Calculating BYU Football's BCS Chances by Simulating 10,000,000 Seasons

Holger DanskeContributor IIISeptember 6, 2012

NEW ORLEANS, LA - JANUARY 03:  The official Bowl Championship Series logo is seen painted on the turf in the end zone as the Virginia Tech Hokies play against the Michigan Wolverines during the Allstate Sugar Bowl at Mercedes-Benz Superdome on January 3, 2012 in New Orleans, Louisiana.  (Photo by Kevin C. Cox/Getty Images)
Kevin C. Cox/Getty Images

I frequently hear and read comments about BYU's chances of being invited to a BCS bowl.  These comments range from "There is no way in (insert undesirable afterlife destination here) BYU is ever going to a BCS bowl game" (as you can probably guess, these tend to come from Utah fans), to the opposite end of the spectrum "BCS here we come!".

Well, I decided to calculate what the actual probability (based on certain assumptions) of the BYU Cougars playing in a BCS Bowl game this season with the help of Microsoft Excel.



1) An undefeated BYU will be invited to a BCS Game.  I think that with the Cougars schedule and the questionable performance of some of the higher ranked teams, this a pretty safe assumption.

2) A one loss BYU team has a 20% chance of receiving an BCS bowl invite.  For the reasons listed above I think this is also a pretty safe assumption. 

3) My predictions for the Cougars probability of winning their various games are accurate.  This is obviously the biggest assumption, but If you can convince me that I should change those probabilities I will gladly change them and redo my calculations.  The individual probabilities will be listed later with a brief justification in a later section.



It would have been easy to calculate the Cougars' chances of going undefeated.  That would have been a simple multiplication of probabilities.  Calculating the probability of BYU winning 9,10, or 11 games is significantly more complex.

So I took the easy way out and ran a Monte Carlo simulation.  Using Excel, I simulated BYU's season 10,000,000 times to see how likely the various win totals were.

After that I simply added the probability of BYU going undefeated to the product of 0.2 and the probability of BYU winning 11 games.  You can see the actual numbers later in the "Results" section.


Assigning Probabilities to BYU's Remaining Games

No. 1: Weber St.  Probability of victory = 1 (or 100 percent).  Technically there is a very remote chance that the Wildcats could win, but you would have to go out to a whole lot more decimal places than would have any realistic meaning.

No. 2: Utah.  Probability of Victory = .6 (or 60 percent).  I am sure Ute fans are wondering how many gallons of blue Kool Aid I have drunk recently, but here is a summary of my reasoning.  While Utah did prevent Northern Colorado (who won only one game at the FCS level last year) from ever crossing midfield, the Ute offense had some surprising struggles. 

The Ute running game averaged only 4.1 yards per carry with only one run going for over 11 yards.

The passing game wasn't great either.  While QB Jordan Wynn did throw for 200 yards with two TDs and only one interception, Utah's own coaches said he struggled with things like accuracy and timing.

414 yards was all that Utah's offense managed against one of the worst FCS teams in the country.  Needless to say, this game will probably be a low-scoring game decided by field position.  The biggest difference between these two teams is how far along their offenses are.  Both defenses are among the best in the country, but Utah seemed to have more trouble moving the ball than BYU did last week, despite playing a significantly weaker opponent. 

No. 3: Boise St.  Probability of Victory = .66 (or 66 percent).  Boise St is a great program, but they have a lot of questions on offense right now.  Here are some offensive stats from their game against Michigan St:

206 total yards.

20:41 time of posession.

1.5 yards per carry

48% pass completion

Zero touchdowns (passing or rushing)

Now, admittedly, Michigan St has a very good defense, but these numbers are more abysmal than many of the FCS teams that played against similarly-ranked competition.  I am sure BSU will get better, but right now I think BYU definitely has the edge.

No. 4: Hawaii. Probability of Victory = .98 (98 percent).  Picked to finish 9th (out of 10) in the MWC, the Warriors are a long, long, long shot to pull off an upset in Provo

No. 5: Utah St.  Probability of Victory = .96 (96 percent).  This number could very well change depending on how the Aggies perform in the next couple of games, but right now I still think BYU will almost certainly win. It just may not be the blowout I expect the Hawaii game to be.

No. 6: Oregon State.  Probability of Victory = .8 (80 percent).  I don't have much to go on since they have yet to play a game, but since the Cougars routed one lower tier PAC-12 team already, they shouldn't have too much trouble with another lower/mid tier PAC-12 team.

No. 7: Notre Dame.  Probability of Victory = .52 (52 percent).  This is the scariest game.  The Fighting Irish have a very good defensive line and of course Manti Te'o in the middle.  Yards between the tackles will be hard to come by.  At this point this game is practically a coin flip, until BYU and Notre Dame have a chance to play some more serious competition.

No. 8: Georgia Tech.  Probability of Victory = .66 (66 percent).  After seeing the speed and athleticism of the Cougar Defense last week, my worries about the Yellow Jackets speed and big play ability diminished notably.  It will still be a tough game, but I don't expect GT to put many points on the board.

No. 9: Idaho.  Probability of Victory = 1 (100 percent).  They got thumped by an FCS team 20-3.

No. 10: San Jose St.  Probability of Victory = .97 (97 percent).  They did give Stanford all they could handle, but this shouldn't even be close (though I'm sure the Cardinal also thought the same thing).

No. 11: New Mexico St.  Probability of Victory = .98 (98 percent).  While both SJSU and NMSU have been improving, they are still very long shots to upset a team that appears to be as good as BYU has so far this season.


The Results

Using these numbers I simulated 10,000,000 seasons for BYU's 2012 football team, and here are the results:

9.73% of the time, the Cougars were 12-0.

29.01% of the time, the Cougars were 11-1.

34.05% of the time, the Cougars were 10-2. 

20.03% of the time, the Cougars were 9-3.

6.17% of the time, the Cougars were 8-4

0.94% of the time, the Cougars were 7-5.

9.73% + 0.2*(29.01%) = 15.53%


With the assumptions I've made, the BYU Cougars have a 15.53% chance of playing in a BCS bowl game this year.


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