Re: What the stats say about play calling: run or pass?

posted at 4/9/2014 10:24 AM EDT

In response to prolate0spheroid's comment:

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Over the past few days, I've been looking closely at NFL game stats to get a better understanding of what teams need to do to score points and prevent their opponents from scoring. The conclusion is that the key to scoring points is being productive on your passing plays, while the key to limiting your opponent's scoring is preventing them from being productive on their passing plays. While productivity in the run is not unimportant, it's impact on scoring is much weaker than the impact of productivity in passing. (I define the productivity of any play simply by the yards gained by the play.)

In comparing runs and passes it's easy to fall into the trap of thinking simplistically that passes are always more productive than runs. After all, passes average about 6.2 yards per play (taking into account sacks and incompletions), while runs average about 4.1 yards per play. On average passes are therefore 50% more productive than runs. It's not too surprising, then, that they seem to have a bigger impact on scoring. Passes are what get you the yards, and yards gained do strongly correlate with points.

While it is clearly true that passing is on average more productive than running, it's important to look beyond averages. The interesting thing about passes is that, while they *average* higher productivity than runs, more of them are complete duds. About 45% of pass plays end up as incompletions or sacks after all. To really understand what's going on we have to look deeper than the averages and start to examine how the distribution of both running and passing plays by productivity (i.e., by yards gained) looks.

Unfortunately this distribution data is impossible to find online, so I bit the bullet and went through the tedious process of looking through game summaries to collect the data myself. My sample size is relatively small--I'd go crazy spending more than an hour or so collecting and recording the data--but it's reasonable: What I did was look at the game summaries for the first 8 playoff games in 2013 and record the yards gained for every scrimmage play in the first halves of those 8 games. I only used the first-half data partly because I didn't want to spend the time to record all the plays in every game, but also because we all know that things often get weird in the second half as teams get away from their game plans either to protect a lead or try to catch up. The first half is therefore probably more reflective of what the team intends to do, and so is probably a better set of data if you're interested in understanding what teams plan to do rather than what they are forced to do. Overall, my sample includes 497 plays, split between 260 passes and 237 runs. Twelve teams are represented, four of them twice, so there's fair diversity in the data.

**The Findings**

*Running Plays*

- About 25% of runs (one in four) get just one yard or less
- Another 25% get 2 or 3 yards, so about half of all running plays get 3 yards or less
- 20% get 4 or 5 yards
- 20% get 6 to 10 yards
- Only 10% get more than 10 yards

**Passing Plays**

- About 45% of passing plays end up with zero or fewer yards
- Another 15% get 1 to 5 yards
- Another 15% get 6 to 10 yards
- Another 15% get 11 to 20 yards
- And the remaining 10% get more than 20 yards

Looked at another way, you can determine the probability of getting the "needed" yardage by run or by pass. Here's what those calculations show:

- Need 1 yard. 85% chance if you run, 56% chance if you pass
- Need 2 yards. 74% chance if you run, 54% chance if you pass
- Need 3 yards. 62% chance if you run, 52% chance if you pass
- Need 4 yards. 53% chance if you run, 46% chance if you pass
- Need 5 yards. 39% chance if you run, 44% chance if you pass
- Need 6 yards. 28% chance if you run, 40% chance if you pass
- Need 7 yards. 23% chance if you run, 35% chance if you pass
- Need 8 yards. 16% chance if you run, 32% chance if you pass
- Need 9 yards. 10% chance if you run, 30% chance if you pass
- Need 10 yards. 7% chance if you run, 25% chance if you pass
- Need 15 yards. 2% chance if you run, 13% chance if you pass
- Need 20 yards. <1% percent chance if you run, 7% if you pass

The value of the run is evident here: in short yardage situations (one or two yards) it's far more reliable than the pass. At three yards, it's still got significantly better odds than the pass and at four yards it's got slightly better odds than the pass. At five yards, the tide begins to turn, with the pass having marginally better odds. With more than five yards needed, the run's effectiveness drops off precipitously, leaving the pass with signficantly higher odds of success.

**What It Means for Play Calling**

None of the above is too surprising, but it is interesting to see the actual numbers rather than just going with our gut sense of what's right. The real interesting analysis, though, is determining what the statistics mean for strategy and play calling.

A major key to scoring is, as we saw in my earlier posts, gaining yards. (Again, nothing surprising.) Typical scoring drives need to get something like 60 or 80 yards overall and also need to be sustained by getting a minimum of 10 yards every three (or, if you're willing to go for it on fourth down, four) plays.

Advocates of running a lot will no doubt jump in here and say why not just run the ball all the way down the field. Running plays average about 4 yards and you have a 50% chance of getting four or more yards, so the odds are that you'll get a first down every three plays. Fifteen to twenty 4-yard plays will get you to the endzone. This sounds nice, but it fails to account for the fact that about half your running plays get 3 yards or less and a full quarter get 1 yard or less. There is a way of calculating the exact probabily of going 80 yards with running plays alone, but I'd have to go back and re-read one of my statistic books to recall how to set up the problem and then do all the calcs. I'm not going to bother. All I'll say is that, because so many runs go for very short yardage, there's a high likelihood that in a 60 or 80 yard drive you are going to run into several third and longs where you are going to have to pass. If you wait until third down to pass, you will become utterly predictable making it easy for the defense to defend you. So every good play caller is going to mix in passes earlier than third down to utilize them when they are less predictable.

Once we start mixing in passing plays, we end up with a different issue: 45% of them are going to be complete duds and 60% of them are going to get 5 yards or less. This means on many sequences, you're going to have to pass at least twice to get the needed yardage. The advantage of passing plays, though, is that a full 40% of them are going to get 6 or more yards and 25% (one in four) are going to get in one single swoop the full 10 yards you normally need for a first down. Nearly half your passing plays are going to be for no yardage or short yardage, but the other half are going to move you down the field at a good clip.

In actuality, most scoring drives are in the 8 to 12 play range, which means teams are averaging about 7 or 8 yards per play on scoring drives--and the only way they're reaching those averages is by being productive in their passing game. They don't necessarily need to pass a lot, but when they do pass, they typically need to get good yardage. Runs at 4 yards per play on average (and with shorter yardage fully 50% of the time) generally don't allow you to sustain drives. While you mix them in for variety in early downs and in shorter yardage situations in later downs, you generally can't rely on them as your primary way of advancing the ball. You need to be good at passing. And as I showed in an earlier post, where Super Bowl champions excel in the playoffs is (1) in being productive when they pass and (2) preventing their opponents from being productive when their opponents pass. A great running game never hurts . . . but it's efficiency in the passing game that gets you your points and effectiveness in pass defense that prevents your opponents from getting their points.

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So based on your stats it would be advantagious to pass on first downs and then pass if over 5 yards to go and run if lesss than 5 to go on 2nd and 3rd downs? Of course every game varies due to strong/weak run/pass defensive teams?