On Monday, I took a stab at forecasting the leaguewide Adjusted Net Yards per Attempt (ANY/A) for 2015. Something I should have mentioned is that I still consider myself a novice at both time series analysis and R programming. Much of the motivation for this series is simply to practice — in an NFL analytics context — what I’ve learned this offseason. Therefore, any feedback is welcome.

With that piece of business out of the way, today’s post will focus on forecasting the leaguewide offensive environment for stats that contribute to fantasy football scoring at quarterback. For all analyses, I used the same methods I used on Monday.

# Passing Yards

The Autoregressive Integrated Moving Average (ARIMA) model that best fits the trajectory of passing yards per game per team (Y/G/T) since 1979 is a random walk (RW) without drift. As the name implies, this result suggests that the passing yardage environment in 2015 is unpredictable, i.e., it will be a random deviation from the 236.8 Y/G/T it was in 2014.

If you’re disappointed by that result, join the club. The good news, however, is that this crime has a prime suspect: The upward trend of Y/G/T that seems to exist today began in 2005. And if we use 2005-2014 to calculate the Y/G/T forecast rather than 1979-2014, then the model switches from a random walk to a differenced, first-order autoregression (AR) with drift; i.e., now 2015 *is* predictable.

In the graph below, I’ve plotted a) actual Y/G/T from 1979 to 2014;b) forecasts for 2015-2019 based on the above-described, dueling models; and c) each model’s 95 percent confidence interval (AR in white; RW in grey):

The two forecasts don’t just differ in terms of their actual values for 2015-2019; they also differ in their forecasting errors (aka confidence intervals). The AR model (2005-2014) has a consistent confidence interval over time **(from 242.8 ± 4.7 in 2015 to 258.1 ± 7.2 in 2019)**, while the confidence interval for the RW model (1979-2014) gradually widens over time **(from 236.8 ± 15.5 in 2015 to 236.8 ± 34.6 in 2019)**.

Granted, this is a simply byproduct of the underlying math, but the divergent results imply that one’s preference for one or the other boils down to answering the following questions:

- Is the predictable, intuitive AR model more trustworthy than the random, counterintuitive RW model even though it’s based on two-thirds less data?
- If so, then what offense-changing leaguewide event during the 2005 offseason (or so)
*caused*a divergence in the trajectory of Y/G/T from then on?

Personally, I don’t have a good answer to the second question, and so I remain skeptical — even though my gut tells me the AR model based on 2005-2014 will be less wrong going forward.

# Touchdowns

My ARIMA for touchdowns per team per game (TD/T/G) based on 1979-2014 suggested a simple exponential smoothing (SES) model without drift. Akin to Monday’s result for leaguewide ANY/A, this result means that the biggest influence on TD/T/G in 2015 is 2014’s deviation from expectations.

But here’s the thing: This finding presents a problem for our answers to the Y/T/G questions at the end of the last section. Why? Because, if it was indeed the case that something happened in 2005 to cause a leaguewide shift towards increased passing *yardage*, then we would expect that same “something” to have also caused a shift towards increased passing *touchdowns*. And yet, I found the opposite: Relying on the past 10 years makes future Y/T/G more predictable, whereas it makes future TD/T/G more random.

Of course, previous research I’ve done showed that yardage rates are more reliable measures of passing performance than TD rates, so maybe this is just a case of a bad apple spoiling the bunch.

In any event, I did the work, so I’ll report the 2015 forecasts for both models:

- Based on 1979-2014, the forecast for leaguewide TD/T/G is 1.55 ± 0.16 in 2015, with that range gradually expanding to 1.55 ± 0.24 for 2019.
- Based on 2005-2014, the forecast for leaguewide TD/T/G of 1.58 ± 0.18 in 2015, with that range expanding is 1.58 ± 0.39 for 2019.

# Interceptions

Luckily, we don’t have any of these which-model-should-I-trust issues for interceptions per game per team (INT/G/T). Focusing only on 2005-2014 shat out utter dog shit for results, which maybe (?) gives a hint about the Y/T/G and TD/T/G models we should trust. In contrast to dog shit, the 1979-2014 data set produced a pure platinum egg called “the damped SES model with drift.”

This is the third passing stat in the past two posts for which my ARIMAs have uncovered an SES model. (The two previous were for ANY/A and TD/T/G.) What’s new about INT/T/G, however, is that this particular SES-based forecast for 2015 not only depends on how much the 2014 rate deviated from expectation; it also depends on how much *the 2013 rate* deviated from expectation. Put simply, if you want to know what this year’s INT/T/G is likely to be, look at the leaguewide average over the past two seasons.^{1}

Getting down to brass tacks, here’s my model’s forecast of INT/T/G over the next five years:

**In 2015, it’s likely to be 0.92 ± 0.11. In 2019, it’s likely to be 0.84 ± 0.15.**

# Applying The Above to Fantasy Football Projections

For the purposes of my own fantasy projections this year, I’m inclined to trust the 2005-2014 version of the Y/T/G model and the 1979-2014 versions of the TD/T/G and INT/T/G models. Specifically, I’m projecting the average NFL game in 2015 to include **242.8 (± 4.7) passing yards per team, 1.55 (± 0.16) TDs per team, and 0.92 (± 0.11) INTs per team**.

Translating that into standard Footballguys scoring,^{2} **my models project the average NFL team to score 17.4 passing points per game in 2015, or 278.7 points over 16 games**. And, to be faithful to probabilistic inference, I’ll place a range around that exact forecast: 263.0 on the low end; 294.5 on the high end.

# DT : IR :: TL : DR

This year’s leaguewide passing yards per game appears to depend on last year’s value and a short-term upward trend; leaguewide touchdowns per game seems random; leaguewide interceptions per game appears to depend on values for the last two years. Using these findings, I’ve forecast the average NFL team in 2015 to score 278.7 ± 15.7 fantasy points via the passing game.