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Why is 3rd-and-2 a passing down?

Posted by Doug on May 24, 2006

Let's start with just theory. No data.

On 3rd-and-anything, shouldn't the leaguewide success rate on runs and the success rate on passes be roughly equal? On say, 3rd-and-3, if running plays succeeded 70% of the time and passes succeeded only 53% of the time(these are made up numbers), then wouldn't teams start to run the ball more often on 3rd-and-3? Then the fact that teams were running more than they used to in that situation would cause defenses to expect more runs and fewer passes, which would cause them to gear their defenses more toward stopping the run, which would cause the success rate on runs to go down and the success rate on passes to go up.

How far would the success rate on running plays go down? It seems to me it would go down --- and the success rate on passes would go up --- just until the point where they are the same. If the success rates on the two kinds of plays are the same, then offenses don't have any incentive to shift their play-calling mixture. Thus, defenses don't have any reason to shift their expectations, and the success rates should stay the same. Equilibrium.

And we should stay in that equilibrium until the system gets a shock from outside. A rule change that favors the run over the pass (or vice versa) could throw it out of balance. A new play-calling innovation in one aspect of the game could do it.

But even then, we should rather quickly settle down into a new equilibrium. Imagine, for example, that everything is cruising along with a leaguewide 3rd-and-3 success rate of 58% on both runs and passes. Now some hotshot defensive coordinator creates a new scheme that allows defenses to achieve standard 3rd-and-3 pass coverage while at the same time making it very difficult to run the ball. Such an innovation would spread throughout the league, and would generally make running on 3rd-and-3 much less attractive than it used to be. Say the passing success rate stays at 58% while the running success rate drops to 40%.

If you're an offensive coordinator and you can succeed 40% of the time with runs and 58% of the time with passes, what are you going to do? You're going to pass more. The defense will notice this and will start to play the pass a bit more, which will open the run back up a little. But as long as the pass is more profitable, offenses should shift from running to passing. As long long as offenses are shifting from running to passing, defenses will adjust accordingly and make the pass less profitable. As soon as the pass is no longer more profitable than the run, all this shifting stops. Equilibrium.

I was using 3rd-and-3 as an example, but the same reasoning should apply on 3rd-and-anything. On 3rd-and-5, for example, the run has a chance to succeed largely because of the surprise factor, so runs will only succeed if they aren't tried too often. Therefore, it may be an 80/20 pass/run mix that achieves equal success rates. On 3rd-and-1, it may be a 30/70 mix. I am not saying that the number of runs and passes should be equal in any given situation, just that the success rate on runs and passes should be equal.

[I should probably stop short of saying 3rd-and-anything. On 3rd-and-16, for instance, teams use the run as a sort of pre-punt to try to improve their field position rather than as an instrument to pick up the first, and my theory isn't applicable.]

Anyway, that's how it ought to be in some sort of idealized world with perfect information and rational choices and homogeneous teams whose only goals are to get the immediate first down or to stop the other team from doing so. In the real NFL, however, this is how it plays out. This is 2003--2005 data.

Rush (success rate) Pass (success rate)
(3rd-or-4th)-and-1 76.5% (71.5%) 23.5% (53.9%)
(3rd-or-4th)-and-2 41.6% (57.1%) 58.4% (48.9%)
(3rd-or-4th)-and-3 25.5% (55.9%) 74.5% (51.8%)
(3rd-or-4th)-and-4 19.2% (50.2%) 80.8% (47.1%)
(3rd-or-4th)-and-5 15.8% (38.1%) 84.2% (42.1%)

To make sure we're clear, the second line says that on 3rd-and-2 (or 4th-and-2) during the past three seasons, teams have passed the ball 58.4% of the time and run it only 41.6% of the time. When they've passed, they've picked up the first 48.9% of the time. When they've run, they've picked it up 57.1% of the time.

The data fits the theory fairly well on 3rd-and-3, 4, and 5. But it's not even close on 3rd-and-1 and 3rd-and-2. That brings us to the title of the post: why is 3rd-and-2 a passing down? An alternate title might be, why does my theory stink so bad?

Maybe my theory doesn't stink, but the pace of innovation casuses the equilibria to be so short-lived that they can't be captured with a 3-year snapshot.

Maybe my theory doesn't stink, but the equilibria show up at the team level and not at the league level. This would be tough to verify, as the sample sizes get pretty smallish if you look at things one team at a time. For the record, here are the three-year average run/pass rates and overall success rates on 3rd-and-2:

TM R/P ratio ConvRate
dal 62 / 38 44.2
den 60 / 40 52.3
buf 59 / 41 44.4
car 54 / 46 50.0
sdg 52 / 48 52.1
nwe 52 / 48 65.5
sea 48 / 52 66.0
stl 46 / 54 38.0
pit 46 / 54 47.5
atl 46 / 54 49.1
jax 45 / 55 54.7
sfo 44 / 56 40.0
nyj 44 / 56 50.0
min 44 / 56 58.0
bal 43 / 57 50.8
mia 42 / 58 54.2
nor 40 / 60 67.3
chi 40 / 60 52.7
hou 40 / 60 49.1
phi 40 / 60 53.5
ari 39 / 61 57.1
ind 39 / 61 52.9
oak 39 / 61 63.3
cin 39 / 61 70.5
was 38 / 62 55.1
kan 37 / 63 58.1
nyg 36 / 64 53.3
cle 35 / 65 40.0
gnb 35 / 65 57.8
ten 28 / 72 44.0
tam 20 / 80 43.1
det 11 / 89 44.3

Are you kidding me Steve Mariucci? You're passing 89% of the time on 3rd-and-2?

I always thought running was standard procedure in short yardage, and I always thought 2 is short yardage. Yet teams pass more than they run on 3rd-and-2. This would make sense if teams were having more success with the pass on 3rd-and-2. But they're not. Why are teams passing in a running situation even though it's not working?

It is possible that the success rates are skewed in favor of the run because of quarterback run-pass option plays or unplanned scrambles. That is, quarterbacks on such plays tend to run only if they know they can get the first, and throw it away otherwise. This would cause the successes to get counted as runs and the failures to get counted as passes, even though it's the same play. But there can't be enough of those plays to make too much difference.

Maybe teams are interested in more than just the immediate first down. On 3rd-and-(1-or-2), 7.3% of pass plays went for 20 more yards, while only 2.4% of running plays did. Maybe, contrary to David Romer's findings, teams will trade in a surer chance at a 2-yard first down pickup for a chance at a long gainer.