June 25, 2021

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The Curious Case of Correlation Between Pass and…

4 min read
The Curious Case of Correlation Between Pass and...


Guest column by Lau Sze Yui

We all know the football analytics talking points: “Running backs don’t matter,” or “establishing the run is meaningless.” But the football analytics community has tended to overlook questions about the correlation of passing and rushing offense that might change the way we see the running game. A better understanding of why pass offense and run offense correlate would lead us to a better understanding of NFL analytics in general.

To demonstrate the correlation, here is a plot of passing vs. rushing DVOA from 2015-2019. There is a pretty significant trend.

Chart 1

What if there is bias in DVOA adjusting for opponent strength and situation? A similar (but slightly weaker) trend can be observed using EPA (from nflfastR) as well.

Chart 2

Here are a few hypotheses as to why this correlation is happening:


Hypothesis 1: Play-action usage leads to better passing efficiency while running the ball more.

For the correlation between passing and rushing offense, the first thing that naturally comes to mind is that teams with the better run game would “sell” the play-action better, and hence better play-action efficiency would lead to an overall increase in passing efficiency.

However, in this piece on play-action passing, Ben Baldwin shows that play-action and non-play-action passing efficiency gaps don’t change with either the frequency or the efficiency of running the ball.

Chart 3

Therefore, rushing has no relationship with “selling” the play fake.


Hypothesis 2: Defenses will have more defenders in the box against a good run offense and hence will give up more yards to passing.

One of the best ways to stop a running game is to send more defenders into the box, but that may hamper pass defense performance. In 2019, for example, the Kansas City Chiefs led by Patrick Mahomes faced the fewest average defenders in the box while having the best passing efficiency. The graph below also shows that when there are more defenders in the box, passing efficiency increases and rushing efficiency decreases as expected.

Chart 4Chart 5

However, on a team level, this trend just vanishes:

Chart 6Chart 7

As a result, the hypothesis that it is the number of defenders in the box that leads to correlation between passing and rushing offense is not supported.


Hypothesis 3: Offensive linemen who are good at pass-blocking are also better at run-blocking and boost both passing and rushing offenses.

It is straightforward thinking that offensive lineman can affect both passing and rushing. However, it is hard to prove with evidence, since the charting of offensive linemen by various companies does not go very far and may not be adjusting correctly for team-level performance.

By using historical sack rate and DVOA data, it is possible that we can build a proxy of offensive line strength and compare it to passing and rushing efficiency.

Chart 8Chart 9

Unsurprisingly, sack rate is more strongly correlated to passing offense than to the running game. To give a comparison, passing offense efficiency can be roughly divided into sack rate, interception rate, completion rate, and yards per completion. Here is the correlation of those other three metrics to team rushing DVOA:

Chart 10Chart 11Chart 12

As shown above, a positive passing metric (i.e., higher yards per completion, higher completion percentage, and lower interception rate) leads to a better rushing offense. However, the data span across more than three decades and the variance of sack rate is larger due to generational differences. Therefore an alternative approach is to calculate the single-season correlation between sack rate and rushing DVOA so we can see how it evolves over time.

Chart 13

The R^2 coefficient is about 0.05, which is pretty mild. As a comparison, here is the plot with other passing metrics:

Chart 14

Looking at all four metrics, a perhaps surprising result is that interception rate actually has the highest correlation to rushing DVOA, while sack rate has the lowest. Still, a low correlation of sack rate to rushing DVOA does not imply that offensive linemen don’t matter since a good blocking lineman can decrease interceptions by allowing less pressure to the quarterback.

To conclude all the points above, neither play-action nor defender count seems to be the culprit explaining why passing offense is correlated to rushing offense. Rushing offense seems to affect all facets of the passing game and sacks actually have the lowest correlation to rushing DVOA. Therefore, the best conclusion so far seems to be “passing and rushing are correlated because both are based on the performance of offensive linemen,” but it’s still not exactly clear and needs further work in the future.

Lau Sze Yui studies sports analytics in his spare time and can be found on Twitter @903124S.


https://www.footballoutsiders.com/stat-analysis/2020/curious-case-correlation-between-pass-and-rush-offense

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