BCS Analysis – The Undefeateds Take 2

Huck, below the table for Alabama you write:

“Probability of an Undefeated SEC Champion – 86.0%”

and I believe you arrive at this number by simply summing the probabilities of Alabama and LSU going undefeated. It has been a long time since I took the class in college, but I don’t think that is the right way to calculate it. In order for there to be no undefeated teams in the SEC, both Alabama and LSU must lose at least one game. Since you estimate the probability of Alabama losing at least one game as 49.8%, and the probability of LSU doing so as 64.8%, I think that you can calculate the probability of both teams losing a game as the product of those probabilities, or 31.9%. Or maybe I have it all wrong.

Also, I think the one thing I left out is that the probabilities are dependent, because LSU and Alabama play each other, but I think the margin of error for the underlying probabilities is large enough that this oversimplification is unimportant.

I left out one thing on my previous post. If the probability of both Alabama and LSU losing a game is 31.9%, that would mean the probability of an undefeated SEC champion is 68.1%.

Finally, can you detail how you calculate the various probabilities in the list of possible number of undefeated teams at the end of the season? You may have already covered this last week.

@DeepEddy — i had the same concern as you — but you have to keep in mind that the reason why both teams have such a large chance of losing a game is b/c they’re playing each other. with that said, they both CAN’T win that game. 1 team is guaranteed to win and 1 team is guaranteed to lose.

If you look at it again with that thought in mind — you’ll see that his odds are correct.

I hate to say this but OU is still in a good position. If they win out they’ll be right there.

OU won’t win out.

I totally agree with you about the 10 team conference. I believe it also will help recruiting for the old big12 north teams, thus making the league stronger.My reasoning is Texas recruits not chosen by the Power south teams will choose a north team over another conference because they will still get half their games played in the south. Good for family , coaches and friends who want to see them play.

DeepEddy -

RIVALWEAR addressed your concern from one perspective. Alabama and LSU going undefeated are mutually exclusive events, and as such their probabilities can simply be added. It may help to look at it in the following manner. If we assume that LSU wins the game, they have an 82.7% chance of going undefeated the rest of the season. If we assume that Alabama wins, they have an 88.4% chance of going undefeated the rest of the season. Given that LSU has a 42.5% chance and Alabama a 57.5% chance in that game, the probability of an SEC team going undefeated can also be calculated as 0.425*0.827 + 0.575*0.884, which is 86.0%.

Another way to look at it is how I explained it late in last week’s thread. We know that the probability that at least one of LSU and Alabama goes undefeated is the probability that both go undefeated plus the probability that only LSU goes undefeated plus the probability that only Alabama goes undefeated. The first option has a probability of zero because they can’t both go undefeated. The second is the probability that LSU goes undefeated times the probability that Alabama does not go undefeated if LSU is undefeated. That is a probability of one because if LSU goes undefeated then Alabama necessarily can’t. So the calculation is:

0 + 0.352*1 + 0.508*1

which is of course the same as merely adding their probabilities.

As for the percentages in the summaries, they are simply calculated by summing up all possible outcomes. As an example, the probability of 3 undefeated AQ teams is

P(SEC) * P(Big12) * P(Stan) * (1-P(Clem))
+
P(SEC) * P(Big12) * (1-P(1-Stan)) * P(Clem)
+
P(SEC) * (1-P(Big12)) * P(Stan) * P(Clem)
+
(1-P(SEC)) * P(Big12) * P(Stan) * P(Clem)

Which is the sum of the probabilities of all scenarios where exactly 3 AQ conference teams are undefeated.

Looking at Ok St, Oklahoma, K state and their schedules, i would not be surprised to see a 2 loss Big 12 champ.

Completely off topic, but it appears the ags are now stalking people IRC style if you write a negative twitter post about them:

http://texags.com/main/forum.reply.asp?topic_id=1943019&page=2&forum_id=5

Watch yourselves out there, and I suggest adding another wrinkle to the secret handshake for the tailgates before scip or sailor admit their true identity.

So if Stanford loses (could easily slip up to Oregon, ND or USC) and OSU loses to OU (or whoever) and K-State loses and Clemson loses then does Boise State REALLY have a chance to be rated ahead of the LSU/Bama loser in the BCS standings?

In other words if Boise is the only other undefeated team do you think they will slip ahead of the loser of LSU/Bama (assuming that’s their only loss) and play for the championship? Hard to believe … and imagine the stink if an undefeated team is passed over for an SEC rematch in the MNC game. Would increase pressure for a playoff system for sure.

The best scenario for us is the max number of undefeateds, leading to massive implosions of BCS-supporting talking heads. Teeth, hair, and eyeballs littering the landscape. Rabid wolves lapping up brain goo and T-day leftovers.

Massey schedule ratings updated.

Huck—

If I hadn’t mentioned this before, you are a damn fine CFB analyst. I am most intrigued by your statement about ten team leagues. Am I the only one who doesn’t believe that we are headed inevitably to 16-team super conferences?

Look forward to your future thoughts on this.

Jones Top 10: I don’t think there’s anything inevitable about 16-team conferences. That’s some idle sports (uh) journalist or blogger, thinking theory and not reality. And, maybe, if there ever is a playoff for the NC, 16 makes some sense. (BTW: great stuff every week on your Top 10. Starts my week off on a high note.)

My view is that the SEC discovered the CCG, and a bunch of sheep followed. ACC. Big 12. The 16-team WAC (for a time). Now the Rose Bowl conferences.

I see the damn CCG as a royal pain. How many times did the Big 12 lose a team that had a shot at the MNC because of a CCG loss? Nebraska in ’96, K-State to the Aggies a couple of years later, us to Colorado in ’01 (but Nebraska sneaked in because of the BCS formula at the time).

I hate the sumbitch. Give me a 10-, even an 11-team conference, with complete round-robin play.

One thing we know is that the 16 team super conference has failed in the past, just ask the WAC. I have a feeling that any quick expansion is due for a major problem in the future.

Nebraska does not really fit the mold of what the BIG was looking for, the loss of UNL’s AAU status had to concern the academic side of that conference no matter what they say publicly.

Utah and Colorado to the PAC did allow them to get a major increase in TV revenue but those schools have yet to win a conference game, and it’s not looking good.

If the SEC takes Missouri, I think it will just further the point that conference expansion is not the panacea it is cut out to be. SEC really your going to add Mizzou for ease of scheduling? Really? That’s bound to work out well.

All that being said, I would much prefer us to be playing a PAC slate or BIG slate vs the Big 12 minus UNL, CU and ATM.

Interesting analysis; I don’t see an undefeated team in the B12-? this year, nor do I see one coming out of any other major conference except the Pac 12. I think Stanford wins it all. I think the BCS would literally tie itself in knots to avoid having to invite the likes of Boise or Houston to play in the Championship game. I see that game as being between the LSU-Bama winner and Stanford.

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