# A Monte Carlo Simulation of the Usage of Vikings Running Backs

I know we’re all sick of running back timeshares.  They are extremely difficult to project and can cause havoc on our draft selections. Realistically it feels impossible to be able to quantify a range of outcomes for participants when you consider random events such as injuries or game script…

…until now.

I set out to create a model of select RB committees using a Monte Carlo simulation. My goal was to give a range of outcomes for the participants’ total usage over the course of each game in a season based on two major components: injuries and game script. For the initial model, I looked at the Vikings backfield with Adrian Peterson and Jerick McKinnon. I thought this would be especially interesting since Peterson is a popular fade at his high second-round ADP in favor of McKinnon, who saw his snaps increase towards the end of 2015.

## Injuries

Injuries are generally a random variable. At any given time, a player could absorb a big hit and suffer a concussion that causes him to miss three weeks. At other times, that same player can be right back in the huddle two plays later unscathed. You even have players who drop their cell phones without injury versus the ones who break their elbows doing so. The point being that injuries are very hard to predict.

Sports Injury Predictor has attempted to quantify injury risk via their algorithm. They predict an eleven percent injury risk for Peterson and six percent for McKinnon. Admittedly, I am a bit unsure of what these numbers actually mean. The best interpretation I could come up with is that it is the risk of the player suffering “any injury in any given game.” In other words, an injury counts the same whether it is a torn ACL or simply getting the wind knocked out of you.

The numbers intuitively make sense. If Peterson is eleven percent and McKinnon six percent to get hurt in any one game, then we can calculate the odds of an injury-free season to be 15.5 percent and 37 percent respectively using the binomial distribution. Jason Phelps reaffirmed this when he recently posted a graph on Twitter showing that the average starting running back has an injury-free season somewhere between 15-20 percent of the time, putting Peterson around the league average.

So I set up two different random number generators for injuries. The first is the risk the player gets hurt in a given game, which is a distribution centered around the SPI game estimates. The second RNG is the severity of the injury, only if the player gets hurt in that game (sometimes a player gets hurt and misses one week, sometimes an injury ends his season, etc.). There is then a separate input that gives the other RB a certain percentage of the injured player’s rushing and receiving share when that player is out. This is mostly a guess, so I tried keeping a sufficiently wide range of outcomes. You can read this as, “If Peterson is out, then McKinnon would see between 50-90 percent of his rushing snaps with an average of 70,” and so on.

## Game Script

McKinnon has been a hot name this year because he saw a big uptick in snaps in the final six games of 2015. The Snap Report shows McKinnon saw just 11 percent of the total snaps before week 11 but 22 percent afterwards. This came at Peterson’s expense as he went from 69 percent to 60 percent.

I didn’t have data available for how many of these snaps were for passing downs versus rushing downs, but a linear regression on snaps showed that Peterson probably saw around six to seven times as many rushing downs. I tried to use this as a baseline estimation for my model.

This table is the distribution of snaps each player could see in any given game.  The ultimate goal in estimating this was to come up with the same weighted range the two players saw over the final six games of 2015.  The weights come from the team’s distribution of run vs. pass. In 2015, this was 51 percent rushing, but I gave it some cushion in case Minnesota decides to pass a little more or less this year.

## Results

Let’s start with the injuries.  The results of the simulation saw Peterson miss an average of 4.1 games per season and 2.3 for McKinnon. If that sounds high, then keep in mind that it is right in line with the league average that Jason Phelps researched. I also set up markers on the charts to show the percentage of games missed between 0-2 games, 3-8 games, and 8-16. We see Peterson actually has a 16 percent chance of missing more than 8 games – the same chance he has of having no injuries.

Here is the distribution of who played more games in each trial. McKinnon (right) plays more games 50 percent of the time while Peterson (left) played more in 39 percent (the middle interval is when they play the same number of games).
Below are the cumulative distributions for the total percentage of snaps each player played in the season. We see McKinnon on average comes up to 27.6 percent from his 22 percent at the end of last season while Peterson crashes down to 50.8 percent from 60 percent. Note that 60 percent of the time McKinnon sees a higher percentage of snaps than he saw at the end of last season, while Peterson only increases in 31 percent and actually drops below 50 percent share in 39 percent of trials.  So Peterson has a better chance of dropping below half the share than he does in seeing an increase from last season.

The most interesting takeaway is just how many snaps Peterson is losing on average. Granted, this is not a surprising result considering the starter has more snaps to potentially lose than the backup will, but even I did not expect to see him lose almost one-sixth of his snaps on average. Peterson projects to be average for injury risk for a starting RB, but this model is agnostic to age. If you believe in the “age cliff,” then the results may actually be worse than they appear since an older player may be more susceptible to injuries over time. Take this as you will, but I have completed over forty MFL10s and still have yet to draft Peterson.

As for McKinnon, I am intrigued. The model found him to see 22 percent of the rushing snaps and 33 percent of the pass snaps on average, but that latter number might be low since the Vikings say they plan to use him more in that role than they did last year. He could also benefit from a change in team splits, as the Vikings were the third run heaviest team in the NFL last year in terms of percentage of snaps.

One flaw in this model is that it is not tracking when a “promotion” would occur. We see McKinnon gets 40 percent of the seasonal snaps 16.4 percent of the time, but we don’t know when those snaps are coming. For instance, there could be seasons where McKinnon plays 40 percent of snaps after Peterson misses Weeks 2-10, but then returns for the higher equity fantasy weeks. Then there could be trials where Peterson only misses three weeks, but they happen to be the fantasy playoffs.

In that sense, the numbers could be deceiving from a fantasy perspective since timing is everything. We can’t really use this to call McKinnon a “potential league winning pick” per se. However, I think we can safely look at these results and say McKinnon is on the rise since he sees a five percent uptick in snaps just on inertia alone, with the potential to see more if the team makes larger changes in its overall passing distribution, plans to use him even more than they did after his promotion at the end of 2015, or if Peterson happens to age poorly.

## Epilogue

This model was largely experimental as it required a lot of estimation on my part. However, I still think there is a lot of utility in this type of study since the simulation by design encompasses a wide range of uncertain outcomes. I will be curious to see how severely the results differ for other RB battles, especially as we look at backs with different types of skill sets. With that said, next time I will bring Tevin Coleman and Devonta Freeman into what I have dubbed “The RB Battle Simulator” and see what we can learn about Atlanta’s backfield.