How likely is it that the Longhorns reach bowl eligibility… or go undefeated? For the past several years I’ve occasionally hopped on my computer and calculated the probabilities for myself. The resulting effect on my enthusiasm for the remainder of the season is usually unaffected by these numbers, but I have to admit that their unbiased assessment of the ‘Horns’ prospects do tend to recalibrate my expectations. And, since there’s recently been a call for fanposts around here, I thought I’d share these probabilities with all of you.

Here are the probabilities that Texas will beat their remaining opponents:

Oklahoma State: 37%

Oklahoma: 21%

Iowa State: 85%

Kansas State: 34%

Baylor: 37%

Texas Tech: 47%

West Virginia: 52%

Kansas: 90%

TCU: 38%

And here are the probabilities of winning at least n more games:

1 game: 99.951%

2 games: 99.011%

3 games: 92.833%

4 games: 74.876% (bowl eligibility)

5 games: 46.721%

6 games: 20.635%

7 games: 5.926%

8 games: 0.978%

9 games: 0.069% (Playoff bound)

So, the odds of Texas making a bowl this year are very good, about 75%. And, while the likelihood that this team wins out is trivial (about 1 in 1,449), there’s a good chance they’ll end up somewhere in between. While the most likely outcome is 6-6 (28.155% chance), 7-5 (26.086% chance) and 8-4 (14.710% chance) are real possibilities as well. I don’t know how that squares with your expectations, but those odds seem about right to me.

Density of outcomes

Calculation

So, how do I arrive at these probabilities? For those who care, read on (I promise it won’t be rigorous).

First, I use Sagarin’s ratings to estimate future game scores. These scores imply point spreads, which I then use to calculate a team’s probability of winning. This requires a distributional assumption on the errors in Sagarin’s predicted point spread and the actual point spread. I don’t have data on that; but, I do have two decades worth of betting point spreads (thank you Goldsheet.com), which I compare to actual game outcomes to see how off, on average, Vegas is at predicting actual point spreads (I hate to say Vegas here because it’s really the combined opinions of millions of bettors that determine point spread lines). It turns out that the betting line is an unbiased predictor of game outcomes (not that surprising), as deviations between the betting line and actual spread conform to a normal distribution with a mean of zero and a standard deviation of just over two touchdowns. What does that mean? Well, if Texas is favored by 3 points and you replayed the game a thousand times, the average outcome would be Texas winning by 3 points! And, we would be 95% confident that the range of expected outcomes would run from Texas winning by 31 points to Texas losing by 25 points.

So what. Well, this information is useful because we can use the distribution of point spread errors to calculate the probability that a team will win the game. You can actually calculate these odds yourself in Excel by using the normal cumulative distribution function: NORMDIST(- points spread, mean, stdDev, cdf). For example, if Texas is favored by 3 points, their probability of winning is given by NORMDIST(3, 0, 14, 1) = 58.48%. Simple!

What does this have to do with the Sagarin ratings? Well, if we assume that the Sagarin ratings are also unbiased predictors of future game outcomes with a similar distribution of errors to that of the betting lines (debatable), then we can use them in lieu of betting lines to calculate expected probabilities of a team winning any future game.

Having calculated those probabilities , I use them to determine the likelihood of Texas’s final record by cycling through every possible combination of wins and losses and logging the cumulative odds of winning 1, 2, 3, etc. more games. I use R to do this; although, you can approximate the cumulative probabilities in Excel by using a binomial model. This will yield biased results, but it’s easy to do and gives a pretty good ballpark estimate of the actual probabilities.

But there are reasons to be leery of these probabilities. Even if you're okay with the assumptions I've made, the ratings only account for information learned up to this early point in the season. The relative strengths of teams will change as we learn more, which will produce tighter estimates. But even still, most of us have an above average number of legs, so use these statistics at your own peril.