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# The Monday Mathematical: YPC Redux

Let’s put some of last week’s figures in context, shall we?

In last week’s installment of The Monday Mathematical, we talked about Jalen Hurd, Alvin Kamara, and how to interpret the “average” carry for each back.

One of the observations was that the median may be a better representation for a typical result on any given play. While Alvin’s median 2015 carry of 5 yards bested Jalen’s median 2015 carry of 3 yards, it was accurately pointed out in the comments that we need additional data points to put those numbers in context.

Enter Week 2 of the Monday Mathematical.

# So...how do those numbers compare?

Using play-by-play data put together by some enterprising soul on the internet (which, honestly, bless you, my man), I was able to expand last week’s analysis to look at every running back in the nation in 2014 (2015’s data set was incomplete, though I will use it below). I limited the analysis to backs that had a similar workload to Alvin and Jalen, which I calculated at 100 or more carries. In 2014, that came out to 167 backs across FBS.

Let’s start by looking at the means of those backs and where Jalen and Alvin would fall.

Looking at this confirms some of what we discussed last week: Jalen’s figures put him toward the lower end of heavily used running backs while Alvin shows up more favorably. Put another way, Jalen’s mean was better than only 23.4% of the 167 most used backs in 2014; Alvin’s mean was better than 84.4% of the 167 most used backs.

That’s nice context, but I said last week that we should be looking at the median carry. So how do our favorite backs look on that dimension?

This finally gives us the context we wanted for Jalen’s median carry of 3 yards last year. It’s the most common median out there, with 50.3% of the most-used runners in 2014 hitting that mark. Alvin, on the other hand, still looks great. No back exceeded his median carry of 5 yards, and it was only hit by the top 4.2% of ball carriers.

We can now start to craft a story based on what we’ve seen in the last two articles. Hurd being roughly middle of the pack on his median carry while being in the lower third on average yard per carry suggests that his distribution is pretty tight. He may bust the occasional long run, but he’s not necessarily a home run threat (which jives with 2.25 years’ worth of what we’ve seen on the field). Kamara, on the other hand, looks more consistent and more explosive.

That’s largely what we concluded last week, but I still haven’t addressed one of the most obvious concerns: the two are used differently. So let’s take a look.

# Unleashing the krakens

Using the 2015 version of the above play-by-play data, we can look at the down and distances in which we ran both backs last year. The data cuts off after UGA, so this only covers the first half of the season, but the carries were distributed evenly compared to the whole season and we’d played some tough opponents already. It should work for our purposes.

Let’s start with a simple look at how Kamara’s 52 carries and Hurd’s 137 carries were distributed across downs.

Jalen’s carries skewed toward first down while Alvin’s were distributed evenly across 1st and 2nd downs. This suggests that Jones and Debord were likely to start a set of downs with a Jalen run and then react accordingly based on the result.

This doesn’t definitively answer the question of whether or not Kamara had the benefit of getting the ball in draw type scenarios where a longer run might be more likely, though, so let’s get a bit more granular by bringing distance into the picture, as well.

Looking at this chart, I think you’d be hard pressed to assert that Kamara just gobbled up garbage yards. A larger share of his carries came on 2nd and medium, but there wasn’t a single 3rd and 10+ draw called. In general, all of the numbers we’ve looked at for Alvin seem to have come through the course of the offense in a distribution that doesn’t differ wildly from Hurd.

Yes, you could argue that Hurd’s higher percentage of 3rd and short carries where the defense largely knows what’s coming caps his upside, but at 8% of his overall carries, that probably doesn’t explain the entire difference.

# No time to explain, let me sum up

I didn’t go into this exercise anticipating Hurd being cast in such a harsh light, but the numbers we’ve looked at in the last two weeks suggest the offense could be improved by reallocating some of Hurd’s touches to Kamara. It’s something that Debord has hinted at and that Justin lamented in last week’s Most Important Vol.

All that to say, there are plenty of caveats to this, as well. I haven’t considered the passing game at all, there’s been no analysis of the offensive line, I haven’t touched on how the defense adjusts depending on who’s in the game, and this doesn’t quantify Hurd’s ability to turn a 1-yard loss into a 2-yard gain. All of those things matter when looking at the success of a running back.

That said, if we want to beat Florida for the first time in a dozen years, I’ve got a simple suggestion: give Kamara the ball. A lot.