When the first play of an NFL game is a pass, the second play is more likely to be a run

It’s no secret that American football lags behind several other sports in its perceived ability to use statistical tools. But in my opinion, one of the most obvious aspects of the game that demands more attention lies in predicting the play-calling of an opponent. Knowing whether or not an opponent is likely to run or pass can make an important difference in terms of both play-calling – should you blitz? should you expect a screen? – and in terms of how aggressive certain defenders should play.

In that regard, I figured it was worth a quick investigation. In this post, I’ll suggest that the link between one play call and the next, at least early in a game, is a bit stronger than I thought it would be.

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The importance of a run-pass balance is a common football narrative. And because coaches want to appear balanced between the run and the pass by the end of a game, they may also feel the need to appear balanced between the run and the pass in small samples of plays. If a coach calls three run plays in a row, he may fear looking too committed to the run-game, or, even worse, too predictable for the defense.

Of course, it’s not just football. If it exists, an evening up of play types would reflect more general human misconceptions rooted in probability. It’s why when we play rocks-paper-scissors, we rarely use the same throw three times in a row. If you aren’t gonna throw rock after throwing rock-rock in rocks-paper-scissors, you probably aren’t gonna run after calling run-run during a football game. And a similar bias also impacts sport officials. In the NHL, for example, referees calling violations on one team are more likely to call the next penalty on that team’s opponent, no matter the game’s score. Just like coaches want to appear balanced, so too do referees.

While a large-scale predictive model of opponent play calls would be one of the first things I would do as an NFL team analyst (see this example or this one), it may not be the most straightforward way to look at whether or not coaches even up play calls. In particular, decisions made as the game progresses are particularly tied to the score. And from my perspective, although the approaches shown in the links above include a term to test for an autocorrelation of play calls, the exact effect remains unknown.

To reduce the impact of other play and game characteristics, I’ll start as simple as possible, by only looking at a team’s first few offensive plays in a game.

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Per usual, I’ll use the play-by-play data provided by Armchair Analysis, which includes each play from 2000-2015. To limit the effect of field position, I only included drives that started between the 10-yard lines, and I dropped penalties to focus on the remaining runs and passes.

Here’s a chart of run percentages on each team’s second play, varied by the play-type of the first play. The error bars account for our uncertainty in each probability estimate.

Screen Shot 2016-12-02 at 9.49.18 PM.png

Teams run more often after they pass, and they do so significantly more often – an absolute difference of about 12%. On a relative scale, teams are about 25% more likely to run when their first play was a pass.

That said, savvy readers may have picked up on the fact that if rushes and passes were to result in different types of second plays (e.g, different yards to go), such a comparison wouldn’t make sense.

But we can look closer. Here’s the same chart above, faceted by the down and distance of the second play (2nd & short: 3 yards or less, 2nd & medium: 4-6 yards, 2nd & long: 7 yards or more).

Screen Shot 2016-12-02 at 9.57.48 PM.png

For 2nd & shorts (bottom right), there’s no obvious difference in the likelihood of running based on the initial play call. Teams tend to run the ball here.

Among other play types – in particular, on 2nd & medium and 2nd & longs, there remains a significant difference in how an offense calls its plays given what it just called. On 2nd & longs, for example, teams rushed 44% more often (an absolute difference of 19%) after passing on first down. That’s an enormous effect.

Of course, there may be other things at play. Perhaps teams failing at one play type (rush or pass) feel the need to try another play type (pass or rush) on the second play. But if you’re feeling the need to vary your play calls based on the first play of the game (literally, that’s the only play on the x-axis), that’s a whole other issue to write about.

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But we can also go just beyond the game’s first two plays. Here’s a histogram of the number of rush attempts using the first four offensive plays for each team in each game. The red bars reflect what we’d expect if teams were to pick four play types (runs and passes) out of a hat (using a run type probability of 49%); the black bars reflect what we see in the data.

Screen Shot 2016-12-02 at 10.34.51 PM.png

The higher black bar in the middle highlights that in the first four plays of the game, coaches make more of an effort to call exactly two runs and two passes (about 46% of the time) than what we’d expect due to chance (37% of the time).  Along similar lines, while we’d expect about 13 in 100 sequences of four plays to include all rushes or all passes, that only happened about 7 in 100 times in the data. Altogether, this matches our conclusion from above; coaches are a bit more balanced than we’d expect them to be if they were randomly dialing up plays.

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Offensive play-callers are probably better at designing plays than we give them credit for. Schemes are enormously complex, and the amount of detail that goes into a gameplan can be awe-inspiring.

But during a game, when faced with split-second (well, 40-second) decisions, it’s natural for those same play-callers to revert to predictable tendencies. In the case of the above evidence, it appears more likely that, all else being equal, runs are more likely to follow early-game passes and passes are more likely to follow early-game runs.

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