As I talked about in my previous post, the run / pass play ratio (for first down, as you can read in the title) depends on field position, time remaining, and point spread. The field position aspect seems to vary pretty independently; no matter what was the point spread or time remaining, the run / pass play ratio was pretty much that curve you can see below. Time remaining was only a factor in the second half, and for the last two minutes of the first half. Also, the relationship of the run / pass play ratio to the point spread depended on time remaining (but again, only in the second half and final two minutes of the first). If you look at all the curves in my previous post, 0.50 is the midpoint of everything, midfield, 0 point spread, lazy time in the first half, so my predicted run / pass play ratio (for a given scenario) started there. So through trial and error, here's the model I came up with:
Predicted Run / Pass Play Ratio = 0.5 + f(Field Position Factor) + f(Point Spread)
Second Half (and Last Two Minutes of the First)
Predicted Run / Pass Play Ratio = 0.5 + f(Field Position Factor) + f(Time Remaining, Point Spread)
f(Field Position Factor) and f(Time Remaining, Point Spread) were both second-order functions. If anyone's really interested I can show the numbers.
So the question I posed last time was, do run plays work better in pass scenarios, and vice versa? I have a graph below, showing the average and median run yardage, plotted up against the predicted run / pass play ratio (from all my formulas above).
For pass plays, I have two graphs, one is the incompletion rate (per predicted run/ pass play ratio), and the other is average and median pass yardage, assuming it's a completed pass.