An upside of the Gophers' disappointing loss in Iowa City yesterday is that, assuming Wisconsin wins at home next weekend against Purdue, the regular season will end with the Badgers playing here in Minneapolis on Saturday, November 30, not only for Paul Bunyan's axe but also for the championship of the Big Ten West. That'll be the second consecutive Gopher home football game with more championship significance than any in program history since the 1960s.

Of the various "what ifs" that people love to discuss after a close loss, the one that sticks in my mind relates to the plays at the end of the first half. The Gophers, trailing 20-3, had the ball inside Iowa's 10-yard line with 10 seconds left and no time outs. We threw into the end zone, where Iowa's d-back interfered with our guy—actually, he interfered with him for the entire pass route and kept it up while the ball was in the air. So the referee called the obvious interference and, by rule, we get the ball, first down, on the 2-yard line. There were now 4 seconds left in the half. We decided to kick a field goal, which our kicker bounced off the inside of one of the uprights, ricocheting it through for 3 points: 20-6 at the half. We ended up losing 23-19.

First thing this makes me think of is that the penalty for defensive pass interference in the end zone at the end of one of the halves seems insufficient. That the offense gets a first down is completely irrelevant if there is only time left for one play anyway. So the defense, to prevent a touchdown, might as well interfere, hold, rough, grab, spit, trip, whatever. If it's not called, great; and, if it is called, you're a few more seconds toward zeros on the clock without a touchdown having been scored. In yesterday's game, the Gophers decided to kick a field goal with the ball on the 2 and 4 seconds left. We were already inside the 10, so holding us to a field goal attempt was the best Iowa could hope for. There was no penalty at all for the touchdown-saving interference.

Second thing I stew about is the decision to kick. It's a hard choice and I'm not saying Fleck was necessarily wrong. But, had we gone for it and scored, then kicked the point, we would have had 4 more points, which in the end is what we lost by—4 points. I tend to think of these hard choices in a mathematical way. A touchdown is twice as many points as a field goal, plus you get the try for a point after. This means that the number of expected points scored is higher if you try for a touchdown, so long as the probability of scoring a touchdown is close to half what the chance of making a field goal is. Just to demonstrate, let's say that the chance of scoring a touchdown on one play from the 2-yard line is 48%, and the chance of kicking for the extra point, or making a field goal of about the same length, is 95%. Then the expected points scored from trying for a touchdown is

(.48)(6) + (.48)(.95) = 2.88 + .456 = 3.336

whereas the expected points scored from trying a field goal is

(.95)(3) = 2.85

and 3.336 > 2.85. It's a significant difference. The chance of scoring a touchdown on one play from the 2 would have to be somewhat less than 48% for the expected points scored from a field goal attempt to be greater. (For what it's worth, the success rate for a 2-point conversion after touchdown in the NFL is 47.9%; the try comes from the 2-yard line, just where the Gophers were after the interference penalty.)

In the event, we almost missed the field goal, which brings up a further little bit of mathematical football that I've sometimes wondered about. In professional football, the hash marks on the field line up with the uprights on the goal posts, which are 18.5 feet apart. Width-wise, then, the ball is always pretty close to the middle of the field. In college football, however, the hash marks are 40 feet apart. This means that if the ball is on the left or right hash mark and near the goal line, the angle to the goal posts is rather severe, and I've wondered whether, mathematically, that makes a field goal try more difficult. It happened yesterday that the Gophers had to kick that short field goal before halftime from the right hash mark, and, from the shot behind the goal posts you usually get on TV, it looks like it might have an effect. It's not a crazy thought, right? If you were kicking a "0 yard field goal" from the right hash mark, there'd be no opening to kick the ball through. If you were kicking a "1 yard field goal" from the right hash mark, almost your only chance would be to kick the ball just in front of the right upright and then bounce it off the inside of the left upright and through. How far back must you go before the effect becomes negligible? I was curious enough to start dusting off my high school trigonometry before remembering it's 2019, so instead I googled "trigonometry of field goal kicking," which led me to this article. My takeaways are:

(1) I was wise not to try and figure it out myself; and

(2) The situation gets better so fast that, considering that the goal posts are at the back of the end zone, and that the try always comes from about 7 yards behind the line of scrimmage, there are no field goal attempts that are short enough so that being on the hash mark means there is less margin for error on the kick. If, for example, you are near the goal line on the hash mark, it would never be wise, from the standpoint of the mathematics, to take a penalty in order to widen the angle: being closer with a slightly smaller angle allows for more error in direction than being a little farther with a wider angle.

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