# Yet Another Article on a Controversial 4th Down Call from a New England Team…Yale

By David Roher

Harvard and Yale played their 126th football game (known around these parts simply as “The Game”) yesterday. We elected not to do a preview on the blog because the outcome was obviously a near certainty. However, it is worth looking at one play in The Game that drew a lot of scrutiny.

Up 10-7 in the 4th quarter but facing 4th and 22 on their own 25 yard line, Yale’s coach, Tom Williams, elected to call a fake-punt, direct-snap-reverse run, which gained them only 15 yards. The call elicited sporadic chants of “Bel-i-chick! Bel-i-chick!” from the Harvard cheering section, according to an anonymous source (fine, my roommate). Harvard went on to score a TD and win.

Compared to Belichick’s call, Williams’ is more difficult to statistically analyze for two reasons:

• To my knowledge, there is no model of win probability developed for college football, unlike the models developed for pro football.
• The play was a fake, so we can’t just look at Yale’s or any other school’s chances of gaining 22 yards based on other plays. It was a fundamentally different call based on game theory, so we would have to look only at punt fakes. Again, I don’t know if this exists in an already analyzable format.

The first problem isn’t that big of a deal, as the data from the NFL for a situation like this is probably a good enough model. But the second is very limiting. It only allows us to determine, at best, the necessary probability of a play in order to justify going for it (rather than taking the actual probability of the play itself into account).

Here’s a chart from Football Commentary showing when to go for it on your own 20 yardline, close to Yale’s field position. If you’re up by three points with 3 minutes to go, the play must have at least a 72% chance of success in order for it to be the correct call. This chart likely assumes that a failure puts the ball on the original line of scrimmage, though. Given that the chart is already 5 yards off and the fact that a failure in this situation would probably result (and did) in a gain of yardage, it’s probably better to use this chart (from the 40), which gives a 65% standard.

All we can do from there is wonder whether the play had a 65% chance or better of succeeding. Given Yale’s strong punter, whose punts had netted an outstanding average of 37 yards, and their defense, which had allowed the fewest average points in the Ivy League, that number is likely higher contextually.

Williams might have thought that the play did have that kind of chance. He said after the game that they “had set that play up all year, and felt it was worth 22 yards.” That quote implies that he thought it would probably work, though. It had to have a significantly better chance than just >50% in order to have been the right call. I have trouble believing that any play, fake or not, could gain almost a quarter of the field seven out of ten times. While most controversial calls to go for it on 4th down, like Belichick’s, are usually correct, this one probably wasn’t, although we can’t be too confident about that until someone (HSAC?) develops both an open-source college football win probability formula and a solid analysis of fake plays.

On the other hand, going for it when down by three points results in a threshold of just 20%. Perhaps Williams was, like me, confused by the fact that his team was ahead at that point.

Edit: It looks like I’ve come to a very obvious conclusion, so let me at least say this: I think the above analysis shows that the play, while not the right decision, was not The Absolute Worst Coaching Decision Ever. The real problem is that we’ll never know how justified Tom Williams was in thinking that his trick play would work. I might venture, though, that the person who has the best guess is Tom Williams. I still think he made a bad call, but perhaps not as bad as the calls we see all the time to punt on fourth and short when losing in the fourth quarter.

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• I was really afraid this game was going to turn into Harvard-Penn ’82.

• Alexander says:

When I first heard about it I assumed(incorrectly) that Yale was simply like so many college and high school teams: Sans a quality punter. However, the fact that Yale has a decent punter who was having a great day makes this choice inconceivable.