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Oregon leads top four with 38% probability to win inaugural College Football Playoff

My probabilistic assessment of the first College Football Playoff shows Oregon is in the driver's seat. What chance do Alabama, Florida State, and Ohio State have to claim the title? Let's do the math!

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If you've read David Foster Wallace's Infinite Jest, you know that the ultimate punter is a product of the junior tennis circuit sporting a wicked-good lob and some knowledge of Eschaton-based game theory. If you've read Mark Leyner's Et tu, Babe, you know that he is a genius and you have incomparable literary taste. However, if you've read James Joyce's Finnegan's Wake, you are probably a lonely person and it's possible that you are terminally insane.

Regardless of what you have or have not read, the fact that most punters grow up playing soccer rather than tennis makes a lot of sense; foot-eye coordination and kicking ability are both cultivated in soccer and nearly universally ignored by the balance of popular North American sports. In other words, I think David Foster Wallace had a nice theory but it just doesn't jibe with the empirical facts. Obviously, this lede will segue into an erudite analysis of the critical importance of the punting game in the upcoming College Football Playoff and my insistence that the big guys are perhaps fatally ignoring this critical detail in their analysis. Or will it?

The Problem with Physicists named Per Bak

Per Bak was a physicist who developed a theory called ‘self-organized criticality’. His idea was that random events subject to a few simple rules displayed behavior that could be accurately modelled by mathematical functions called power laws. He believed that because the experimental results followed mathematical rules, the random process somehow organized itself, or that randomness implicitly contains order that manifests under observation. He wrote a book extending this idea to the fundamental nature of our universe. It’s an interesting theory that is pregnant with fascinating implications, but it’s wrong.

Let’s review: step 1 (random process) – step 2 (a few simple rules) – step 3 (observe results) – step 4 (results follow mathematical functions) – step 5 (claim order emerges from randomness)

Per Bak’s conclusion that random processes display ordered outcomes ignores the fact that some rule (or rules) has (or have) been imposed on the random process. The self-organized criticality is not some inherent property of the random process and the universe, it’s an artifact of the "simple rules" applied to the random process. ‘OK, Dr. Nerdenstein!’, you exclaim, ‘I don’t care about Per Bak and what the heck does this have to do with the College Football Playoff?!?' This goat path may not be an easy climb, and there’s nothing I can do about that smell, but if we endeavor, we’ll be rewarded with a wicked-nice view. Trust me.

The Central Limit Theorem

There is a famous result from probability theory that states that the average value of the sum of many independent random variables approaches a normally distributed variable, regardless of the summand distributions. In other words, the sum of many random events can be described by a normally distributed random variable.

Let's review: step 1 (many random variables) – step 2 (compute sum of many random variables) – step 3 (observe results) – step 4 (results are normally distributed) – step 5 (the Central Limit Theorem)

So, when Oregon and Florida State meet in the Rose Bowl, there are legion random variables affecting the outcome. To name a few of these variables: athletic potential, strategy, execution, coaching, injuries, the contents of Jameis Winston’s pockets, weather, BUR approach and departure patterns, whether or not Vladimir Putin is wearing a shirt, illicit extraterrestrial mineral extraction on the dark side of the moon, etc. Think "butterfly effect". Per the Central Limit Theorem, the sum of these random variables is accurately described by a normally distributed random variable.

Per Bak should have taken a course in probability theory.

Onto the College Football Playoff

I’ve described my method of probabilistic assessment here and here. To recap, I consider points scored and points allowed to be normally distributed random variables resulting from the sum of many independent random variables a la the Central Limit Theorem. Given these normal distributions, I can compute the probability that points scored exceed points allowed, e.g. - the probability that Oregon will win the Rose Bowl. I can also analyze and rank the four finalists based on average offensive and defensive performance and evaluate their consistency over the course of the season.

In 2014, Oregon scored the most average points among the four finalists. Oregon’s offense and defense were also the most consistent performing units. Alabama’s defense permitted the fewest average points allowed. However the Alabama offense is the least consistent compared to the other finalists. Ohio State’s defense is the least consistent of the top four while Florida State’s offense scored the fewest average points and the Florida State defense permitted the most average points allowed. Based on these metrics, Oregon looks like a favorite and Florida State looks like an underdog. We all know that Oregon’s consistent, high-scoring offense is quarterbacked by this year’s Heisman Trophy winner, Marcus Mariota. In my opinion, these statistics clearly support that result.

Rose Bowl & Sugar Bowl

Looking at the semifinal match-ups, I calculate the following probabilities for each team progressing to the final.

Oregon                 73%

Florida State       27%

Ohio State           56%

Alabama              44%

I can use these probabilities to compute the probability of all four possible final match-ups as follows; the probability that Oregon meets Ohio State is equal to the product of the probability of each team winning its semifinal game, e.g. – 0.73*0.56 = 41%. The probabilities are listed here in order from most probable to least probable:

Oregon – Ohio State                       0.73*0.56 = 0.41 = 41%

Oregon – Alabama                          0.73*0.44 = 0.32 = 32%

Ohio State – Florida State             0.56*0.27 = 0.15 = 15%

Alabama – Florida State                0.44*0.27 = 0.12 = 12%

I calculate that the most probable final game is Oregon – Ohio State. The least probable final game is Alabama – Florida State. Note that the sum of these probabilities is 100%, as it should be.

The College Football Champion

The probabilities of each team winning the final game and thus, the NCAA Championship will change based on performance in the semifinal games. But, I can still compute probabilities for each team based on the current data. The probability that Oregon wins the Championship is equal to: the probability that Oregon wins the Rose Bowltimes the probability that Ohio State wins the Sugar Bowl times the probability that Oregon beats Ohio State plus the probability that Oregon wins the Rose Bowl times the probability that Alabama wins the Sugar Bowl times the probability that Oregon beats Alabama. If you followed that, you can deduce all of my calculated probabilities from the following list, ordered from most probable to least probable:

Oregon                 0.73*0.56*0.50+0.73*0.44*0.56 = 0.38 = 38%

Ohio State           0.56*0.73*0.50+0.56*0.27*0.71 = 0.31 = 31%

Alabama              0.44*0.73*0.44+0.44*0.27*0.65 = 0.22 = 22%

Florida State       0.27*0.56*0.29+0.27*0.44*0.35 = 0.09 = 9%

Again, note that the sum of these probabilities is 100%, as it should be.

Quantum satis: Oregon is the most probable (38%) inaugural College Football Champion.

Caveat venditor: If Oregon meets Ohio State in the Championship game, the calculated win probability is identical to a coin flip.

Caveat emptor: I’ve tried to read Finnegan’s Wake twice. o_O