Project WOPR is Coming

With the Bayesian draft tool completed, I can now focus on completing Project WOPR. For those who might be fans of mid-80s Matthew Broderick movies, you may have figured out what the WOPR is.

I'll give another clue:
It's purpose to answer the un-answerable questions of football strategy.

But for now, it's taking up my entire basement and has driven my electricity bill through the roof. The liquid-nitrogen cooled 32-core processors aren't cheap either.

Live Updates Tonight

I'll be updating the Bayesian draft model live tonight. I was triple-booked for this evening, and I thought I wouldn't be able to make it happen. But now I'm only double-booked, so in the immortal words of Bill O'Reilly, "F--- IT. WE'LL DO IT LIVE!"

As players are chosen, the probabilities will obviously start changing rapidly.  The fact a player is off the board and no one else could fill that slot is information (with absolute certainty) that can be fed back through the model. The effects will cascade through the rest of the available picks.

Unfortunately, the interface won't update automatically for users. You'll need to click refresh or hit F5 after each pick. There will be at least two or three minutes of lag for the updates to work through the system, so be patient.

New Feature on the Draft Model

In my last job I worked with a team of software developers. The interfaces they designed didn't make much sense to me. The interfaces were always, at heart, a giant expanding tree of classes, objects, and properties. Huh? Lots of tiny plus and minus marks everywhere to expand and contract the accordion. Left click to view something. Right click to modify it. If you ever had to deal with the Windows registry, it was like that. Steve Jobs would not have been thrilled.

When I learned a little about object oriented programming, it all made sense. The software engineers were designing the interface for their own convenience, not for ease of use. It made sense from an efficiency standpoint...a programming efficiency standpoint. But from the perspective of the user, it wasn't so efficient. The least used feature was just as accessible as the most common feature, and all of them were hidden until you expanded the right portion of the tree.

Yesterday I realized I was doing the same thing with the draft model. From my point of view, it's easiest to think in terms of players and their probability to be selected at each pick number, because that's how the software that runs the model works. It goes down the list of prospects, player-by-player, looking at the probability he'll be selected pick#-by-pick#.

For the players and their agents, and for fans of particular players, this is ideal. They want to know where and when they'll go. But the user is probably thinking of things from a team's perspective. Whether the user is a team personnel guy or a fan of a team, he'd rather see things from the perspective of a pick #. Right now, a Vikings fan (or exec) would have to click through over a dozen or so of the top players to see who's likely to be available to them at pick #8. And if they were wondering about who'd be available if they trade up or down, that's another few dozen clicks. Scroll, click. Scroll, click...

Podcast Episode 21 - Cade Massey

Cade Massey, Professor of the Practice at the Wharton School of Business, joins the show to discuss his research on the NFL draft. Professor Massey is the co-author of "The Loser's Curse: Decision Making & Market Efficiency in the National Football League Draft", a paper analyzing the market for draft pick trades. He and his co-author, Richard Thaler, discovered that teams picking at the top of the draft actually sacrifice a great deal of what he calls "surplus value" by not trading down for additional selections.

Dave and Cade look at the reasons why teams employ less than optimal strategies, including risk aversion, adherence to norms established by "The Chart" and other psychological factors. Professor Massey defends his paper against critiques, and discusses why he believes the draft is such a compelling spectator event.

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Bayesian Draft Analysis Tool

This tool is intended to help decision-makers better assess the NFL draft market. Specifically, it estimates the probability each prospect will be available at each pick number.  The estimates are based on a Bayesian inference model based on consensus player rankings and projections from individual experts with a history of accuracy.

For details on how the model works, please refer to these write-ups:

 - A full description of the purpose and capabilities of the model
 - A discussion of the theoretical basis of Bayesian inference as applied to draft modeling
 - More details on the specific methodology

If you want to jump straight to the results, here they are. But I recommend reading a little further for a brief description of what you'll find.


The interface consists of a list of prospects and two primary charts. Selecting a prospect displays the probabilities of when he'll likely be taken. You can filter the selection list by overall ranking or position.

The top chart plots the probabilities the selected prospect will be taken at each pick #. I think this chart is pretty cool because it illustrates the Bayesian inference process. You can actually see the model 'learn' as it refines its estimates with the addition of each new projection. Where there is a firm consensus among experts, the probability distribution is tall and narrow, indicating high confidence. When there is disagreement, the distribution is low and wide, indicating low confidence.

The lower chart is the bottom line. It's the take-away. It depicts the cumulative probability that the selected prospect will remain available at each pick #. For example, currently there's an 82% chance safety HaHa Clinton-Nix is available at the #8 pick but only a 26% chance he's available at #14. A team with an eye on a specific player could use this information in deciding whether to trade up or down, and in understanding how far they'd need to trade.

Hovering your cursor over one of the bars on the chart provides some additional context, including which team has that pick and that team's primary needs (according to nfl.com).

The box in the upper right gives you the player's vitals - school, position, height, weight. The expert projections used as inputs to the model are also listed. Currently those include Kiper (ESPN), McShay (Scouts, Inc.), Pat Kirwan(CBS Sports), Daniel Jeremiah (former team scout, NFL Network), and Bucky Brooks (NFL Network). Experts were selected for their  reputation, historical accuracy, and independence--that is, they don't all parrot the same projections. Not every prospect has a projection from each expert.

Link to the tool.

Bayesian Draft Model: More Methodology

Boomer, when you think about a guy like Thomas Bayes you think high motor, long arms, quick off the snap. Huge upside in any 3-4 scheme. Gets leverage on those tricky probability theorems right off the block. Game 1 starter for 90% of the teams out there. Writes proofs all the way through the end of the whistle. Definitely like him in the late first, early second round...

The new Bayesian draft model is nearly ready for prime time. Before I launch the full tool publicly, I need to finish describing how it works. Previously, I described its purpose and general approach. And my most recent post described the theoretical underpinnings of Bayesian inference as applied to draft projections. This post will provide more detail on the model's empirical basis.

To review, the purpose of the model is to provide support for decisions. Teams considering trades need the best estimates possible about the likelihood of specific player availability at each pick number. Knowing player availability also plays an important role in deciding which positions to focus on in each round. Plus, it's fun for fans who follow the draft to see which prospects will likely be available to their teams. Hopefully, this tool sits at the intersection of Things helpful to teams and Things interesting to fans.

Since I went over the math in the previous post, I'll dig right into how the probability distributions that comprise the 'priors' and 'likelihoods' were derived.

I collected three sets of data from the last four drafts--best player rankings, expert draft projections (mock drafts), and actual draft selections. In a nutshell, to produce the prior distribution, I compared how close each player's  consensus 'best-player' ranking was to his actual selection. And to produce the likelihood distributions I compared how close each player's actual selection was to the experts' mock projections.

Theoretical Explanation of the Bayesian Draft Model

I recently introduced a model for estimating the probabilities of when prospects will be taken in the draft. This post will provide an overview of the principles that underpin it. A future post will go over some of the deeper details of how the inputs for the model were derived.

First, some terminology. P(A) means the "probability of event A," as in the probability it rains in Seattle tomorrow. Event A is 'it rains in Seattle tomorrow'. Likewise, we can define P(B) as the probability that it rains in Seattle today.

P(A|B) means "the probability of event A given event B occurs," as in the probability that it rains in Seattle tomorrow given that it rained there today. This is known as a conditional probability.

The probability it rains in Seattle today and tomorrow can be calculated by P(A|B) * P(B), which should be fairly intuitive. I hope I haven't lost anyone.

It's also intuitive that "raining in Seattle today and tomorrow" is equivalent to "raining in Seattle tomorrow and today." There's no difference at all between those two things, and so there's no difference in their probabilities.

We can write out that equivalence, like this:

Bayesian Draft Prediction Model

Let's say you're a GM in need of a safety. You really like Ha Ha Clinton-Dix (FS Ala.) but are unsure if he'll still be on the board when you're on the clock. Do you need to trade up? How far? What if you're a GM with a high pick and would be willing to trade down if you're still assured of getting Clinton-Dix? How far down could you trade and still get your guy?

I've created a tool for predicting when players will come off the board. This isn't a simple average of projections. Instead, it's a complete model based on the concept of Bayesian inference. Bayesian models have an uncanny knack for accurate projections if done properly. I won't go into the details of how Bayesian inference works in this post and save that for another article. This post is intended to illustrate the potential of this decision support tool.

Bayesian models begin with a 'prior' probability distribution, used as a reasonable first guess. Then that guess is refined as we add new information. It works the same way your brain does (hopefully). As more information is added, your prior belief is either confirmed or revised to some degree. The degree to which it is refined is a function of how reliable the new information is. This draft projection model works the same way.