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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:
- If possible, pair players so that a victor is guaranteed within a win group.
- Except where superseded by the above rule, do not remove a player from victory contention by denying them the opportunity to face a player that they need to defeat.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.
- What each player needs to do to become a victor should become progressively harder as one goes down the rankings.
- 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.