### Using Chaos Theory to Simulate the 2013 NFL Draft

#### by Jerome's Friend

Mocking the NFL Draft accurately is an impossible task. There are an infinite number of variables to consider, including the many unknown human elements involved in the actual draft day decision making process. After all, who can know exactly what is happening inside the Chip Kelly/Howie Roseman/Tom Gamble collective? In essence, the NFL Draft can be mathematically defined as “chaotic” and therefore subjected to explanation by Chaos Theory.

Oddly, the mathematic definition of chaos is not entirely explicit. According to Tabor (1989), a chaotic system is one “whose outcomes are very sensitive to initial conditions.” And according to Rashband (1990), “We often say observations are chaotic when there is no discernible regularity or order.” There are indeed initial conditions that affect the outcomes of the Draft, like team needs, college stats, combine results, etc., and these initial conditions help our attempts at prediction. However, there is no semblance of order, no predictive algorithm that aids prediction when the Draft system is active. Quite the contrary, it is utter chaos. Just ask Mike Tice. Unfortunately, Chaos Theory can’t help predict Draft outcomes either. It can however, help explain them.

Let’s assume for a moment that there are two primary decisions that fuel a team’s draft pick. The first is to make a decision based on team need, the second is based on the best player available. If we assume that the rate of change (or error) between these two decisions is relatively small, and we were to graph what that would look like from the start of the draft to the end, it might appear to be something like this:

At the beginning of the draft there is more variance, and as time increases, the variation between the two possible decision points decreases. This could be because there are less players to choose from as the draft progresses and thus less room for error. However, if we increase the rate of change (error) just a little bit, the graph of the Draft as time goes on will look like this:

In this scenario there is less variance at the beginning of the draft, but that variation increases more quickly with time. However, the differences between drafting based on need and best available is still consistent. In other words, there does not exist a lot of chaos. These two scenarios represent close-to-ideal circumstances, and even then, accurate prediction is not possible without error. More representative of what actually occurs in the draft is illustrated if we push the rate of error to its upper limit:

What you get is the equivalent of white noise. Some picks have low variation, others have large, but it is utterly unpredictable. There are some hits, some misses. Once you think you identify a pattern, there is an element that throws you off. And that is the essence of Chaos Theory. Small differences in initial conditions (and each successive pick in the Draft can be defined as a point of initial condition) create huge differences in outcomes (the butterfly effect). There is no mathematical formula that can tell us what any one pick (x) can be at any specific time (t). But… that doesn’t mean we can’t try.

Rather than mock the Draft, we can try running a simulation (or multiple simulations) using the principles of Chaos Theory (and mocking the simulation is still obligatory). The simulation is relatively basic (relative when compared to real life… it was rather difficult to make work). Each team’s decision at each pick is based on two primary, random variables: picking based on draft need, or picking based on the best player available. That decision will be a result of two random numbers. If the first random number is greater than the second, then the team will pick based on need, otherwise they will pick the best player available. In any given draft simulation, there will be an aggregate variance between the total number of picks based on need and the total number of picks based on the best available, but if the simulations were run infinitely, that ratio would reach a 50/50 limit. Also, in order for the simulations to work, they required an overall prospect ranking (courtesy of CBSSports.com) and a ranking of each team’s need by position (gleaned and modified from Walterfootball.com). In this regard, the results are still somewhat subjective. Regardless, using these parameters I ran five draft simulations simultaneously in Excel and came up with these first round results (five simulations because the formulas involved are either volatile or use up a bit of processing power):

According to these results, Kansas City’s first pick of the draft four out of five times is based on the best (top) player available, and only once did they select based on their primary draft need (DE). The Philadelphia Eagles selections are based on need three out of five times, when they are able to take Dee Milliner. Otherwise their selection was Damontre Moore. Here are the complete simulation results for the Eagles:

Even though the top five picks across each of the five simulations are relatively consistent, I should note that there is even further variation when the simulations are run ten, fifteen, twenty times and so on. For example, some additional simulations have the Eagles selecting Chance Warmack, Bjoern Werner, and Luke Joekel, depending on the “decisions” made by teams before them. Further variations can be made when the prospect rankings and team need priorities are adjusted, but these make the results no less interesting to look at.

Granted, there are more variables at play than a mathematical coin flip can determine. Ultimately though, Chaos Theory demonstrates that the NFL Draft cannot be predicted. The Draft is simply too chaotic a mathematical system that relies too much on uncertainty (in fact, that’s a principle). But this isn’t anything new. Thousands still try to predict outcomes and fail to varying degrees, but hell, that doesn’t mean it ain’t fun.

***If you would like to play around with the simulation, here you go: 2013 NFL Draft Simulation.*

*You can follow Philly’s Inferno on Facebook and Twitter (@JeromesFriend). Jerome’s Friend is not a mathematician, just an Eagles fan.*

One large variable that can’t be accounted for is the miscalculation of players value either by the team (see Tim Tebow) or by the collective body (see Tom Brady or Vince Young). This element can’t really be normalized greatly increases variation. However, your absolutely right that the player to player variation seems to reduce deeper into the process and there is likely a threshold within the draft where teams will place more weight on best available versus team need.

That was a fun way of looking at the draft, and would be interesting to see how a statistically significant (~30?) number of runs would average out and compare…at least to the 1st round…I bet you’d be close!

Thanks brotha! Yeah there is definitely that subjective element in there. Also, forgot to mention in the article, but I can’t account for trades. Maybe I’ll run this a series of times and come up with an ADP for each player. Does this “fantasize” the actual NFL?

Rather than modeling the exact player selection, perhaps you can find greater order in the selection of players by position, or position group. It might be more deterministic based on team needs and perceived positional value. Then, which player within the position group is modeled as a truly random variable.

Hmmm… Well, in these simulations, if it’s determined that a team is drafting based on need, then the formulas refer to the team need table, where team needs by position are ranked. Whatever the first, unsatisfied position is, the formulas refer to the top ranked player in that position left on the board. Is this what you’re referring to? If not, then you might be on to something, but I’m not quite sure I get it.

Don’t try to match the exact names, try to match the portfolio of position groups out of the first three picks.

The Eagles need OT, S, and CB in their first three picks.

Forget trying to match which specific ones they will pick.

Ok… gotcha. So, for example, if the Eagles were to draft based on need (rather than best available overall), then instead of looking at players in their highest ranked position of need, instead look at players in a group of positions of need. Then take the best player available from that portfolio of position groups. That might be doable. Great suggestion.

[…] Using Chaos Theory to Simulate the 2013 NFL Draft | Philly’s InfernoMocking the NFL Draft accurately is an impossible task. There are an infinite number of variables to consider, including the many unknown human elements involved in the actual draft day decision making process. After all, who can know exactly what is happening inside the Chip Kelly/Howie Roseman/Tom Gamble collective? In essence, the NFL Draft can be mathematically defined as “chaotic” and therefore subjected to explanation by Chaos Theory. […]

Isn’t this similar to what they do at drafttek.com?

It’s possible. I’ve never heard of them but will definitely check it out. Thanks!

I don’t really understand the graph, like how do you derive it and what exactly are the axes? Would it be ok if you give a more detailed description/explanation? Thanks!

Hi Autumn… Great questions. The graphs illustrate a logistic map, with increasing rates of growth/decay over time. It’s often used as a simple example of chaotic behavior. Here, I use it to illustrate the variation of draft choices over time, as the rate of growth, or in this case, the complexity of the decisions, increases. For more basic info on logistic maps, and the formula used to graph, check out this wiki:

http://en.wikipedia.org/wiki/Logistic_map

This is great! Thank you

What is the Excel Password, Jerome?

Some things I cannot divulge! 😉 But DM me on twitter @jeromesfriend.

And also check out my follow up to this: http://www.highphive.net/2013/04/03/simulating-the-2013-nfl-draft-with-more-chaos/

New model with 1,000 sim runs and ADP. And I have an updated file there.