Pass rushers can disrupt an offense’s plan in a number of ways, most obviously by sacking the Quarterback.  More and more, though, the public has realized that there are other ways to disrupt the offense, without actually getting a sack.  Quarterback hurries and hits have appeared in television broadcasts for a few years now, and SI’s Greg Bedard is suggesting a new, yet unnamed stat, that would credit players for assisting in a teammate’s sack, for example.

Interestingly, he also rewards players for drawing holding penalties, something I’ve only previously seen on advanced stats sites.

The average sack sets the offense back by about 6 yards (it was 6.4 yards lost per sack in 2012 according to ESPN) and costs a down, while the holding penalty costs 10 yards with no loss of down.  So how does a holding penalty measure up against a sack?  Which is more valuable to the defense (or put another way, when an offensive lineman gets beat, should he hold his opponent, or allow the sack)?

For this analysis, I am using the Expected Points metric from the excellent Win Probability Calculator on Brian Burke’s Advanced NFL Stats site.  I’m also only going to look at 1st-and-10 situations, since they are the most common, but I recognize that things may be different on 3rd downs.

The chart below shows the loss in a drive’s Expected Points after a sack or holding penalty.

We see that a sack always sets the offense back more than a holding penalty, despite only being a 6-yard loss (again, on average).

What is interesting, is how the relationship between a sack and hold changes.  Most obviously, a holding penalty is a lot less damaging deep in an offense’s own territory, due to the half-the-distance rule.  In these cases, the offense in not actually penalized 10 yards.  A sack is only slightly more damaging than a hold penalty around midfield, likely due to the neutrality in field position, and inside the 10-yard line, likely due to a high field goal make rate.

I also find the spike in a sack’s impact between an opponent’s 10- and 40-yard line to be interesting.  My hypothesis is that somewhere around the 25-yard line (where this spike peaks) is where a few yards can make the biggest difference in field goal success rate.  After a holding penalty (rather than a sack), the offense has an extra play to make up the 4-yard difference, which can usually be done (in 2012, Arizona had the league’s worst yards per play, at 4.1).

This hypothesis is backed up by the another metric on the WP Calculator – 1st Down Probability.  When it’s 1st and 10 at an opponent’s 25-yard line, a holding penalty gives the offense a 39% chance of converting a 1st down, while a sack gives them a marginally smaller 38% chance.  I think the rest of the gap in EP is due to using the extra down to get in better field goal position.

So, when rewarding drawing a holding penalty, how should it compare to a sack?  It seems too complicated to change the value of the drawn penalty based on field position, so to simplify things, we’ll just use this fact: a holding penalty’s impact on expected points is, on average, 78% of a sack’s impact.  It seems that Bedard has it right when he gives a player 0.75 points for drawing a hold.