This is an attempt to use Bayesian probabilities to narrow down the list of legitimate national title contenders in 2014 using two data points: (1) The percentage of blue-chip recruits on a teams roster and (2) A team's Pythagorean Win Difference from the prior year. Both have used in prediction models and are well-accepted as useful statistical tools in an analyst's toolbox. As far as I know, though, they haven't been used together to develop a conditional (Bayesian) probability of reaching a given win total. I'm using 12-wins as the benchmark that a team must reach in the regular season if it's going to be in the running for a berth in the national championship tournament.
Thomas Bayes was an 18th Century English statistician and minister. Among his many accomplishments was an idea that didn't gain traction until long after his death: the idea of conditional probability. Bayesian probability attempts to use multiple data points to narrow down the likelihood of a given result by asking the question "what is the probability of A happening if B happened?"
Before I dig into the results of the analysis, here's a quick summary of how I derived my starting data and the assumptions I had to make.
First of all, Bayes Theorem requires at the data points used to estimate the probability be mutually exclusive and independent. In this case mutually exclusive was not an issue...I chose the condition "12 or more wins" and "less than 12 wins" as a condition. Since a team can't be both, it's mutually exclusive. The independence is harder to establish.
The Pythagorean Theorem of Football is based on average points for and average points against a team. It gives a number between 0 and 1 which, when multiplied times the total number of games a team played in a season gives an expected wins total for the season. It is a direct calculation from on-field play. The blue-chip percentage has an impact on the expected wins...it's been well established that having blue chips on a team is important if a team aspires to playing at an elite level. Because of this, I cannot say with confidence that the two are independent for that reason. It doesn't invalidate the utility of Bayes Theorem, however. The results, however, are less useful as the direct relationship between data points grows closer. I believe that the dependent relationship between a Pythagorean Expected Win Total and the percentage of blue-chip recruits on a team is sufficiently distant to find significant goodness in this approach.
I chose the Pythagorean Theorem of Football because it is a good indicator of whether a team's win-loss record is congruent with its performance on the field. It is a good indicator of whether a team will do better or worse the next year. Using the blue-chip percentage is a good proxy of the amount of pure talent on the team. In doing a prediction model this way I'm making the assumption that a team's schedule will be similar from year to year.
The analysis is built on calculating the probability that a team will reach 12 regular season wins. In order to calculate this, I developed probabilities that a team with a difference between it's actual wins and expected wins would experience an improvement in its win totals of a given amount. For instance, In 2013 Bowling Green had an expected win difference of -1.9. This is strong evidence that its actual win total was not truly indicative of its potential. There is strong historical evidence that teams that fall 2 games or more below their expected win totals will experience a bounce back the next year. For this reason, the probability that a team with a Pythagorean Win difference between -1.75 and -2 will improve at by no more than 3 wins is about 30%. Florida State won all its games, so it had an expected win difference of .54. The probability that it would improve by no more than -1 wins is .52.
I've attached the table of probabilities at the end of the article.
Next, I calculated the four-year average blue-chip percentage for each team from 2008 to 2013 and used that to establish probabilities that a team with a given blue-chip percentage would reach 12 wins. The table of probabilities for this at that end of the article as well.
With those two probabilities I calculated the probability that a team would reach 12 wins, GIVEN that it had a certain percentage of blue-chip recruits on the team.
The top-10 in this method are below.
|Rank||School||Prior Pythag Diff||4 - year BC %||P(12 wins)|
Florida State at #1 is no surprise. They were dominant all year and are loaded in talent. The disparity in its probability of 12 wins and the rest of the FBS is telling. They are, and deserve to be, the odds on favorite to win the national championship next year.
Bowling Green's and Marshall's presence on the list has a lot do with the effect of having seasons in which they fell well below their expected win totals for the year. Because of this, there is a probability boost toward a higher win total in 2014.
Despite losing its final two games, Ohio State still won a half game more than the Pythagorean Expected Total. It's hard to know what to think of that, especially given its recent dominance in recruiting. Still, because it has an outstanding 4-year blue-chip average, Ohio State has the third highest probability of 12 regular season wins.
Alabama, on the heels of the kick-six and a deflating loss to Oklahoma in the Sugar Bowl, fell almost a full game short of expectations. That, along with its dominance in recruiting, keeps it toward the top of the list.
|Rank||School||Prior Pythag Diff||4 - year BC %||P(12 wins)|
|88||San Jose State||0.524||0.000||0.000|
|93||San Diego State||1.950||0.000||0.000|
|102||North Carolina State||-1.200||0.025||0.000|
|117||New Mexico State||0.114||0.000||0.000|
The probability of a change in total wins of no more than:
|Pythag Diff Grp||-4||-3||-2||-1||0||1||2||3||4|
|2 to 2.25||0.839||0.736||0.607||0.464||0.326||0.209||0.121||0.063||0.029|
|1.75 to 2||0.728||0.566||0.392||0.237||0.124||0.055||0.021||0.007||0.002|
|1.5 to 1.75||0.802||0.691||0.559||0.420||0.290||0.183||0.105||0.054||0.025|
|1.25 to 1.5||0.887||0.789||0.653||0.493||0.335||0.201||0.106||0.049||0.019|
|1 to 1.25||0.785||0.678||0.552||0.422||0.299||0.196||0.118||0.065||0.033|
|0.75 to 1||0.929||0.845||0.712||0.542||0.364||0.211||0.105||0.044||0.015|
|0.5 to 0.75||0.891||0.798||0.669||0.516||0.361||0.226||0.125||0.061||0.026|
|0.25 to 0.5||0.950||0.894||0.802||0.673||0.520||0.363||0.227||0.125||0.061|
|0 to 0.25||0.950||0.895||0.805||0.681||0.531||0.377||0.241||0.137||0.068|
|-0.25 to 0||0.932||0.868||0.772||0.646||0.501||0.356||0.229||0.133||0.069|
|-0.5 to -0.25||0.943||0.890||0.808||0.696||0.563||0.421||0.289||0.181||0.102|
|-0.75 to -0.5||0.966||0.921||0.842||0.723||0.572||0.409||0.261||0.146||0.072|
|-1 to -0.75||0.961||0.919||0.849||0.749||0.621||0.478||0.338||0.218||0.127|
|-1.25 to -1||0.982||0.955||0.900||0.809||0.679||0.523||0.363||0.224||0.121|
|-1.5 to -1.25||0.986||0.962||0.914||0.831||0.708||0.555||0.393||0.248||0.138|
|-1.75 to -1.5||0.984||0.961||0.916||0.842||0.733||0.597||0.447||0.304||0.186|
|-2 to -1.75||0.945||0.902||0.840||0.755||0.651||0.534||0.415||0.302||0.206|
|-2.25 to -2||0.961||0.926||0.870||0.791||0.688||0.567||0.440||0.319||0.215|
The probability of a team reaching 12 wins based on percentage of blue-chip recruits:
|BC% Grp||p(12 wins)|
|0 - .1||0.025|
|.1 - .2||0.044|
|.2 - 3||0.057|
|.3 - .4||0.072|
|.4 - .5||0.256|
|.5 - .6||0.207|
|.6 - .8||0.337|