# Why Zero RB Works: Quantifying Positional Injury Rates

Training camp is finally here. In a few weeks we’ll even have actual football. I’m pretty damn excited. Yet alongside all the noise and activity that accompanies this time of year there’s also a wretched, unshakable sense of impending doom.

Each time I check the news I unconsciously gird my loins knowing that one of my players might have just broken his ankle, tweaked his hammy, or dislocated the majority of the fingers on his hand. It happens every year. And every year it makes me want to kick a kitten. Injuries suck.

If you’ve listened to the latest Fantasyland podcast on Predictions, you know that a big part of making accurate projections is using base rates to anchor things. For instance: What is the probability that a wide receiver gets injured in a given year? What is the probability a running back gets injured? Basic stuff, really. Yet the answers are surprisingly hard to find.

There are other questions: Does age play a role in injury rates? What about usage and volume; how do they affect things? And most of all for Zero RB advocates, do RBs really get injured more than WRs? And if so, how much more often?

The answers might surprise you.

## Injury Rates for WRs and RBs are even?

The biggest problem with injury data is that very little of it is public. Probably the best and most comprehensive database is the one maintained by Football Outsiders (FO). Unfortunately it is proprietary. Thankfully, late last year Zach Binney wrote a great four-part series summarizing their data. The articles can be found here, here, here and here.

The chart above from FO shows injury rates by position from 2000-2014, and the results are pretty surprising. Running backs, tight ends and wide receivers all appear to have the same risk of missing at least one week of the season due to injury.

Interestingly, while the bars are hard to read, it does appear that RBs have a higher percentage of injuries that could be deemed “serious.” About 17-18 percent of injuries for RBs fall into the “greater than four weeks lost to injury” category, while WRs appear to see 15-16 percent of injuries persist that long.

Still there are problems with this data. First, we don’t really have any idea what effect age has on injury rate. We also don’t have a good grasp on what effect player usage^{1} has on injury rate. The FO injury rates were derived using all players on a 53 man roster, per team, per year in the sample as the denominator. Surely starters are at greater risk of injury than bench players. Finally it would be nice to put some confidence intervals around these injury rates.

## Age ain’t nothing but a number

Using data from mangameslost stretching from 2009 to 2015 that I cleaned and cross-checked with injury data from KFFL/USA today, I ran both Poisson and Zero-Inflated Poisson regressions on the data set with a dummy “injury occurred” value as the response variable.^{2}

Zero-Inflated Poisson (ZIP) is typically used in risk statistics studies when analyzing injuries and other binary outcomes with many zeros.^{3} I found no statistically significant relationship between age and injury for NFL wide receivers using either the Poisson or ZIP method.

This doesn’t mean that no relationship exists between age and injury. I simply wasn’t able to find one. If you graph injury rates by age using FO’s data, you can see a spike in injuries at age 30-32, which seems to match our intuition about injuries and aging.

This is then followed by a fairly steep reduction in injury rate for players that continue to play past the “age cliff.” I found roughly the same graph using the 2009-15 data. Overall though, injury rates are pretty constant across ages.

## Bootstrapping confidence intervals

With age out of the way we can turn to the effects usage has on injury rates. By adding ADP data to the sample^{4} and eliminating all but the top 80 WRs by draft position, we can do a decent job controlling for players who actually see snaps.

From this new sample of 560 player seasons I took 5000 random samples with replacement, and calculated the mean and 95 percent confidence interval for those 5000 samples.^{5} Then I did the same for the top 70 RBs by ADP.

## RBs Get Injured More often than WRs

Injuries are becoming increasingly common in the NFL. It’s likely that somewhere between 42-50 percent of draftable WRs will miss at least one week due to injury. The story is slightly worse for RBs. It’s likely that somewhere between 45-54 percent of draftable RBs will miss at least one week to injury.

A t-test shows that the means are **extremely**^{6} unlikely to be equal, so we can say convincingly that RBs do in fact get injured more frequently than WRs – so long as they see a reasonable amount of snaps on the football field. Moreover, the relative risk of choosing a RB over a WR is right around 1.07, or seven percent riskier.

Again, this was all just the risk of missing one or more games. Now let’s look at serious injuries, which are conventionally defined as injuries that cause a player to miss four or more games. These are the injuries that are the real sticky wicket in your path to victory.

## Running backs are far more likely to get seriously injured

More bootstrapping, this time on “serious” injury rate. Serious injury rate simply means that if you did get injured, what is the likelihood that the injury caused you to miss four or more weeks? As you can see from the table below, this time there is a much larger difference between WRs and RBs.

Running backs are anywhere from 24 to 31 percent more likely to come up lame from a serious injury than a wide receiver. These numbers are supported by some excellent work done over at Dynasty Football Factory by Jeremy Funk. Jeremy’s work and our dialogue on Twitter was very helpful in shaping the design of this study, and I encourage you to read his stuff over at DFF.

Again, a t-test shows the means are almost certainly different. If you graph the two distributions you can see that some sampled means do overlap. Probability distribution curves like this are useful for visualizing how often values occur in a sample. The x-axis on the chart is injury rate and the y-axis (“Density”) is the probability that the corresponding injury rate is in the sample. The area under each of the two curves must equal 1, or 100%.

If we integrate the area where the two probability density curves overlap we get approximately 15 percent of samples being equal. While making inferences from this is fraught for a whole host of reasons,^{7} I’m fairly confident in saying that in any given year RBs will very likely have a higher serious injury rate than WRs.

## What about running backs taken in high leverage rounds?

At the suggestion of RotoDoc, I looked at just RBs and WRs taken in the first five rounds of fantasy drafts. Twenty-four RBs and WRs were taken on average in the first five rounds of drafts from 2009-2015, so I trimmed the sample to 168 player seasons for both positions and bootstrapped the mean injury rates as before. The results were eye opening.

While the non-serious injury rate for WR stays relatively constant, the non-serious injury rate for RBs skyrockets. The relative risk for RBs in the first five rounds is 31-45 percent higher than that for WRs. And when we look at serious injury rates, things just go bananas.

WRs drafted in the first five rounds are actually * less* likely than the rest of the WR population to suffer a serious injury. Meanwhile RBs drafted in the first five rounds continue their upward trend, and are far

*likely than the RB population to suffer a serious injury. When combined, these two results cause the relative risk of choosing a RB in high leverage rounds to balloon to a ludicrous 200-360 percent more than choosing a WR.*

**more**If we graph the two distributions as before, we can see that the overlap has almost completely disappeared. Therefore we can say with great confidence that in a given year RBs will see a higher serious injury rate than WRs. Moreover, the difference in the serious injury rate between the two positions is likely to be enormous.

## Conclusions

The takeaways from looking at WR and RB injuries are the following:

- The probability of getting injured and missing a game is fairly even across the league and across positions when looking at the
*entire*player population. Over 45 percent of NFL players at non-QB fantasy relevant positions are likely to miss time to injury. - Age doesn’t appear to be a reliable predictor for WR injury.
- Running backs do indeed get hurt more than wide receivers when usage is taken into account.
- Fantasy relevant (top 70 positional ADP) running backs are anywhere from 24-31 percent more likely to incur serious injury than fantasy relevant wide receivers (top 80 positional ADP).
- RBs drafted in the first five rounds are 200-360 percent more likely to suffer a serious injury than WRs. This is a large reason why Zero RB works as well as it does. When running backs go down, and you’ve invested high draft capital in them, you stand a strong chance of losing four or more weeks of production.

Recommendation: Draft for depth and go Zero RB in all formats.

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- In other words, players that play more snaps. (back)
- Among other nice features, Poisson regression allows you to work with error distributions that are non-normal. (back)
- In this case the zeros represent healthy seasons – approximately 54 percent of the sample – and ones represent that an injury occurred. (back)
- ADP data is from My Fantasy League. (back)
- The validity of bootstrapping relies on the assumption that the population that we are trying to estimate – NFL receivers – is effectively represented by our 2009-2015 sample. If that assumption is satisfied, then taking smaller random samples from our larger 2009-2015 sample will let us estimate the true value of WR injury rate. After comparing the 2009-15 data to the larger FO sample, I’m comfortable saying this assumption is satisfied. (back)
- The p value is indistinguishable from zero. (back)
- For example, this calculation is not really the correct way to approach the problem, the integration is very sensitive to the bandwidth setting used on the density function (in this case, 2), etc. (back)

Great article. Thanks for the hard work on this one

Awesome. Thank you. I have always been a little confused with the football outsiders data. It makes sense that the injury rate is low because they are including all the RBs sitting on the sideline.

Thanks very much JLags!

@dkpsports It confused me as well. Glad it helped.