Thursday, April 26, 2007

The "defense first" strategy in college football OT

If a college football game is tied after four quarters, the game goes to overtime.

The college OT rule is different from the NFL rule. It works a lot like extra innings in baseball. Each team gets one possession at its own 25. If, after both teams have completed their drive, one team is ahead, the game is over. But if it's still tied – perhaps each team scored a field goal on their one possession – it goes to another "inning," and each team gets another possession. This continues until the tie is broken.

A coin flip decides which team gets the ball first in overtime. The team winning the toss gets to choose whether to go on offense first, or on defense first. Almost always, it chooses defense first. (The choice applies only to the first OT; in each subsequent OT, the order is flipped from the previous.)

Is choosing "defense first" a good strategy? That's the subject of a paper from the newest JQAS, just released yesterday. The study is called "An Analysis of the Defense First Strategy in College Football Overtime Games," by Peter A. Rosen and Rick L. Wilson. (Download is free if you give an e-mail address.)

Rosen and Wilson looked at 328 overtime games they found since this overtime rule was instituted in 1995. They found that it appears that forcing the other team to go on offense first is, indeed, a good strategy. How good? The team going on defense first won 54.9% of overtime games.

.549 Team going on defense first
.451 Team going on offense first

The reason for the advantage is kind of obvious: the team "going second" (on offense) already knows what the first team did. And so, it won't make the mistake of settling for a field goal when the "first team" (on offense) scored a touchdown. On the other hand, the first team *can* make that "mistake." Faced with fourth-and-10 on the opponent's 20, it'll go for the 3 points, because it doesn't know yet that the opponent will score a TD.

It's important to keep in mind that this argument is not a proof. It points out the advantages of going second, but none of the disadvantages. What are the disadvantages? Well, they're probably small, but, in theory, teams can defend differently depending on the score. If the first team fails to score on their possession, a field goal will beat them. And so, they might set up some sort of defense that minimizes the chances of the second team scoring (it would increase the chance of a touchdown, but not as much as it decreased the chance of a field goal).

So, by theory alone, we couldn’t be sure, in advance, that going second is the optimal strategy. We needed the numbers to confirm – and they do.

(Here's an example of where the advantage might be reversed. Suppose that in overtime, there's a rule you're only allowed to go for a field goal if the defense explicitly allows you to. In that case, the advantage of choice switches sides -- whether you go for a touchdown or a field goal depends on the *defense*, not the offense. So in that case whoever is *defense* last has the advantage. They would use it by *never* letting the second team try a field goal if they had failed to score themselves.)

Alas, after showing us the results, the study doesn't really give us much extra useful information. The authors do run a regression, predicting the odds of winning from several variables: point spread, home/road, "momentum" (who scored last before overtime), and "pressure" (the points the first team scored in overtime).

As you would expect, "pressure" dominates the equation -- once you know how many points the first team scored, it's much easier to predict who's going to win. Only pressure and point spread turn out to be significant. The authors are surprised that home field advantage doesn't turn out to be important, but they don’t seem to realize that HFA is already included in the point spread.

They do note that the second team advantage seems to have declined recently. From 1995 to 2000, their winning percentage was .624; but between 2001 and 2006, they won at a rate of only .492 – less than .500! The authors don't have any firm explanation for this, and I can't think of one either. (Perhaps underdogs won a lot of coin tosses in the last several years, or something.)

In their conclusions, the authors state that going second is a good strategy. But then they write that "in situations where pressure is seven points (the offense first team scores a touchdown) and the defense first team is not a large favorite, the offense first team holds a considerable advantage." Er, yes, that's true, but I'm not sure that has anything to do with which strategy is better, and I'm not sure what the authors are trying to say here.

Indeed, they seem to treat "pressure" the same as all the other variables all the way through the study, which leads to confusion. The other variables are known prior to the overtime, and it makes sense to predict the outcome from them. But predicting the outcome of overtime from what actually happens in the overtime, and combining that with all those other variables ... well, it seems to me you can't learn much about strategy that way.



At Thursday, April 26, 2007 4:43:00 PM, Blogger Jason Lisk said...

As to the split between 1995-2000, and 2001-2006, at some point as a result of OT games going several rounds, the rule was put in that teams must go for 2 pts following each td after the 2nd OT period. I can't imagine this rule change would significantly impact the expected outcomes, if at all, since most OT games are probably decided in OT period 1 or 2.

The only other thing I can think of, other than it just being random, is that over time, maybe the "offense first" teams became smarter on strategy necessary on their end, such as being more aggressive on fourth down if that improves win expectancy.

It is not exactly surprising that going second is an advantage. A better question is when should teams going first on offense go for a first down on fourth rather than settle for a FG, hope to hold the other team to the same, and advance to another OT.

Doing some back of the paper very rough calculations, and assuming, for average college teams, a roughly 50% chance of achieving a first down/touchdown on any given set of downs, and a 70% of making a 30-40 yard field goal by an average college kicker, then the breakeven point where teams should consider going for it rather than kicking is about 35-40% conversion percentage on fourth.

I would be more interested in knowing if coaches are too conservative on fourth down situations when on offense first. Attempting the field goal first makes that (average) team an underdog with about a 33% chance of winning the game, taking into account the chance of the other team scoring a td, or a missed fg on the attempt.

At Friday, April 27, 2007 1:59:00 PM, Blogger Phil Birnbaum said...

Interesting theory about offense-first teams taking more chances on fourth down. I'd love to see data on that.

At Sunday, April 29, 2007 1:16:00 PM, Blogger Bob Timmermann said...

I only have anecdotal data from watching college football overtimes, but the team that is offense first will almost always go for a field goal if it is in a fourth down situation. I don't believe I've ever seen a coach have his team go for a first down in that situation.

The Fiesta Bowl this year demonstrated a coach who had a grasp of his team's probabilities of winning in overtime.

After Oklahoma scored on its first play in overtime, Boise State countered on a fourth down play and then went for two to win the game. I think that if Boise State had gone first and scored a TD, they would have just gone for one.

That game was a special case of an undersized team trying unusual strategies to overcome obvious physical deficiencies.

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