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By The Numbers: Rushing Efficiency

Spoiler Alert: the Browns aren't very good at it.

Benny Sieu-USA TODAY Sports

As some people may remember, I took a stab at evaluating running back efficiency a few years ago. The basic idea was to come up with one number to describe how well a particular running back produced for their offense. I've done this by focusing in on two different but (I believe) equally important parts of running the ball. The first is simple, how dependable is a given running back? This is represented by Success Rate, the percentage of plays where a running back makes the minimum gain necessary for "success." It's explained in detail by Football Outsiders here, but here's the basics of what's considered a success:

In general, a play counts as a "hit" if it gains 40% of yards on first down, 60% of yards on second down, and 100% of yards on third down.
If the team is behind by more than a touchdown in the fourth quarter, the benchmarks switch to 50%/65%/100%.
If the team is ahead by any amount in the fourth quarter, the benchmarks switch to 30%/50%/100%.

What you may notice is that there's no "extra credit" for breaking a big run. This is simply a measure of consistency. A back who always picks up exactly two yards on third and one will have a perfect success rate. Meanwhile, a back who breaks half of his third down attempts for long touchdowns and gets stuffed on the other half will have a 50% success rate. But is that first scenario really preferable to the second? I don't think so.

That's what brings us to part two: how many explosive plays is a back making? For this, we'll turn to an old standby, yards per attempt. Analysts commonly use YPA as a measure of consistency, and in theory that makes sense. But in practice, YPA tends to be dominated by long runs, which are relatively rare events. Because of this, YPA tends to be a better indicator of explosive play ability than consistency. It's not perfect for what I'm trying to do here, but it will do.

Last time, I had a convoluted formula for combining these two statistics. The issue is that they are on very different scales, so simply averaging the two isn't a smart idea. Instead of going through a few confusing steps, this time I turned to a more simple solution, the geometric mean. If your math is a little rusty, the geometric mean is defined as the nth root of the product of n numbers. The important property of the geometric mean is that it "normalizes" the data being averaged, so that a 10% change in success rate will have the same effect as a 10% change in YPA. So for any given player, I simply take the geometric mean of their success rate and YPA, and voila, Rushing Efficiency. Like last time, I wanted to turn this mean into an easily digestible value. To do that, I express each player's Rushing Efficiency (just RE from now on) as a percentage relative to that season's average across all running backs. For baseball fans, this ends up looking similar to metrics like OPS+ or ERA+. If you're still not sure what's going on here, the short explanation is that values above 100 are good, and values below 100 are bad.

With that out of the way, let's look at some results. The final table is too big to reproduce here in full, so I'll only be looking at the top ten, but I've created a google sheet that should be viewable by anyone. It includes all running back seasons from 2011 through week 10 of this season. To qualify, a running back needed 100 carries.

Player Team Year RE
G. Bernard CIN 2015 131.8
CJ Spiller BUF 2012 129.7
L. Miller MIA 2014 124.4
D. Murray DAL 2011 123.9
P. Thomas NO 2011 122.9
D. Brown IND 2013 122.4
A. Peterson MIN 2012 122.4
J. Charles KC 2014 121.1
J. Hill CIN 2014 120.9
L. Blount NE 2013


There you have it, the ten most efficient running back seasons in the past five years. Yes, you are reading that right, Giovani Bernard is in fact in the middle of the most efficient season since 2011. There are some other names on that list that might seem out of place too. For instance, Pierre Thomas, LeGarrette Blount, and Donald Brown were/are decent backs, but this good? This is a good place to remind everyone of what exactly we're looking at. First, even though I assigned these numbers to running backs, offensive lines and schemes are intimately wrapped up in there as well. Good lines can make decent running backs look great, and so can good quarterbacks or good play calling. Another wrinkle here is that I'm explicitly looking at efficiency, I have not accounted for volume at all. As a case study in why this matters, look at the difference between CJ Spiller and Adrian Peterson in 2012. RE ranks Spiller's season ahead of Peterson's, but Peterson had almost 150 more carries than Spiller, and 800 more yards overall. There's a very good reason I've avoided calling anyone "better" than anyone else here, only more efficient.

For an added bit of fun, let's see if we can do something for volume control. It turns out that the average running back carries the ball something like 180 times per season. So if I divide a back's carries by this average, I get a "scale factor" I can apply to their efficiency, and thus give some credit to backs who are true workhorses. After applying this scaling, the top ten looks like this:

Player Team Year Scaled RE
D. Murray DAL 2014 252.8
A. Peterson MIN 2012 235.6
A. Morris WAS 2012 208.9
L. McCoy PHI 2013 206.3
M. Jones-Drew JAC 2011 200.0
M. Lynch SEA 2012 197.3
A. Foster HOU 2012 190.9
D. Martin TB 2012 185.9
L. Bell PIT 2014 181.3

M. Lynch




That looks more like it. That's a who's who of all-pros and future hall of famers. Comparing this table to the one above helps make a point that's generally true across sports. As you increase usage, efficiency decreases. There are a number of reasons for this, but in football the most obvious one is that defenses adjust to stop run plays they know are coming. This makes Peterson's 2012 season all the more amazing. Defenses knew he was getting the ball, and he still produced at an incredibly efficient level. For my money, that 2,000 yard season is the best by a running back in the past five years (and probably my lifetime).

Now, this is a Cleveland Browns site, so I would be remiss if I didn't point out how our favorite rock carriers have done. Unsurprisingly, they haven't done particularly well. The Browns have had six running backs get 100 carries or more in a single season since 2011, and none of them have been above average. Three of them came close, but it's still not a pretty picture. For the most part, I don't think it's fair to pin this failure on the running backs entirely, they haven't had much help. But it would be nice if Peyton Hillis wasn't near the top of this list anymore.

Player Year RE
Terence West 2014 99.3
Peyton Hillis 2011 98.6
Isaiah Crowell 2014 98.2
Trent Richardson 2012 88.3
Willis McGahee 2013 82.5
Isaiah Crowell 2015 77.1

So there you have it, a reintroduction to Rushing Efficiency. There's a lot more that can be done with this data. Maybe in the future I'll look at how RE correlates from one year to another for particular running backs, or perhaps I could see how backs playing for the same team fare. But for now this is a good start. Let me know what you think in the comments, and let me know if you want to explore a particular question.