Super Bowl Calibration Post

Now that football’s over, I’m about to enter my annual “What should I do with my weekends?” phase. Before that, I’d like to revisit my predictions under the cold light of morning (but not the blue light of mourning). If you’re not interested in the Super Bowl, here’s a video of a Superb Owl. More math posts are on the way.

On January 27th I wrote a six point list entitled “Reasons the Pats will win.” Let’s see how I did in hindsight. Continue reading →

Predicting NFL Scores: A Bayesian Approach

With the 2013 football season behind us, I’ve been spending my weekends developing a Bayesian model of the NFL with my college friend and UT math phd candidate Chris White.

To generate a Bayesian model, one first comes up with a parametric model that could generate the observed data. For simple problems, one uses Bayes rule to calculate the probability of parameters equaling certain values given the observed data. For complicated models, this is an extremely complicated task, but there are some monte carlo methods, such as Gibbs Sampling, which produce satisfactory approximations of the actual distributions. There are R packages available that make Gibbs Sampling fun.

I want to touch on many of these topics later in more in-depth posts, but first, here’s some results.

As of the end of the 2013 regular season, this is how our model ranked the NFL teams.

NFL Fig 1

These are the mean estimates of our Bayesian model trained on the 2013 NFL regular season. Our model predicts that, on a neutral playing field, each team will score their oPower less their opponent’s dPower. The former is the mean of a poisson process and the latter is the mean of a normal distribution. Homefield advantage is worth an additional 3.5 net points, most of which comes from decreasing the visitor’s score.

So we predict the Rams would beat the Lions by a score of 27.4 to 25.8 on a neutral field. Since we know the underlying distributions, we can also calculate prediction intervals.

Here’s the same model trained on both the regular season and the post-season. The final column shows the change in total power.

NFL Fig 2

I have a list of ways I want to improve the model, but here’s where it stands now. Before next season, I want to have a handful of models whose predictions are weighted using a Bayesian factor.

I’m very excited about this project, and I’ll continue working on it for a while.

Superbowl Special: Kelly Criterion

WrG88EmMerry Superbowl Sunday, and a happy offseason.

Like most finance types, I have a life-long fascination with risk and uncertainty. If I had my druthers, I’d move to Vegas and start a sports gambling show co-hosted with Jennifer Lawrence. It’d be called “Jenny and the Bets.” If that’s not possible, I’d get Kelly Clarkson to join me in the “Kelly Clarkson Criterion.”

Suppose you woke up in Vegas today and wanted to bet the Broncos would cover the 2 point spread. Assume you estimate a 55% chance of this happening. How much of your bankroll (or, analogously, your portfolio) should you wager on the bet? The kelly criterion answers questions like these. To help you celebrate this American holiday, I’ve created an excel workbook for this calculation.

The Kelly Rule has three inputs: your bankroll, the payoff odds and your estimated probability of winning. In this case, I’ve assumed a bankroll of $5,000 and that the bet odds are -110. In the gambling world, odds of -110 means that you have to risk $110 for the chance to win $100.

In this example, the Kelly Rule states that you should risk 5.50% ($275) of your portfolio on this one bet.

Kelly 1

Personally, I’m often surprised by the aggressiveness of the Kelly Criterion. If your probability of winning is actually 55%, then you should optimally wager $275. Any less and you leave winnings on the table. Any more and you will be too decimated by the losses.

Here’s another “plus money” example.

One of the prop bets today is picking the Superbowl MVP. If Seahawks Quarterback Russel Wilson is selected, sportsbooks will pay bettors at +300. This means that they will win $300 for every $100 they risked. If you think there’s a 35% chance of Wilson winning the trophy, you should actually bet 13.33% of your portfolio on that outcome.

Kelly 2

A bet of $666 on a Seahawk. As a Niner, that feels appropriate.

Kelly Criterion.xlsx