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Big East BCS Scenarios!

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Seven and a half months ago, Clemson and West Virginia faced off in the NCAA Men's Basketball Tournament. Could these schools play each other again in the Orange Bowl?
Seven and a half months ago, Clemson and West Virginia faced off in the NCAA Men's Basketball Tournament. Could these schools play each other again in the Orange Bowl?

That's right boys and girls, it's time for wacky permutational fun! In this space we will calculate each team's probability of winning the Big East BCS bid, assuming the conference hasn't disbanded since I started writing this.

According to the Big East official website, the tiebreakers are:

2-way tie: head to head winner.
3-way tie: if one of the teams in the tie swept the other two head to head, that team gets the BCS bid (as was the case with UConn last year). Otherwise, it goes to the highest ranked BCS team of the three.
4-way tie: if one of the teams swept the other three, that team gets the BCS bid. If two teams went 2-1 and two teams went 1-2 against the other teams in the tie, the highest ranked BCS team between the two who went 2-1 (which is not necessarily the team who won that game).
5/6/7-way tie: It doesn't say, but presumably they would use a similar technique as with a 4-way tie: highest ranked BCS team among those tied with the best record against other teams in the tie. Do you want to tie me up with one of your ties, Ty?

There are 16 Big East football games remaining, which means there are 2^16, or 65,536, possible ways the season can play out. With the above tiebreakers in mind, I have looked at each of these scenarios and determined  who would win the BCS bid in each case. Some can't be determined, because they are too complicated, or because they depend upon the result of game(s) not yet played. But we can come up with some reasonable probabilities for each team.

If calculating Rutgers' chance of going to the Orange Bowl seems like a silly exercise, I would remind you of what I said in this space last year:

UConn's chances of winning the Big East are better than you think. Their losses were to teams that aren't really in the race (Rutgers and Louisville) and their wins are over teams that are (WVU and Pitt). Since head-to-head results are the primary tiebreaker, UConn already holds tiebreakers with anyone they might end up tied with.

At the time UConn was 2-2 in the Big East, 5-4 overall, and ended up going to the Fiesta Bowl by virtue of the tiebreaker described above. So everybody's still in this race, and some of these oddball rules may end up making the difference. Below the jump are detailed scenarios for each team. Yes, even USF.

CINCINNATI (2-0)
Option 1: Win all remaining games.
Option 2: Lose one game, as long as it's not to Pittsburgh or West Virginia.
Option 3: Lose to Pittsburgh or West Virginia, but the team they lost to loses at least one other game.
Option 4: See "5-2 scenarios" section below.

As the only unbeaten team, the Bearcats essentially have a game and a half lead on the field. They've already beaten one of the one-loss teams, Louisville, and have a margin for error in dealing with the others (Pitt, WVU). In fact, Cincinnati can lose to Rutgers, Syracuse, or Connecticut and not be harmed, as long as they win the rest of their games to go 6-1, since no one else only Louisville could go 6-1 in this scenario. Even at 5-2 they're in the strongest tiebreaker position... though I wouldn't chance that if I were the Bearcats.

WEST VIRGINIA (2-1)
Option 1: Win all remaining games.
Option 2: See "5-2 scenarios" section below.

Since WVU has not played Cincinnati yet, they can erase the Bearcats' lead by defeating them and winning all other games, which include Louisville and the Backyard Brawl. They would be 6-1, and would either win the league outright or be tied only with Cincinnati, whom they beat. Therefore WVU controls its own destiny.

PITTSBURGH (2-1)
Pittsburgh's situation is identical to West Virginia's. Re-read the WVU entry and replace "WVU" with "Pitt."

LOUISVILLE (2-1)
Option 1: Win all remaining games, while Cincinnati loses at least two games.
Option 2: See "5-2 scenarios" section below.

Louisville has it worse than WVU and Pitt in that the Cardinals have already lost to Cincinnati. Therefore the Cardinals do not control their own destiny; even if they win out to 6-1, they don't win the BCS bid unless Cincinnati drops to 5-2 or worse. They would trail UC or be tied with them, in which case Cincy wins the tiebreaker. (There cannot be a three-way tie at 6-1 this season.)

RUTGERS (2-2), SYRACUSE (1-2), CONNECTICUT (1-2)
These teams also have pretty much the same situation, so I'll group them.

Option 1: Win all remaining games. Cincinnati loses at least one other game. Louisville and West Virginia lose at least once each. That's just to have a shot at it; they would need a bunch more help beyond that.

There are too many possibilities to sort through, but basically these teams need to win out and hope they end up tied with the right teams. They need to root for teams they've beaten and against teams they've lost to, since the primary tiebreaker is always head-to-head play. (Paradoxically, it's better to lose to bad teams than good ones. If two teams are tied, and Team A beat Team B, Team A wins the tiebreaker, even though Team A must have lost to a worse team.)

Since BCS rating is one of the tiebreakers (in 3-way or more ties that can't be broken head-to-head), Rutgers' non-league game against Army could be a factor. Winning that one won't help much, but losing it would seriously hurt their chances.

SOUTH FLORIDA: Oh, God, you actually want to know this, don't you? All right, all right, I worked it out.

USF is 0-3, which means the best they can do is 4-3, and at 4-3 they will be tied with at least three other teams. However, that four-way tie could be with some combination of Louisville, Rutgers, Syracuse, and West Virginia -- teams USF hasn't played yet. USF would win the tiebreaker since they would have to sweep those teams to get to 4-3, and they would thus be 3-0 against the other teams in the tie. It's even possible for USF to be part of a 5-way tie with all four of those teams, in which case USF would also win the BCS bid. There may be other ways for USF to win a multi-way tiebreaker as well. But let's win a game first.

5-2 SCENARIOS: These are too complex to get into just yet, so what I'll do is post a list of probabilities of who wins the BCS bid when the best record is 5-2. Some of these are by tiebreaker; in some cases there is only one 5-2 team. Teams are ranked in order of how hopeful you should be for your putative 5-2 club:

Cincinnati: 21%
West Virginia 20%
Pittsburgh 17.5%
Louisville 14%
Rutgers 7%
Syracuse 5%
Connecticut 4%
USF 0% (cannot reach 5-2)

The above does not add to 100% because the percentages do not include large multi-way ties, ties that would have to be broken by BCS rankings, or ties that cannot be broken because too few games have been played.

4-3 SCENARIOS (aka That's Armageddon!): There is about a 5% chance that no team will reach five Big East wins. If that happens, there will be at least a 4-way tie, with 5-, 6-, and 7-way also possible. (In the 7-way tie, USF goes 0-7 and everyone else goes 4-3. That'd be tough to live down at the final Octonion meeting. "Did anyone here *not* win the Big East football championship last year?") Anyway, the tiebreakers in this situation are way at the top of this article, and are too involved to sort through yet.