# Performance Pairings

## Motivation

Performance Pairings are used by WGVC at some large events in an attempt to generate effective 'computer-assisted' pairings by giving the director access to a large number of parameters which can be adjusted according to the circumstances of each round. This document describes an overall pairing strategy which would use Performance Pairings at the end of the event. Gibsonization doesn't effect this strategy except that it eliminates consideration of "1st Place Contenders."

### Initial Pairings

The initial pairings are either a fixed number (typically 3 but possibly more) of "InitFontes" pairings (a set of round robins among groups of four chosen from different strata of the division) or a complete round robin, depending on the size of the division and number of rounds.

### Swiss Pairings

At the completion of the Initial Pairings or one round prior (depending on session breaks), Swiss Pairings are applied. These continue only as long as 'reasonable' Swiss groups can be maintained without introducing repeats.

Swiss pairings will be omitted if the event opens with one or more complete round robins.

### Performance Pairings

Once Swiss Pairings become infeasible, Performance Pairings are applied based on dividing the division into three groups, each of which is paired independently.

#### 1st Place Contenders

1st place contenders are defined as those players who are no more than N/2 games behind the division leader, where N is the number of rounds left to play at the time pairings are being determined. For example, after round 18 of a 24-game event with the division leader having a record of 12-6, players with (12 - (24 -18) / 2 ) = 9 or more wins are considered 1st place contenders.

This reckoning may be adjusted if the bottom such players have large negative spreads.

#### Money Contenders

Among players who are not 1st place contenders, those in contention for place prizes are defined as those who are no more than N/2 games behind the player in Xth position, where X is the number of place prizes being awarded. For example, if in round 18 of a 24-game event with 5 place prizes being awarded the player in 5th place has a record of 10-8, players with (10 - (24 - 18) / 2 ) = 7 or more wins who are not being treated as 1st place contenders are considered "Money Contenders".

Again, the group size may be reduced as for 1st place contenders.

#### Non-Contenders

Non-contenders are the players remaining after 1st place and Money Contenders are accounted for. Pairings among non-contenders will always be chosen so as to minimize the total number of repeats regardless of record. Class prizes are not taken into consideration.

In cases where strict application of the "Money Contenders" formula would include a small or empty set of non-contenders, some players from the bottom ranks of the money contenders may be selected as non-contenders.

#### Contender Pairings

For each of the two groups of contenders, the first consideration in pairing is to match players who have not played each other as often as the maximum number of prior repeat pairings among the group. This consideration may be discounted if it distorts the overall pairings for the group.

Once the matchup history is accounted for, factor pairing is applied to pair players who are N (number of remaining games) apart in rank. This may not be possible if the group is small.

#### Final Round

Final round pairings will probably be King Of the Hill for contenders except in unusual circumstances. Non-contenders will be paired so as to minimize repeats.

#### Notes

See also Assigned Firsts And Seconds.