Hold the presses! USC's BCS scenarios ain't half bad.

I'm happy to report that I was wrong and, thanks to the power of the Internet, I was corrected in record time. I doubt The Smoking Gun has ever solved anything this complex, this fast.

A few hours ago I posted about the possible scenarios that would take USC to the BCS title game and calculated that the Trojans could make it in only 0.24% of the possible outcomes. The scenarios were correct. The math? Not so much. Turns out that in a land of hypotheticals and coin flips, USC has better than a 50% shot.

Several of you smelled something fishy. Fortunately, a USC graduate student named Anthony Christodoulou cleared the air. When in doubt, e-mail an engineer!

"There are really only eight games of any importance that are out of SC's control, not 11," explained Anthony. Why? "The Big 12 championship is one game, not three (it doesn't matter who plays in it) and you said yourself that Alabama-Auburn doesn't matter. That means you have 2^8 = 256 possible outcomes."

That's a big step down from the 2,048 I suggested. I also neglected the fact that slipping ahead of either the SEC or Big 12 champ would render the scenarios in the other conference irrelevant, since USC would already be in the title game.

He broke it down in several tables (they don't fit here, but e-mail me if you want them) and explained what the odds really look like from a mathematical perspective, assuming USC leaps any two-loss team:

"131 outcomes of 256 games actually result in a USC appearance in the championship ... In other words, if all of these teams were evenly matched, USC would be most likely in. Nobody thinks Baylor, Texas A&M, The Citadel, Missouri, or FSU are nearly evenly matched with their opponents, of course, so if you give each of those 5 teams a 25% chance to win (Mizzou probably has more, but the rest of the teams probably have less), and estimate that the other 3 games are evenly matched, the probability drops to about 28%."

All this depends on USC running the table against archrivals Notre Dame and UCLA, and Anthony pointed out that 25% might be generous odds for some of the underdogs. Before you rush off to Vegas, remember that 64 of the 131 scenarios depend on Florida losing to The Citadel (a Division II school with a 4-7 record) for the first time in history and 30 depend on Baylor beating Texas Tech (which last happened in 1995).

One more caveat: five of the outcomes that place USC in the title game depend on the Trojans winning a popularity contest in the BCS end-of-days scenario. That's where voters would have to choose between an 11-1 USC team, an 11-2 Big 12 champion Mizzou, and two 11-1 Big 12 teams that were shut out of the conference championship game. As explained in this post, USC isn't getting enough style points for that.

The final 32 scenarios depend on Florida State upsetting Florida, then a two-loss Florida upsetting Alabama. Even that could lead to some voter turmoil.

Thanks again to Anthony, who gets the final word: "Fight on Florida, fight on Mizzou!"

-- Adam Rose

Comments

[gerrrg]

Those odds aren't weighted for strength of teams, so USC's chances are still fairly low.

That's where style points come in.

If any team(s) above USC loses really badly - no matter who the opponent - the pollsters will see those teams as another reincarnation of the 2004 Oklahoma team that was walloped by USC in the national championship game...and inevitably, USC's name will come up.

But that's three weekends away.

[Tony S.]

I don't think that SC will play for the championship, but I don't really care about that game. I think the better scenario is Florida losing to 'bama and some how UF & SC being matched in a bowl game. That would by far overshadow any other matchup including the title game and give SC the chance to smack down the SEC. Second best matchup for SC, playing Texas.

[Mike]

I like your style, Adam. Admitting you weren't quite correct and giving equal space to contravening opinion was classy. Of course, it's still a longshot for SC to be in the national championship game, but it's fun to think about. I'm more concerned with SC taking ND and/or UCLA lightly. Two of SC's biggest losses have come after bye weeks (Oregon St. this year and Cal back in 05). Hope the extra time off doesn't make SC lethargic. Fight on!

[Steven Frith]

Any way we can ask Anthony to do the math again, telling us the odds if Florida beats the Citadel and Texas Tech beating Baylor? Florida isn't going to lose. Baylor conceivably COULD beat Texas Tech, but that too is highly unlikely. The rest at least have a somewhat realistic chance of happening.

The simple way would be to subtract 64 and 30 from the 131 scenarios where they get in, but I know it isn't that simple since some of those scenarios overlap.

My best guess without doing the Math is that 131 would drop to about 55 chances or so, or about 22%. So basically we are counting on the chances of guessing a coin flip correctly 2 flips in a row.

[LynnMor]

Sounds like a great storyline for "Numb3rs"

[Henry David]

Adam, give it up. You guys are screwed. Probably won't even make it into the Rose Bowl....

;-)

[John]

One thing I didn't see factored into these numbers is Oregon State. Assuming Oregon State wins out and is the Pac 10 champion, USC won't have any way to argue they are better than the other 11-1 teams. (like if Alabama loses to Florida and Texas and Texas Tech are 11-1 but stay out of the Conference Championship). I think USC needs to be sole conference champion for a lot of these scenarios to work.

[Rick]

I almost hope that USC doesn't get into the Rosebowl. Playing Penn St isn't my idea of a challenge. It'd probably be closer if we played Long Beach Poly. Bring on the Tide, Gators, Longhorns, Tigers, or the Red Raiders. I want to see a challenge.

I would love to see how TT deals with the SC defense.

[Dwight Barber]

I would love for SC to be able to bypass the Rose Bowl and have a shot at playing Alabama, Florida, UT or Oklahoma which might have happened anyway had we taken care of business in Corvallis. As it is, we have no one to blame where we end up. Watching OU run all over TTU is giving me flashbacks of an invicible OU team we ran over in the Orange Bowl a few years back. The other problem is ending up out of the Rose Bowl and any other significant bowl. No one to blame but ourselves.

[Ezekiel]

I live in the great state of TX, and I for one are pulling for SC. Hoping to see a SC & UT rematch. It will bring a large number of tickets sell and will be a competitive high intensity game.