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# Statistical In-Ferentz, Iowa State: Field Goal Follies

You are the coach of a college football team, let's call it the Upper Midwest Raptor Noses. Your team is down six to the Upper Midwest State Weather Spirals with a little more than 14 minutes left in the game, and you are facing a fourth and goal from your opponent's three. What do you do?

If you kick the field goal, you cut the deficit to three, but to win the game you will still need to a) prevent the opposition from scoring, b) get the ball back, and c) score yourself. Also, if having done all that you kick a field goal, you will merely have tied the game, not won it. If you go for the touchdown, you have to weigh the upside of taking the lead against the downside of giving the ball back to the other team down six.

In the Iowa-Iowa State game, Iowa's coaching staff was faced with precisely this dilemma, and we all know what they chose: the field goal. I let out a little groan when that happened, and it seemed like the crowd in Kinnick was frustrated by the call as well. It seemed like a bad decision on the face of it, especially considering Iowa's anemic offense that day; relying on that team to not only get the ball back but actually move it in the vicinity of the endzone seemed unwise. In the event, Iowa very nearly pulled it off, thanks to a heroic James Morris interception and a semi-competent two-minute drill. But was taking the easy three points the right decision there? Luckily we have a tool to give a more definitive answer to these types of questions: win probability.

Readers of last year's Statistical In-Ferentz columns will be familiar with the concept, but if you're not, the basic idea is this: by looking at thousands of past football situations -- down, distance, yard-line, time left in the game -- smart people at sites like Advanced NFL Stats are able to create a model that estimates how likely a generic team is to win in that situation. Say you're down 21 with a half left to play and you just received the ball at your 20. According to the Advanced NFL Stats model, a generic team in that situation has a 4% chance of winning the game. The powerful aspect of this tool is that it allows you to compare the win probability (WP) before and after various situations and compare those results to the WP if you had taken a different path. To take the example at hand:

• Iowa had a fourth down at the Iowa State three yard-line with 14:20 left in the game. The WP for this situation is .34 (i.e. a generic NFL team in that situation would win, on average, 34% of the time).
• If Iowa kicks a field goal -- which for simplicity's sake we're going to assume they will make -- they will be down 3 and Iowa State will have the ball on, let's assume, their own 25 yard-line after the ensuing kickoff. The WP for Iowa State in that situation is .66, making Iowa's WP .34.
• If Iowa goes for the touchdown, on the other hand, we have to look at two possibilities. If they score the touchdown, then they will be up one point and Iowa State will get the ball back on the ensuing kickoff (again, let's assume they take it to their 25). In this situation, Iowa's WP would be .52. In other words, scoring a touchdown there would have made Iowa the favorite to win the game, but only slightly. After all, a one-point lead with 14 minutes left is hardly secure. Still, going from a 34% chance of winning to a 52% chance with one play is no small feat.
• If Iowa failed to make the touchdown, Iowa State would have the ball at their own three yard-line and a six-point lead. The WP for a team in this situation is .77, meaning that Iowa's chances would be .23. So failing to convert there would have meant a significant drop in Iowa's chances of winning the game (although not as big a change as scoring would have been).
So it appears there is no clear decision -- there were tradeoffs no matter what the coaches did. By doing a little arithmetic, however, we can at least see how confident Iowa would have needed to be about their chances of converting a touchdown to make going for it the right decision. I'll spare you the math*, but the way it works out is that Iowa would have needed to score the touchdown more than 38% of the time to make going for it the correct decision.

* Here's the math:
.34 = .52p+.23(1-p)
.11 = .29p
p = .38
[where p is the probability of successfully converting the fourth down and 1-p is the probability of failing to convert]

Would you have given Iowa better than a 38% chance of scoring a touchdown there? If so, going for the touchdown would have been the better choice. Iowa's offense was bad that day, but was it so bad it couldn't get three yards in two out of five chances? And if it was that bad, would you trust it to ever get in position to take the lead again? That was my reasoning for favoring going for it, but I could see how opinions might differ on that.

Let's be clear: Iowa didn't lose the game on this one decision. Anemic offense, too many penalties and two critical interceptions were the main culprits. In fact, if it weren't for several heroic plays by the defense, Iowa could have easily lost this game by two or three touchdowns. It will be much more important for Iowa's coaching staff to figure out why the offense failed to score three times from the three rather than worrying about whether they should have gone back for a fourth try. Still, it's important to recognize that going for the touchdown in this situation, while a gamble, is a very, very reasonable gamble. And given the apparent quality of this year's team, it may take a few reasonable gambles to win games.

GENERIC WP CAVEAT: To calculate WP figures for this article I used the WP Calculator at Advanced NFL Stats. The model used there is based on NFL results, not NCAA results, and thus only approximately applies to college football. I wish I could do better, frankly, but that's the only WP calculation tool I could find. So when you read "Iowa's WP" or "Iowa's opponent's WP", you should really insert mentally "a generic NFL team's WP" and "a generic NFL team's opponent's WP".