Tuesday, December 11, 2012

football playoffs

Major college football has been very gradually moving toward a playoff system, with many fans clamoring for a quicker move to a larger playoff. Proposed playoffs are almost always single-elimination; insofar as one is more likely to accurately determine which team is the best on the basis of more information than less, allowing a single loss in an expansive post-season playoff to eliminate a team from contention, with the playoff including a number of teams that lost two or even three games during the regular season, amounts to throwing away information, and makes it less likely, not more, that the winner of the playoff will actually have been the "best" team on a season-wide basis. A compromise idea I've played with is privileging the teams that seem, on the basis of the regular season, most likely to be the best, but allowing lower-ranked teams into the playoff under less advantageous terms; a top team would be permitted to remain in the playoffs after a loss, while a lower-ranked team would not. A couple years ago, I suggested a playoff system to my brother and he informed me that the playoff system for the Australian Football League is essentially what I had proposed. A couple weeks ago, CNNSI assembled a mock committee of actual people who might be on a real committee selecting a college football playoff as will happen in a couple of years. If I use this to seed an Australian Football League style playoff, I get a bracket like
Notre Dame
GeorgiaTexas A&MTexas A&M
Texas A&MOregon
FloridaNotre DameAlabama
LSUStanfordNotre Dame

with game results projected in the first three rounds in part to clarify the structure of the bracket; two games in the first round pit top 4 teams, and Florida and Notre Dame, by virtue of losing those, are sent across the bracket to their second-chance games against lower-ranked teams that entered on single-elimination terms.  The semifinals here feature Oregon against an SEC team and Notre Dame against an SEC team.
One feature of playoffs in all four "major professional sports" in the US(/Canada) is that the leagues consist of two "conferences" and that the playoffs keep each "conference" separate; the playoff systems thereby create a championship match (or series) that has one team from each half of the league, rather than seeking straightforwardly to pair up the top two teams. In baseball the two halves of the league play with slightly different rules, and in basketball and hockey they have a certain geographical logic, but in the NFL in particular the division is entirely historical; having "AFC champions" and "NFC champions" I suppose gives the team that loses a little bit more euphemistic title than "Super Bowl loser" — and perhaps even a team that "has been to n of the last m AFC championships" even feels it's accomplished more than a team that "has been to n of the last m quarterfinals". It feels a bit hollow to me, and I'd just as soon see a single tournament. In the regular season, at the moment, each team plays 12 games within its conference and only 4 against the other conference; this could be modified, but as a first step, perhaps we should take six teams from each conference into the playoffs, seeded separately, and have them play
The top two teams from each conference don't get byes — at least not at first.  They are placed in a four-team single elimination tournament of which the winner gets a double bye, both the third and the fourth round.  The other eight teams play their own games, of which the winners "catch" the three teams that lose from the top-four tournament; the first-round losers play 4/5 winners in the second round, and the second-round loser plays the "champion" of a four-team 3/6 tournament in the third round, as the winners of the 4/5-1/2 games play each other.  After round 3 there are 3 teams left: the undefeated 1/2 team, and two teams that are each either an undefeated 3–6 seed or a one-loss 1/2 seed. If we let the latter teams play in round 4, the winner of that gets a(nother) shot at the undefeated 1/2 team. A 3–6 seed can win the championship, but needs five wins in a row, with a few of them probably top seeds; a 1/2 can win with a loss, but it requires that the team go 4–1. Perhaps a different visualization would be useful; one spot in the Super Bowl is filled by a four-team single-elimination tournament, and the other is filled by
AFC 1w(loser)w
NFC 1w
AFC 3ww
NFC 3w
AFC 1(loser)ww
AFC 4w
NFC 1(loser)w
NFC 4w
Note that the 1/2 games, listed twice in the table, aren't played twice; a w denotes that the winner of the previous round advances to that spot, while (loser) denotes that the loser from the previous round advances to that spot.

As a couple final remarks,
  • The NFL playoffs as currently constituted are, as far as I know, unique in that there is not a fixed "bracket"; a team that gets a bye into the second round doesn't have a particular game of which it plays the winner. What I have produced here is a more traditional "bracket" in that sense. I'm not necessarily opposed to the NFL's system in that regard; this is just what I did.
  • Major college football does have a number of "conference championship" games, all of which take one team from each of two "divisions" of a conference, rather than taking the top two regardless of division. This year Ohio State, because of previous misdeeds, was ineligible to play in the championship game of its conference, but was declared the champion of its division; the team in its division that finished highest in the standings while also not being under instutitional sanctions went to the championship game instead. There was some lack of clarity, midway through the season, as to whether Ohio State would be allowed to be the "division champion"; it seems to me that the decision that was made vitiates much of the reason for the structure of the championship game. If the point isn't to match the two "division champions", it should be to match the top two teams. The asymmetric schedule makes a case for some preference toward having teams from different divisions, but in this case the team that went in Ohio State's place was a full two games behind a team from the other division that didn't make the championship game and that would have seemed to have a rather better case for being invited.
Update: Let's do a mock bracket.  (Updated Dec 31.)  I'm adopting a proposal by SI writer Petere King that division champions be guaranteed a playoff spot, but not a top 4 seed. I'm also, naturally, making some guesses about how the rest of the season will play out; that said, my teams are
New EnglandSan Francisco
HoustonGreen Bay
which might lead to something like
DenverSan Francisco(New England)New England
San Francisco
New England
New England
HoustonHoustonGreen Bay
Green BayGreen Bay
San Francisco
New England
and the winner of the New England vs. Baltimore match gets to play San Francisco in the Super Bowl.  To clarify, a team in parentheses lost its previous game in order to land in that spot.

I will note some features of the bracket that should perhaps have been mentioned before (they aren't specific to this simulation):
  • As long as no lower seed beats an upper seed, teams from the same conference won't play each other until at least the third round; any such matchup must follow a team beating a seed at least as high as itself.
  • Two teams will not play each other a second time — there will be no "rematches" — until at least the fourth round (as there is in the mock bracket), at which point there are only three teams left and you're running out of ways to avoid them.
Both these points are to say that I've laid it out to create a lot of "mixing", so that teams that are a bit hard to compare before the game — they're in different conferences, so they have few common opponents, and they haven't played before in the tournament at least — are more likely to be paired than teams that are more readily ranked relative to each other.

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