Continuing my series of recent posts attempting to forecast the offensive environment in 2015, it’s time to pivot towards the running game. On the menu for today are the two rushing stats that impact fantasy football scoring: rushing yards and rushing touchdowns. As always, the methods I employed for the analyses I’m presenting below were the same as the methods I used last week.

Before getting started, however, a valid question might have popped into your mind, especially if you’re familiar with my previous work on rushing stats: Why try to forecast yards and touchdowns when we already kind of know they’re statistically random over time? My possibly unsatisfying answer is that analyzing the trajectory of *leaguewide* rushing over time is a different statistical animal than analyzing the trajectory of *individual* rushing over time.

Here are three (related) reasons why I think that’s true:

- The main reason why touchdown rate (TD%) and (especially) yards per carry (YPC) are so inconsistent for individual running backs (RB) is because the majority of RBs
*never*reach the (same-team) carry thresholds at which these stats stabilize: 667 and 1,978, respectively. The league as a whole, however, runs the ball about 14,000 times per season. - If we’re going to take heed of my past research (which is a great thing to do! Thanks!), then we shouldn’t ignore my repeated findings that NFL data is multilevel. What’s “true” of individual rushing data (e.g., means and variances) may not be “true” of team-level data, or in this case leaguewide data.
- Even more fundamentally, my previous research on the randomness of box score rushing stats looked at TD% and YPC, whereas what I’m about to present looks at rushing yards per game per team (Y/G/T) and touchdowns per team per game (TD/G/T). It’s a subtle difference, but (perhaps) not an inconsequential one.

# Rushing Yards

The Autoregressive Integrated Moving Average (ARIMA) model that best fits the trajectory of rushing yards per game per team (Y/G/T) since 1979 is a differenced, first-order autoregression (AR) without drift. Below is the familiar graph:

Before contemplating the forecast for 2015 and beyond, you’ll no doubt notice that Y/T/G was on a clear downward trend from 1979 to 1994, but has since meandered upwards. This is noteworthy because it’s the opposite of how leaguewide *passing* Y/T/G has changed over time. In my forecasting post on that trajectory, I couldn’t adequately come up with a *causal* reason for why an ARIMA based on more recent seasons should be trusted over one based on all 36 seasons since the Mel Blount rule — although I leaned towards the former. Well, in applied statistical work, the above graph is what we call “a clue,” and so I should probably re-run the passing Y/T/G model based on 1995-2014.

Moving on to the forecast for 2015-2019, it’s not exactly a straight line, but it’s pretty close, and the 95 percent confidence interval (shaded in grey) is pretty wide, especially in the out years. These characteristics are due to two things:

- Related to the above discussion, there’s no current “drift” in the average rushing Y/T/G over time like there was with passing Y/T/G. It’s remained between 105 and 115 Y/T/G for two decades.
- With more leaguewide consistency comes more forecasting error.

In terms of specifics, all of this translates to the league average forecast going **from 112.2 ± 8.2 Y/T/G in 2015 to 111.9 ± 13.1 Y/T/G in 2019.**

# Touchdowns

The best-fitting ARIMA for rushing TD/T/G is the simple exponential smoothing (SES) model without drift, which just happens to be the same type of model I found for *passing* TD/T/G. Hmmm.

And here’s the graph showing the past, present, and (estimated) future of NFL rush TD/T/G:

I’ve tried my best to present this on a scale similar to that of Y/T/G, so as to not render their obvious resemblance some statistical sleight of hand trick. If I’ve succeeded at gaining your trust in that regard, then we can all agree that it’s hard to ignore that both yards and touchdowns took a shit from 1979 to the mid-90s, then rebounded somewhat for the following decade, and then plateaued in the mid-00s. I’m not sayin’, I’m just sayin’.^{1}

In terms of my model’s forecast for the next five seasons, it once again shows a flat trend with a widening range of plausible values: **from 0.77 ± 0.12 TD/T/G in 2015 to 0.77 ± 0.17 TD/T/G in 2019**.

# Applying The Above to Fantasy Football Projections

OK, so the two ARIMA models I’ve detailed here forecast the average NFL game in 2015 to include **112.2 (± 8.2) rushing ****yards per team and 0.77 (± 0.12) rushing TDs per team**. Translating that into standard Footballguys scoring,^{2} **the average NFL team will score 15.8 (± 1.5) rushing points per game this season, or 253.4 (± 24.0) points over 16 games**.

# DT : IR :: TL : DR

Given what I’ve reported previously on I//R about randomness in the rushing game, it might seem futile to try to forecast this upcoming season’s offensive rushing environment. For various reasons, it actually isn’t. To boot, it turns out that leaguewide rushing performance over the past 35 seasons appears to have followed the inverse trajectory of leaguewide passing performance.

I know right? Shocking!

With respect to fantasy football forecasting, my models suggest that the average rushing game for the average team will produce 15.8 (± 1.5) points per game.

That (not) said, as much as the two graphs

*look*the same, it bears repeating that they reflect (somewhat) different underlying processes (i.e., they’re not*mathematically equivalent*): The Y/T/G time series is best explained by autoregression (AR), whereas the TD/T/G time series is best explained by a moving average (MA). Here‘s an explanation of the subject if you’re interested. ↩0.1 points per yard, 6 points per TD ↩