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:

PI1

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:

PI2

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:

PI3

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):

PI4

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:

PI5

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.