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Six-Team Playoff Brain Teaser

Six-team playoffs are a solved problem. In football, the top two teams get bye weeks. Seed 3 plays seed 6 and seed 4 plays seed 5. After that, the highest ranked team plays the lowest ranked team that's won the previous week.

However, my winter hockey league has six teams, but they're guaranteeing each team two playoff games (every team makes the "playoffs"). I can't come up with a solution that rewards the season-long record and gives teams two games guaranteed.

Three games are being played one week, three the next, and one for the finals.

Can you concoct a playoff schedule that nominates two teams to go to the finals and rewards the top seeds for their season achievements? Everything I can come up with could result in three 2-0 teams and three 0-2 teams or six 1-1 teams in the playoffs. Do you just use the season-long record as the tie-breaker in that case?

Or is there actually a schedule that could work?

4 Responses to "Six-Team Playoff Brain Teaser"

  1. There is probably just a consolation bracket for the second game. The guarantee is that you play a second game, not that you can lose a game and still advance to the championship.

    The loser of 3 vs 5 plays the loser of 4 vs 5. This game determines 5th place.

    Then the losers from second round play each other for 3rd place.

    The winners of the second round play for 1st place.

  2. If you have to play three games in Week 1 you're out of luck. Even creating a relatively fair schedule for Week 2 would be a difficult task, not to mention deciding which two teams deserve to play the title game.

    If you have any flexibility at all on that point, you can use a modified version of the NFL system as follows:

    WEEK 1

    Game 1: seed #4 vs seed #5
    Game 2: seed #3 vs seed #6
    Bye: seeds #1 and #2

    WEEK 2

    Game 1: the two losers from week 1
    Game 2: seed #2 vs highest seeded winner from week 1
    Game 3: seed #1 vs lowest seeded winner from week 1

    WEEK 3

    Championship: the two remaining undefeated teams
    Consolation Game: if necessary

    To determine the participants in the consolation game:

    If the top two seeds are playing in the title game then every team has their two games, and this game is not necessary
    If the top two seeds lost in Week 2 then they play each other in this game
    If only one of the top two seeds lost in Week 2 then that team plays the winner of Game 1 from Week 2 in this game

    This plan gives you controversy-free resolution in three weeks, a guarantee of at least two games per team, rewards for the top seeds, and assurance that the playoffs will not include any rematches. Plus, the possibility of getting into the consolation games gives the two teams in the "losers bracket" in Week 2 something to play for.

  3. Chas said on February 4, 2008:

    There is probably just a consolation bracket for the second game. The guarantee is that you play a second game, not that you can lose a game and still advance to the championship.

    That'd be fine if you had an even number of teams that would be 1-0 after the first week, but with three teams, one of them is bound to get screwed.

    Cuz after week 1, three teams are gonna be 1-0 and the other three will be 0-1. You could make two of them play each other, in which case one will be 2-0, one will be 1-1, and the third 1-0 team will either win or lose. If they lose (to an 0-1 team) they're 1-1, but are they better than the other 1-1 team that started out 1-0, equal, or worse? If they win, they're 2-0, but they didn't play another 1-0 team like that same loser of the 1-0 battle.

    Scott said on February 4, 2008:

    If you have to play three games in Week 1 you're out of luck. Even creating a relatively fair schedule for Week 2 would be a difficult task, not to mention deciding which two teams deserve to play the title game.

    That's what I think, yeah. One game is played each on March 22, 24, and 26. The next round of games occur on the 29th. The championship is on the 30th.

    Given the spacing, I think it's unlikely your proposed schedule is the way it's going, but I agree that'd be ideal. The two losing teams in Round 2 could be said to be playing for fifth place, I suppose.

  4. Week 1
    Game A: 1 plays 2
    Game B: 3 plays 4
    Game C: 5 plays 6

    Game D: W:A plays W:C
    Game E: W:B plays L:A
    Game F: L:B plays L:C

    Game G: W:D plays W:E

    The three winners advance from week 1. Both #1 and #2 advance, but the winner plays a guaranteed easier opponent.


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