# How to calculate FIDE's Perfect Tournament Performance (PTP)?

How to calculate FIDE's PTP?

The PTP is defined in https://handbook.fide.com/chapter/TieBreakRegulations042024 as:

This is a whole number corresponding to the lowest rating that a participant should have for their expected score to be greater than or equal to their tournament score. For a zero score, this number is set 800 points The expected score is the sum of the scoring probabilities which are defined in the FIDE Rating Regulations by the conversion table of rating differences into scoring probabilities.

Each rating difference is calculated by using the aforementioned lowest rating and the rating of each opponent faced by the participant during the tournament. The full rating scale is used in this conversion (i.e. no ±400 cut).

Since different ratings are discussed here, what is meant by the rating of each opponent faced by the participant during the tournament?

Is it:

1. the player's rating according to the actual FIDE Chess rating list,
2. or the Tournament Performance Rating as defined in chapter 10.2,
3. or recursively the Perfect Tournament Performance (PTP) rating itself?
• Words like "recursively" seem too advanced for FIDE but often come into national rating systems to make use of games agaist unrated players. Commented Jun 3 at 9:40

"The rating of each opponent" has to be the opponent's rating according to the actual FIDE rating list.

"Performance rating" isn't mentioned in 10.3, so if they had meant the performance rating they would have said so.

They aren't going to make a recursive tiebreaker, especially with no hints on how to start calculating it (you can't calculate your tiebreaker until you calculate your opponents' tiebreaker, but since you're one of their opponents you can't calculate theirs until you calculate yours.) And again, they would have said PTP if they had meant that.

As support for "they would have said so", take a look at the wording in 10.4 and 10.5, where they do say so:

10.4 Average [Tournament] Performance Rating of Opponents (APRO)
The average of the performances (TPR) of the opponents played over the board

10.5 Average Perfect [Tournament] Performance of Opponents (APPO)
The average of the perfect performances (PTP) of the opponents played over the board, rounded to the nearest whole number (0.5 rounded up).

Compare that to 10.1, which also uses "rating" but clearly isn't using TPR or PTP because they aren't even defined yet:

10.1 Average Rating of Opponents (ARO)
The average of the ratings of the opponents played over the board, rounded to the nearest whole number (0.5 rounded up).

So: "rating" is just the FIDE rating.