You’re down nine points and your defense has earned a 4th and 1 at the opponent’s 35 yard line. Time to get the ball back, right? Hold on. There’s a flag on the offense that could push them back 11 yards. The catch is the defense has to execute another down. The normal play is to make the opponent punt and take the ball.
Not if you’re Mike Tomlin.
Tomlin was questioned for this decision that occurred early in the third quarter against the Jaguars when he accepted the penalty and gave the leading team one more chance at a first down. Turns out from a mathematical point of view Tomlin’s decision was a neutral one, but given the deficit and how well his defense was playing, it was a pretty good bet.
To get underneath the decision we need to establish some baseline tools. One of those tools that’s been around for nearly 50 years is a metric called Expected Points. From any point on the field the number of points expected to be scored next can be calculated. A team on the 3 yard line is expected to score 6 points on average and a team 97 yards from the goal is expected to score -2 relative to the opponent. There’s pretty much a linear connection between those two points.
Further work has been done that breaks that curve into the four possible downs and that analysis can be found here. That data plus play-by-play data for the last nine seasons will form the basis for the analysis of Tomlin’s decision.
First let’s look at the 4th and 1 situation and where the Steelers were likely to get the ball. Using the play-by-play data the average starting field position of the opponent following a clean punt by the offense can be seen in the following chart (removing blocked punts from the equation for the purpose of simplicity and the fact that the Steelers almost never block a punt).
Mike Tomlin expected his team to get the ball roughly at the 24 yard line had he declined the penalty. Now let’s look at what that outcome was worth to him.
The above charts represents three different models and one that includes the down of the play. The Steelers were looking a first down at their own 24 yard line, 76 yards from goal, which model of focus claims is worth about 0.8 points.
But by accepting the penalty Tomlin opened the door for a wide swing in outcomes. Over the last nine seasons teams faced with a 3rd and 11 situations convert about 26% of the time, including penalties on the defense that result in first downs. In those cases the offense gains 19 yards on average. That outcome would have put the Jaguars on the 43 yard line and would have given put them in a situation where they were expected to score about 2.2 points.
The other 74% of the time the opponent gains just 1 yard on average and punts. The expected outcome in that situation is that the Steelers would get the ball back at their 33 yard line.
By Tomlin betting on his defense he was poised to earn 9 yards of field position. Those nine yards of field position are worth about 1 point.
If you multiply the probability of the outcomes by the expected points of each outcome (26% by -2.2 and 74% by 1.8) the result is 0.76, which is essentially the same as the 0.8 points Tomlin would have gotten had he declined the penalty. It was a neutral decision in a normal situation.
But given Tomlin was losing and therefore wanted to increase volatility of outcomes, and Blake Bortles has completed just one pass more than 11 yards in the game so far, there was a clear reason to take the gamble. Turns out the result was better than he bargained for. A T.J. Watt sack took the Jaguars back another 8 yards and the resulting punt put the Steelers at their 39 yard line, and 2 point next score advantage. Tomlin’s decision ultimately created 1.2 points.
A more detailed analysis that considers more outcomes with smaller probabilities would result in an even more accurate assessment, but at a high level Tomlin acted reasonably with situation he was given.
Steelers ended up winning the game by 4 points, so the decision was not the difference. Ben Roethlisberger was intercepted on the resulting drive and turned that 2 point advantage into a -1 point issue anyway, but what seemed like a reckless gamble was more likely a well measured decision by coach Tomlin.