Stanford Cardinal football 2015: The Biggest Obstacle to Stanford’s Success Is Probability

Yesterday, I posted a piece indicating that if Stanford won out, it would be insanely likely for Stanford to make the College Football Playoffs.

That is, IF Stanford won out. But how likely is it for Stanford to win out?

A lot of commentators have looked at Stanford's remaining schedule, and concluded that winning out isn't so difficult at all. After all, the only two road games left on Stanford's schedule are against two very beatable teams: Washington State and Colorado. After that, Stanford has nothing but home games (against Oregon, Cal, and Notre Dame). It really shouldn't be that difficult at all for Stanford to win out, right...?

...right?

But this underestimates one very important thing: just how difficult it is to win out. Yes, Stanford will likely be the favorite in all of its games moving forward (barring injuries or USC sneaking into the Pac-12 Championship, either of which is definitely a possibility). But, again, what is Stanford's likelihood of winning out?

Before answering that question, let's start with

A Word on Methodology

My methodology is the same as in yesterday's piece. I took Bill Connelly's S&P rating system and calculated the point spread between Stanford and each team remaining on Stanford's schedule. I used a linear regression to convert each point spread into a win percentage, and made an adjustment for home-field advantage. All of this was done using data from 1996 onward (why 1996? Because 1996 is when college football changed the overtime rules, which created a different point-scoring environment than those scores that occurred before 1996).

Got it? Great. Here we go!

Probability of Stanford Winning Out

@WSU	@Colorado	Vs. Oregon	Vs. Cal	Vs. Notre Dame	Pac-12 Champ	Win-Out %
79.99%	90.81%	85.59%	79.92%	51.1%	53.85%	13.66%

Stanford is a favorite in every game remaining this season, and Stanford's even a heavy favorite in all remaining games except for Notre Dame and the Pac-12 Championship. Despite that, though, Stanford is still only 13.66% to win all of its remaining games, which shows just how difficult it is to win out.

But let's engage in the best-case scenario and assume that Stanford does, in fact, win out. How would Stanford stack up against each possible foe from the South?

Probability of Winning the Pac-12 Championship against Each Pac-12 South Foe

Utah (59.51% to win South)	USC (29.85% to win South)	UCLA (9.16% to win South)	ASU (1.25% to win South)	Arizona (0.23% to win South)	Pac-12 Champ Win %
55.92%	48.86%	51.51%	85.59%	85.59%	53.85%

First, I wanted to determine how likely each team was to win the South. In order to determine this, I ran a Monte Carlo simulation; it simulated the remaining season 10,000 times and determined the likelihood of each team from the South winning the South title. As you can see above, the two most likely opponents are Utah (59.51%) and USC (29.85%). These two opponents alone are almost 90% likely to appear against Stanford in the Pac-12 Championship.

Of course, it would be nice if one of the Arizona teams somehow won the South (in which case Stanford would be a very heavy favorite), but this is really nothing more than a dream scenario since the probability of either of the two Arizona teams winning the South is at less than 1.5%. Barring the miraculous ascent of the Arizona teams, Stanford will be a tossup among all of the most likely opponents from the South. Of the most likely opponents, Utah represents the best chance for Stanford, but even against Utah, Stanford is only a little bit better than a coin toss to win (55.92%).

Putting It Altogether

Yes, Stanford is a favorite (and often a heavy favorite) in all of its games moving forward. But sometimes being a heavy favorite just isn’t enough. And, honestly, the biggest obstacle facing Stanford as it continues its run for a College Football Playoff spot is just probability.

That said, Stanford’s odds are still about as good (and oftentimes much better!) than almost every other college football program throughout FBS. With the exception of only a very few, Stanford is in one of the very best positions to reach the CFP.

And even if Stanford doesn’t make the CFP, there is still a consolation prize: Stanford will almost certainly represent the North in the Pac-12 Championship. Just as I ran a Monte Carlo simulation for the South (above), I also ran a Monte Carlo simulation for the North, and it yielded the following probabilities for each team to win the North:

Stanford	WSU	Cal	Oregon
97.18%	1.48%	0.9%	0.44%

So, Stanford is 97.18% to win the North, and after winning the North, as you saw above, Stanford is 53.85% to win the Pac-12 Championship. Combined, this means that Stanford is 52.33% to win the Pac-12 Championship and with it, a berth to the Rose Bowl.

This means that the best-case scenario for Stanford is a slot in the CFP, and that even if Stanford fails to do that, Stanford is still a favorite to appear in the Rose Bowl. I guess this isn’t such a bad year to be a Stanford fan after all, is it?