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Pairing Two-Victor Tournaments

Introduction

This document describes how to pair the last round in a tournament in which two players are expected to share a victory of roughly equal value. This situation occurs in preliminary tournaments followed by a two-player playoff, and in qualifying tournaments for the WSC. It is a work in progress, and was last revised on 2003-09-03.

Terminology

KOTH
(King-Of-The-Hill) pairings which match each pair of players adjacent in the rankings
Swiss
pairings which match the top half of each win group against the bottom half, in corresponding order
Victor
a player who derives tangible benefit from performing well at the tournament
Winner
a player who wins a game
Win Group
the group of players who have the same number of wins

General Principles

Pairings are based on the following axiomatic principles:

  1. If possible, pair players so that a victor is guaranteed within a win group.
  2. Except where superseded by the above rule, do not remove a player from victory contention by denying them the opportunity to face a player that they need to defeat. If there is a set of players not all of whom can remain in contention, the highest ranked ones should remain in contention.
  3. What each player needs to do to become a victor should become progressively harder as one goes down the rankings.
  4. Do not allow players to engineer a tie to share victory.

Pairings

This section describes how to pair players depending on the "Games Behind" configuration. For example, a "Games Behind" configuration of 0/0/1/2 indicates that the top two players are tied on wins, the third player is one game behind the leaders, and the fourth player is two games behind the leaders.

0/0/0/0
1-4, 2-3. By GP1, all GB0s must be paired with each other. GP2 is overridden. GP3 is met, to the extent that players need to win, if more than two players win, and higher-ranked players have an a priori spread advantage; while if two players don't win, they need to be the highest-ranked tie, which directly favours higher-ranked players. #1 is favoured slightly by playing a theoretically weaker opponent. For more GB0s, pair top vs. bottom, e.g. 1-8, 2-7, 3-6, 4-5. If GB0s are odd, do as in case 0/0/0/1.
0/0/0/0.5
1-3, 2-4 GP1 is satisfied, as one GB0 victor is guaranteed. GP2 requires the top-ranked GB0.5 to be included in the pairings. GP3: #1 needs to win, or tie and have #2 win; #2 needs to win, or tie and have #1 tie; #3 and #4 need to win, period.
0/0/0/1
1-4, 2-3 if 1 has better cume than 4; otherwise, 1-3, 2-4. GP1 is satisfied, as one GB0 victor is guaranteed. GP2 requires the top-ranked GB1 to be paired with a GB0. GP3 (1-3, 2-4): #1 needs to win, or stay ahead of #3 and have #2 win; #2, #3 and #4 need to win, period. GP3 (1-4, 2-3): #1 needs to win, or keep above #4; #2 and #3 need to win, period; #4 needs to win, and beat everyone on spread.
0/0/0/1.5+
1-4, 2-3. GP1 is satisfied as per 0/0/0/1: two GB0 victors are guaranteed. GP2 does not apply. GP3: #1 needs to win, or stay ahead of #2 and #3 on cume; #2 and #3 need to win, or get ahead of #1.
0/0/0.5/0.5
1-4, 2-3. GP1 is satisfied, as one GB0 victor is guaranteed. GP2 is overridden. GP3: Every player needs to win. GP4: pairing 1-2, 3-4 would be in violation.
0/0/1
Swiss. GP1 is satisfied, as one GB0 victor is guaranteed. GP2 is overridden. GP3: #1 and #2 need to win, or stay ahead of the highest GB1 winner; any GB1 needs to win by enough to get ahead of the GB0 loser. GP4: pairing 1-2, 3-4 would be in violation.
0/0/2
Gibsonize GB0s, rest Swiss. GP1 works: both GB0s are victorious. GP2 does not apply. GP3: GB0s don't have to do anything.
0/0.5/0.5/0.5
1-4, 2-3
0/0.5/0.5/1
1-4, 2-3 if 1 has better cume than 4; otherwise, 1-3, 2-4.
0/0.5/1/1
#1 plays GB1 with lowest cume.
0/0.5/1/1.5+
Gibsonize #1, 2-.3
0/0.5/1.5+
Gibsonize #1, 2-3.
0/0.5/2
Gibsonize #1 and #2.
0/1/1/1.5+
Gibsonize #1, rest Swiss. GP1 is okay: we have a GB1 victor. GP2 does not apply. GP3: GB0 doesn't have to do anything, GB1s have to win.
0/1/1.5+
Gibsonize GB0, GB1 plays lowest GB2, rest Swiss.
GP1 works: we have a GB0 victor. GP2 does not apply. GP3: GB0 doesn't need to do anything, GB1 needs to win or stay ahead of all GB1.5s; GB1.5s need GB1 to lose, and need to win big.
0/1.5+
Gibsonize GB0, rest Swiss.
GP1: guaranteed GB0 and GB2 victors. GP2 does not apply. GP3: GB0 does not need to do anything; GB2s need to win and end up with best spread.