents actually played over the board are then averaged, and the result is rounded to the nearest whole number with 0.5 rounded upward. The full rating-difference scale is used, without a 400-point cap on each comparison.

The word perfect does not mean the opponent made no mistakes, found engine-best moves, or scored 100 percent. It names a mathematical construction. APPO differs from ARO, which averages ratings, and APRO, which averages tournament performances calculated by another method.