Run Offenses vs. Run Defenses
I am satisfied with the method I used to calculate fantasy pass and run defenses from last week, but that’s only the first step. Just because a defense has been effective in stopping the run or pass does not guarantee that trend will continue. Now, I need to test whether the average difference in fantasy points allowed by a defense can actually improve the projection of an offense’s production over its own averages alone.
To do so, I ran two sets of regressions. The first set compares each team’s rolling one-year average production in rushing yards, touchdowns, and fantasy points to their actual rushing yards, touchdowns, and fantasy points in the subsequent week.
As you would expect, there is a positive relationship between an offensive team’s average rushing yards entering a week and its actual rushing yards in that week. However, like so many things in football, the correlation is weak.
The correlation between a team’s average rushing touchdowns and its actual rushing touchdowns in that week is even weaker, but there is a positive relationship. So rushing touchdowns aren’t entirely rooted in luck. If you are confused why this scatter plot looks like horizontal stripes, it is because teams cannot score fractional touchdowns.
When you put those two together in standard fantasy points, the positive relationship continues to exist and the strength of the correlation falls somewhere in between. Keep in mind that this test deals only with rushing yards, so whatever receiving yards and touchdowns each teams’ running backs accumulate are not considered.
That first set of tests establishes the baseline. The second set applies a defensive adjustment to the offense’s rolling-one year averages with the method I used last week, and then it does a similar comparison to actual rushing yards, touchdowns, and fantasy points in the subsequent week.
It looks like the defensive adjustment made a difference. When I used only an offense’s average rushing yards to predict its rushing yards in the subsequent week, I saw an r-squared of 0.05. The addition of the defensive adjustment to the offensive average boosted that r-squared to 0.08 for rushing yards.
For rushing touchdowns, the improvement of the model was smaller. The r-squared increased from 0.02 to 0.03 when I added the defensive adjustment. However, that is still an improvement.
Combined in fantasy points, the r-squared of the model increased from 0.04 to 0.07. Applying the defensive adjustment to an offense’s rushing averages did a better job of predicting its actual production in that subsequent week.
Based on these results, I will consider a team’s opponent when I create my weekly running back rankings. Next week, I’ll apply these same tests to see if defenses have a similar impact on passing performance.
Scott Spratt was named Newcomer of the Year by the Fantasy Sports Writers Association. He also writes for RotoGraphs and contributes to ESPN Insider as a research analyst for Baseball Info Solutions. Feel free to ask him questions on Twitter – @PFF_ScottSpratt