Run / Pass Play Selection: First Down (Part 2)

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:

First Half

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).

Run plays work a bit better in passing scenarios (and a bit worse in running scenarios), but it's not an overall strong bias.  And you can see why I included both average and median run yardage per play, averages are universally higher than median values.  It's pretty easy to understand, long-yardage runs weight the average higher.  So while on average the yards per run play is around 4-5 yards, the odds that a run play is going to be longer than 3 yards is about 50/50.  The sheer bias demonstrated above leads me to believe that average yard-per-play is kind of a meaningless statistic.  I mean, think about it this way: say it's third down with 2 yards to go.  The average run yardage is, let's say, 4 yards.  Hey, a pretty good chance at a first down.  However, that average run yardage is based on a bunch of plays that go 1 yard, and a handful of plays that go much longer.  So, on average, your run play will go 4 yards, but that's not the same thing as saying that, yes, on average, you'll convert the third down.

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.

The behavior is a little different for pass plays; the success of a pass play doesn't get that worse in passing scenarios, just more chaotic.  In running scenarios, I assume that teams aren't going for long passes. Below I combine the two graphs, average and median pass yardages (assuming, of course, that an incomplete pass is 0 yards).

So if you kind of squint at the data, median yardages for both pass and run plays falls around 3-4 yards.  And this makes sense, generally the run / pass play ratio is 50%, I assume if there was a bias in run / pass yardage that one would be more prevalent than the other.  And finally, this is all for first down; my next posts will cover second and third down.