So far the Pairing Tiebreaker works especially in Swiss tournaments with the same number of players in all rounds and all players playing all rounds. The Pairing Tiebreaker is a tiebreaker for the final placement order after the last round. It presumes that during each round - except for the pairing-related trivial first two rounds - a placement order was given for pairing purposes by means of criteria, of which some may be tiebreakers themselves (example: 1) Number of Wins Score 2) SOS).
A player's value is calculated as a sum over all rounds. However, rounds with trivial pairing decisions are ignored. In a Swiss depending on SOS, these are the first two rounds, where are players have the same trivial SOS values.
A player's Pairing Tiebreaker depends on (here defined as in the example)
group size := the size of the score group the player's opponent is in
group place := place of the opponent in his points group by points - SOS, so that all places with equal points - SOS get the first number of these places
Hence, within each points group, counting places starts from 1. The opponent(s) with the top SOS in their points group have place 1 in it, etc. When opponents tie their place on points - SOS, then each of them is identified with their smallest relative place number.
(If one is more interested in bottom players, one might define group places differently by starting from a point group's bottom.)
This is the definition of the player's Pairing Tiebreaker:
V := sum [all rounds] ( normalized round confidence * group size / group place ) = sum [all rounds] ( round number * group size / group place )
Since different rounds have different degrees of confidence, this is also considered: by the normalized round confidence. Due to a constant player number in all rounds, normalization is easily defined as follows:
normalized round confidence := number of players / average group size = round number
As it turns out, the round number describes a normalized round's confidence. The equation explains why it does make sense: The average of all points group sizes contains the number of players as a value. Since V is calculated at a round's beginning(!) (recall: we are considering the quality of the pairing), there are exactly as many points groups as the number of rounds R: from (R-1) to 0. (Even if some of them have the size 0, they exist.)
The Pairing Tiebreaker was invented by RobertJasiek, who also suggests an application for a measurement of the tournament's pairing quality.
It has been suggested that also further alternative tournament pairing methods should be invented. Apart from minor variants of the Pairing Tiebreaker definition, other measurements of how well every single player has been paired have not been suggested yet, havn't they?