Summer Coed Hat League (2011)

Playoff Format

Here is a detailed description of this year’s playoff format.

You may also be interested in the playoff standings and schedules.

Note: (July 22) After an extended and useful e-mail discussion with an interested party, the rules on this page have been reworked a bit.  This is hopefully the final version (though edits may still be made for the sake of clarification.)

An Experiment

In an attempt to maximize the number of meaningful, challenging games (e.g. against similarly skilled oponents) in playoffs, we are going to try something new this year: a modified Swiss tournament format.

After each round of playoffs, teams are ranked first by the number of playoff games won, then by total number of games won by their playoff opponents. For the next round of playoffs, teams play closely ranked teams: the first ranked team plays the second ranked, and so forth (though the pairings may be shuffled a bit in the third and fourth rounds to avoid playing multiple playoff games against the same team.)

This is a bit of an experiment. To our knowledge this has never been used for an Ultimate playoff series before. (A variation has been used as a replacement for the "pool play" portion of a tournament.) We have run a number of simulations of how the playoffs may turn out, and this system seems to give pretty good results.

Detailed Rules

Schedule

There will be four rounds of playoffs. All twelve teams will play in each round.

Seeding

Teams will be ranked from 1–12 based on their regular season performance. This rank will be refered to as the regular season ranking (RSR).  The criterion used to rank the teams are, in order

  1. Number of regular season wins (RSW).  Ties count for half.
  2. Total points scored in the regular season (with a maximum of 15 points per game.)  Regular season forfeits are scored as 1–0.
  3. Average spirit score after the regular season.
  4. Coin flip.

First-Round Pairings

Up until playoffs, the 12 teams in the league have been partitioned into two groups. Each group has played each of the six teams in the other group and none of the five other teams in their own group.

In the first playoff round, each team will play against a team from its own group.  Within each group the first ranked team will play the second ranked, the third with play the fourth, and the fifth will play the sixth.

Subsequent Rounds

After each round of playoffs all teams will be re-ranked.  The following statistics are computed, for each team:

PW (playoff wins): the total number of playoff games won (ties count for half.)

OW (opponent’s wins): the total number of playoff games won be the team’s playoff opponents.  (OW equals the sum of the PWs of the team’s playoff opponents.)

ORSW* (modified opponent’s regular season wins): This is the team’s RSW (regular season wins) plus the sum of the team’s playoff opponents’ RSW.

OSI (opponent’s strength index) = ORSW* + 2 × OW

PGF* (modified playoff goals for): The total number of points score in playoffs, with a maximum of 15 points per game. Playoff forfeits are scored 15–0.

Pairing for rounds 2, 3, and 4

The teams are ranked in order by:

  1. PW (playoff wins)
  2. OSI (opponent’s strength index)
  3. PGF* (playoff points scored)
  4. RSR (regular season rankings — higher seed teams win).

For the next round of playoffs, the first ranked team will play the second ranked team, the third will play the fourth, and so forth. Going into the third and fourth rounds, the ordering may be shuffled a bit to insure that there are no repeat games (between teams which have already played each other earlier in the playoffs.)

Since this is a bit of an experiment, and since the shuffling rules are still somewhat vague, the league coordinators have final god-like say over how the standings are shuffled.  That said, the pairing procedure to be followed is:

  1. Pair the top-ranked with the next-highest ranked team which has not yet been met in playoffs.
  2. Pair the lowest-ranked with with the next-lowest ranked team which is has not yet met in playoffs.
  3. Pair the highest ranked unpaired team with the next-highest ranked viable team.  (Here, viable means the team has not yet been met in playoffs, and is unpaired for the current round.)
  4. Pair the lowest unpaired team, with the lowest viable opponent.
  5. Repeat step 3.
  6. Repeat step 4.
If, during this process, one gets stuck, back up one step, and redo the previous pairing skipping one extra viable team in the rankings.

Final Ranking

After the final round of playoffs, teams are ranked by:

  1. PW (playoff wins)
  2. OW (opponent’s wins in playoffs)
  3. PGF* (point’s scored in playoffs)
  4. Head-to-head matchups in playoffs.  If the tied teams have met during playoffs, resolve ties in favor of the winner of that match.   In the case of multi-way ties, the head-to-head results may not result in any consistent ordering of the tied teams, in which case this tie-breaker is ignored.  See below for more details on the resolution of the head-to-head tiebreaker.
  5. Head-to-head matchups considering both playoff and regular season games.   Again, see below for details of the resolution of this tie-breaker in the non-obvious cases.
  6. ORSW*
  7. RSR

On the head-to-head tie-breaker

In the case of multi-way ties (and when considering regular-season matchups) the head-to-head results can be ambiguous with respect to tie resolution.  In order to avoid confusion, here’s the procedure.

  1. Construct the directed-graph of all the head-to-head matchups pertinent to the tie be resolved.
  2. Identify any cycles in the graph (e.g A beat B, B beat C, C beat A).
  3. Discard from consideration all matchups involved in those cycles.
  4. Infer any unambiguous ordering from the remaining matchups. For this step, transitivity can be assumed to hold.  I.e. if A beat B and B beat C, A can be assumed to have beat (or be able to beat) C.
Examples

Discussion

Advantages

  1. Games are always played against similarly ranked teams. In theory this should make for close games.
  2. Every game affects the final standings in a meaningful way. E.g. a team is not relegated to the bottom half of the standings once they lose their first playoff game.
  3. Going into playoffs, all teams still have a shot at the championship.
  4. If a team wins all four of its playoff games, it is the champion.

Disadvantages

  1. The system is very confusing.
  2. There’s a good chance that the last round of playoffs will not include an "A pool final", winner-vs-winner type of game. It is possible (though not a given) that, entering into the final round of playoffs, more than than two teams will be in contention for the championship. This, for the most part, is a corrollary of advantages one and two: if all playoff games are against evenly ranked teams (and are thus equally important), then there is no "most important game" to be saved for last.
  3. It is possible that the overall championship may depend on a final round playoff games (or games) between teams, neither of whom is in contention for the championship.  This could make it hard to compute the season champion on the fields after the fourth round.

Changes

July 22, 2011

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