There's really not much need to go into the statistical intricacies of the Northwestern game; how many ways are there, after all, to say "total ass-whomping"? But there were a couple of interesting fourth down situations that are worth taking a look at. After that, I recommend we all check ourselves into "Eternal Sunshine of the Spotless Mind" memory-erasing machines so that we can forget about the ignominy of Northwestern running for 300+ yards on Iowa.
Situation #1: Iowa ball, 4th and 8 at NW 38, 15:00 left in second quarter, NW leads 7-3
This was the second of Iowa's three costly delay of game penalties, and it couldn't have come at a worse time. Iowa was actually ready to make the smart play and go for it on 4th and 3 at the Northwestern 33, but a delay in getting the play in (and Vandenberg's inability to get the ball snapped or call a timeout) led to a much more difficult 4th and 8 from the 38.* On the 4th and 3, Iowa's break-even probability to make it was just 39%. The funny thing is, Iowa's break-even probability actually decreased after the penalty. In the 4th and 8 situation, Iowa would have only needed to convert the 4th down 29% of the time to make it worthwhile. How can this be? The answer has to do mostly with the increased difficulty of making a field goal from the 38. According to the AdvancedNFLStats model, NFL kickers make field goals from the 33 yard-line 55% of the time, and that percentage drops all the way to 40% when you move out to the 38. It's a good question whether Michael Meyer is anywhere near as reliable as an average NFL kicker (almost certainly not), but that just means that he was less likely to make both the 50-yard field goal and the 55-yard field goal. My hope is that the difference between college and the pros comes out in the wash.
*Some blame goes to Vandenberg, but this delay was also on the coaches. This is just a guess on my part, but I think Iowa's coaches are still somewhat conflicted psychologically with the thought of going for it on fourth down in unconventional situations, and this decision anxiety is reflected in slower play-calls. To avoid this anxiety, my recommendation would be for the coaches to draw up a situational chart that dictates ahead of time whether to go for it (given a score difference/yards to go/yard line), then call two plays on third down. This would avoid the delay of game penalties and allow Iowa to get the jump on confused defenses by lining up without a huddle.
The really important thing to note is that punting from either the 33 or the 38 doesn't do you any favors, and is scarcely better than just giving up the ball at the 33 or 38. If you manage a good punt (say to the opponent's 10), their win probability in a situation similar to Northwestern's (up four, 15 minutes to go in the second quarter) is .62. If you just turn the ball over at the 33, their WP increases to .66; if you turn it over at the 38, it goes up to .67. Not a huge difference either way. While if you manage to convert the first down, their win probability drops all the way to .51. This will sound stupidly obvious, but there's really no substitute in football for scoring. Turning the ball over without scoring, whether at the 33 or the 10, exacts a major cost on the team, not really because the other team gets a new chance to score (they would anyway), but because of the opportunity cost of not scoring. I wish the Iowa coaches could have the following phrase embroidered on a needlepoint sampler: "You don't win friends with punting" (I would also be in favor of a commemorative plaque with "field goals are for suckers" but that's another story).
Iowa managed to land the ball on the one, but amazingly, that doesn't really change things in the WP model. Northwestern's WP would have been .62 whether they started on the one or the 10 yard-line. And of course Northwestern managed to get the ball back to their 38 in about 4/7th of a play when Venric Mark broke through for a 72-yard run. Which is all to underline the plain fact: giving up the ball sucks, no matter how it happens. If an interception 40 yards down the field on third down would bum you out, then a 40-yard punt should bum you out just as much.
Situation #2: Iowa ball, 4th and 3, NW 24, 1:49 left in 4th quarter, NW leads 28-17.
This is a more interesting proposition. As this play happened, I felt fine about Iowa going for it here -- they would need to score a touchdown eventually, and getting to the 24 was pretty close -- but the consensus on Twitter was that the Hawks should have kicked the field goal. Which was the better option?
Well, the first thing to point out is that Iowa was in a bad position either way. Going into that fourth down, their WP was .01, i.e. they had a 1 in 100 chance of winning in the AdvancedNFLStats.com model. The model only goes down to 1%, too, so their chances may have been even worse. No matter what Iowa did, they did not have great odds of winning the game, and that goes back to the whole ass-whomping that took place over the first three quarters.
With that said, with a little work we can figure out which option would have been better. I'll spare you the boring details, but it involves working through the following probability tree. The relevant information is: how often would Iowa convert the fourth down/make the field goal; how often would they score the TD/FG after converting; how often would they recover the onside kick; and what their WP would be if they did recover. If you really care, you can look at the chart and see the various values corresponding to the branches of the tree.
The big upshot of all this: going for it on fourth down was the slightly better option, but very, very slightly. Like 1% better. And given the sensitivity in the model to even slight changes in yardage and time on the clock, there's no saying that the difference would be consistently in favor of that option. Long story short, Iowa was screwed no matter what they did. They had a about a 2.5% if they went for it, and about a 2.5% chance if they kicked the field goal. I doubt anyone was rending their garments about this decision, but if you were, rest easy. Iowa made plenty of mistakes earlier in the game, but this wasn't one of them.