## Statistical In-Ferentz: The P-Word

Horace E Cow

Iowa punted on 4th and 1 with less than five minutes left in the fourth quarter against Indiana. We examine whether the coaches made the right call.

I doubt many fans want to dissect the corpse that is a loss to Indiana, but there was one particularly interesting malignancy on the body that deserves special attention. You all know what I'm talking about: that punt in the fourth quarter. Iowa was down three with 4:43 to go in the game and had a 4th and 1 on their own 28. Given the amount of time left in the game and the success of Indiana's offense in the second half, my instinct was for Iowa to take the risk and go for it, but what do the Win Probability numbers say?

According to the Advanced NFL Stats model, Iowa had a .16 WP going into that fourth down. A conversion to, let's say, the 30, would have raised their WP to .35, for an increase of .19 WP. A failure would have been costly, dropping Iowa's WP to .05, or a decrease of .09 WP. Alternatively, a punt to Indiana's 32 (which is what happened) would have kept Iowa's WP at .16. If we call Iowa's probability of making it p, then we can figure out how confident they would have needed to be to go for it by solving the simple equation:

.16 = .35p + .05*(1-p)

.11 = .30p

p = .37

In other words, if Iowa thought it could make that one yard 37% of the time, they should have gone for it. The Advanced NFL Stats 4th down calculator agrees, although it puts the break-even probability at 38% for some reason. Whether you think Iowa should have gone for it depends on your confidence in their fourth down offense. Iowa had struggled to run the ball up the middle, which might have contributed to their hesitancy to go for it, but of course they still could have passed the ball and possibly taken Indiana's defense by surprise for a big gain.*

* Kirk Ferentz said after the game that he had planned to go for it by hurrying to the line, but changed his mind once the officials stopped play to measure the yardage. Presumably, Ferentz was hoping to go with a quick quarterback sneak (a favorite of his on short yardage situations). I'm not a huge fan of that play, both because the rush seems to lead to just as much confusion on Iowa's line as the opposition, and because there's limited upside on the play (unlike a play-action pass). However, if that is the play that Iowa is committed to on fourth and short, I can understand their reluctance to go for it.

So from a WP perspective, the message is pretty clear: if Iowa had even meager confidence in their ability to get one yard, they should have gone for it. Another way to look at the problem, though, is to consider what Iowa would have needed to happen to get the ball back with a reasonable amount of time left. On average, Indiana's drives prior to that point had taken about two minutes and covered 39 yards (although that includes the zero-yard, five second "drive" that consisted of Christian Kirksey's pick-six). So if Indiana had just met their averages, they would have moved the ball from their own 32 to Iowa's 29, and the clock would have run down to 2:45. If we assume that Indiana would run the clock down as much as possible, however, their 3-4 first downs (i.e. about 10 plays) would have taken closer to five and a half minutes (assuming Iowa took its two remaining time outs) and would have ended the game.

As things stood, Indiana played it safe, moved the ball 20 yards on nine plays (before a deliberate delay of game to set up a punt) and took 4:25 off the clock. They didn't quite match their averages for the day, but they came pretty darn close. So if Iowa had simply assumed that Indiana would do exactly what they had done all day (at least in terms of yardage and first downs), they could have known that they would get the ball back with little or no time left on the clock, deep in their end of the field. As it was, they got the ball back with 18 seconds left at their own 20, with no timeouts, and not surprisingly were unable to score.

The decision to go for it must have been predicated on a belief that Iowa's defense could force a three and out. That was the only scenario (barring a catastrophic turnover by Indiana) that would have given the Hawks the ball with a reasonable amount of time to score and decent field position. Even giving up one first down to Indiana would have run the clock down by about three minutes and led to a punt to Iowa's 20 yard-line. Given how Iowa's defense had played against Indiana on the day, that mindset seems excessively optimistic now. Going for it on fourth down would have been a risk, but relying on the defense to get the ball back in an expeditious manner was an equal (if not greater) risk.

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