By Brian Burke
Before you read on, what do you think the break-even yardage is? What do you think most coaches think it is?
The first criteria we'll use is simple first down probability. Offenses go on to convert 1st and 20 situations 46% of the time. For to go distances that the defense can expect to allow a conversion on 2nd down less often than 46% of the time, they should normally decline the penalty. According to this criteria 2nd down and 13 situations are generally converted 44% of the time, meaning it's probably a good idea to decline whenever the 1st down loss is 3 or more yards.
We can also evaluate the question using a more advanced tool--Expected Points (EP). EP could be useful because it considers field position and factors in things like the likelihood of turnovers. For instance, a 1st and 20 may force the offense to pass more often, giving the defense and enhanced opportunity for a turnover.
We'll need to translate (shift) the EP curve to account for the difference in field position. A 1st and 20 at the 50, and a 2nd and 13 at the 50, are not our choices. It would have to be a choice between 1st and 20 at the 50, and a 2nd and 13 at the defense's 43 to be consistent. The chart below slides the 2nd & 13 line to account for the 7-yard difference. In this comparison of EP values across all field positions, the 1st & 20 situation has the same or higher EP value than for the 2nd and 13, meaning the defense should usually prefer the 2nd and 13. This includes the outer field goal range area, when a defense would most prefer to set the offense back in terms of field position.
So how do coaches fare in reality? I suspected that coaches would overvalue yards and undervalue downs (like they typically do), meaning they would accept the penalty taking the yards but giving back the down to the offense. It turns out they do pretty well. The chart below shows the proportion of offensive holding calls declined according to the yardage lost on the play. The data includes 874 plays outside field goal range (the 35) which did or would have resulted in a 10-yard enforcement from the line of scrimmage. At the 3-yards-lost mark, coaches declined the penalty exactly 50% of the time.
Next, we'll look at 2nd downs.