## Run/Pass Distribution by Win Probability

One question that came about as a result of Saturday's very modest attempt at fantasy football analysis -- a question particularly in the wheelhouse of the present site -- concerned the relationship between run/pass distribution and game situation. Because we know that a team with a lead will try to use the game clock to its advantage -- and because, with few exceptions, the run is the best way to maximize time of possession -- it follows that a team with a lead will call more run plays. This idea is nothing new.

What I haven't seen before, however -- and it could very well be from a lack of looking -- is an illustration of the precise relationship between run/pass distribution and in-game win probability (WP).

Thanks to Mr. Brian Burke, that thing now exists, right here, in table form (numbers from 2006 though Week Eight of 2011):

And here, once again, in graph form:

In fact, as we would have guessed, there's a rather strong relationship between pass percentage (as a percentage of total plays) and WP. Run/pass distro evens out in the 0.80-0.90 range and then skews run-heavy in the 0.90s. Teams with less than an 11% chance of victory are considerably more likely to go down field in an attempt to score quickly.

The Indianapolis-Tennessee game from Week Eight bears out this relationship. For most of the first half, the teams were fairly even. Tennessee was winning, but the Colts maintained a WP of at least 0.20 through most of the second quarter. The Titans scored a couple times right before the end of said quarter, however, bringing the Colts' WP down to 0.05 by the end of the half. The Colts' WP never exceeded 0.11 for the rest of the game, and they ultimately lost 27-10.

While literally every football game is a tale of two halves, the Indy-Tennessee game was particularly a tale of two halves -- the first, a mostly competitive game; the second, a blow-out.

The play calling of the two teams is just as we would expect, too, given the above table/graph combo. Consider the following (pass percentages in parentheses):

FIRST HALF

Indy: 32 plays, 11 runs, 21 passes (66%)

Ten: 36 plays, 14 runs, 22 passes (61%)

SECOND HALF

Indy: 45 plays, 15 runs, 30 passes (67%)

Ten: 29 plays, 17 runs, 12 passes (41%)

FINAL

Indy: 77 plays, 26 runs, 51 passes (66%)

Ten: 65 plays, 31 runs, 34 passes (52%)

Given the single-game samples, there's bound to be some error regarding run/pass mix by WP, but we can see the broad strokes, at least: in the more competitive first half, the play-calling between the teams was fairly similar; in the less competitive second half, Tennessee ran almost 60% of the time, while the Colts kept passing. In the end, Tennessee had both the higher percentage and higher raw total of rushing plays.

Not all games work out so nicely, of course -- the week before, for example, Indianapolis lost 62-7 to New Orleans while only attempting passes on 23 of their 46 plays (50%) -- but the Indy-Tennessee game is more the rule than the exception.

This relationship between run/pass distro and WP has some interesting implications. For example, if I asked you whether the Packers were a running or passing team, what would you say?

The best answer, of course, would be "It depends."

In terms of raw play-calling, the Packers are pretty neutral. This season, the average NFL team (through Week Eight, at least) is averaging 63.6 plays on offense, 26.6 of which are runs and 37.0 (58.2%) of which are pass plays. The Green Bay Packers, for their part, are averaging 62.6 plays (again, through Week Eight), 26.0 of which are runs and 36.6 (58.4%) of which are passes.

So, in terms of outcome, the Packers have been a neutral team, basically in line with NFL averages.

The thing is, through the first eight weeks of the season (seven games plus a bye week), the Packers were undefeated* -- and spent the vast majority of the game clock ahead of their opponents. In fact, on average, the Packers first reached the 0.91 WP point just three minutes into the second half of games one through seven -- meaning, even if they didn't hold that level of WP over every play for the entirety of the second half, that they were generally in a very comfortable place, with the game clock very much on their side.

* And remain undefeated, turns out, after beating San Diego on Sunday.

As with most teams, the Packers exhibit a tendency towards the run as their WP increases. The following table illustrates this. (Note: the Packers only reached the 0.11 WP mark twice in Weeks One through Eight -- both running plays against the Falcons).

Here's that information in graph form (minus the two data points from 0.11 WP, which were effing with the best-fit line):

(Before we continue, one note on the Green Bay numbers: they represent "intended plays," which includes plays nullified by penalty. So, for example, a pass interference call doesn't go down officially as a pass play, even if it certainly was a pass-play call. That might alter the ratios a little bit.)

From these Green Bay numbers, we see that, in the middle ranges of WP -- from 0.41 to 0.61 -- the Packers are calling passes about 70% of the time. That's about 10-15% more often than league average. However, as noted above, the Packers spent large stretches of their first seven games in the 0.91-1.00 territory of the WP graph. Because of that, the Packers' run/pass distribution has appeared average, even if they've profiled as a pass-heavy team under "normal" football conditions. And it's likely that, in future instances -- if and when the Packers find themselves in more competitive games -- that their run/pass outcomes will more closely resemble what we see in their run/pass distro from the middle ranges of WP.

For fantasy owners, this information could be important. Games that are projected as blowouts by the Weekly Game Probabilities could very well visit the extremes of run/pass distribution for the team involved -- the winning team running more often than usual; the losing team, passing. For those in need of last-minute pick-ups, this could serve as a tool for extracting value from freely available talent. Whether this suspicion is borne out in fact, that will have to remain an issue for another post.

Thanks to readers Boston Chris and Albert Lyu for their early feedback on the fantasy stuff from Saturday.

### 8 Responses to “Run/Pass Distribution by Win Probability”

1. DSMok1 says:

This is excellent research. The distribution looks like it fits a cubic curve.

2. Boston Chris says:

Awesome article, Carson!

3. James says:

I agree with DSMok1 - I think a curve is more appropriate than a linear approximation as the tailing off at both ends is likely real. I'm impressed by the turnaround time on this article!

Also, this is off-topic but did anyone read Peter King in MMQB on Strahan vs Ware's sack rate? He adjusted for the number of passing plays each player saw in 2001 and 2011 respectively to determine which season was more impressive, which is a great start. Unfortunately he didn't take into consideration the overall declining sack rate (a ~13% decrease from roughly 7.5% sacks per dropback in 2001 to 6.5% in 2011), which makes Ware's identical 3.97% sack rate much more impressive.

Then again, Strahan did it over an entire season while Ware's only done it for 8 games. But even if Ware finished with just 21 sacks that would be more impressive than Strahan's 22.5 once you consider the total number of dropbacks and "sack rate environment" (assuming Ware continues his pace to see 604 dropbacks).

4. Brian Burke says:

There may be more attempts these days but a lot of them are un-sackable--bubble screens, etc.

5. Steven says:

I wonder whether this shows up in success rate. For example, if the team with the ball is way up, they should call more running plays than is optimal in EP terms, and the defense should anticipate more running plays, so I would expect that the passing plays that do get called would be more effective - and the running plays less effective - than they would otherwise be.

6. Sampo says:

If running is used mainly to control the clock, a success rate based on the win probability added could tell us more.

Brian, have you ever run the numbers for a WPA SR?

7. bigmouth says:

The next time some idiot says Win Probability is useless as a stat, I'm pointing them to this post. Great stuff, Carson.

8. notque says:

Can you give the distribution for NFL average? I'd like to implement these numbers into my football game.

I don't know how to generate win % perfectly, but I can probably use some rough guesses of time left, and number of points behind.

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