To Punt, Or Not To Punt?

My college roommate and I have long held, without rigorous empirical evidence, that NFL coaches punt way too often. This week's Tuesday Morning Quarterback makes that case and even backs it with some non-trivial evidence derived from a 2005 David Romer paper. This is by no means an airtight argument, but it's sound enough -- i.e., certainly worthy of more than 3 percent credence -- that really someone or other ought to think outside the box and give it a try.

Let me also say that Easterbrook doesn't even throw on to the pile one of the considerations in favor of a much more aggressive fourth down strategy -- it would make defending third down situations harder. One major structural advantage the offense has is, of course, that the defense doesn't know what play the offense is going to run. In certain circumstances, though, you can get a pretty good guess. Third down situations, in particular, get fairly predictable. If you need short yardage, you're goign to run; if you need long yardage, you're going to pass. If, however, you plan on going for it on fourth down and the other team knows you're going to go for it then everything gets much harder to predict.

Comments

Here is another article at the lovely football geek site www.footballoutsiders.com, that speaks to the same point.

http://www.footballoutsiders.com/index.php?p=4059

Posted by: Uncle J on September 26, 2006 05:05 PM

The gang at Football Outsiders is perfectly positioned to answer this or pass it off to someone who can. For early-game situations, you can basically convert field position+down and distance into a scoring likelihood, I'd have to imagine. Weight punting plays, weight going for it, and compare the two. It's done all the time in baseball to argue against overzealous running games and most sacrifice bunts.

Posted by: jfaberuiuc on September 26, 2006 05:05 PM

There is nothing more cowardly than punting from inside the opponent's 45. I'm not sure that I'm sold on going for it in other field positions, although as Matt says, the author makes it sound at least plausible.

Posted by: dj moonbat on September 26, 2006 05:07 PM

Dammit, Uncle J, with your citations and rapid googling skills! Real blog commenters only partially form an idea and then post it, without doing research or last-second checking for new comments!

Posted by: jfaberuiuc on September 26, 2006 05:10 PM

I knew that sounded kinda familiar, but the 2005 date seemed a bit too recent. Apparently, it is the same data/paper that was floating around in 2003.

http://emlab.berkeley.edu/users/dromer/papers/nber9024.pdf

BTW....I would much rather go with the play action pass in a short yardage 3rd down situation.

Posted by: zAmboni on September 26, 2006 05:11 PM

Forgot to add....when I read the post title, I thought Matt was going to debate the administration's Iraq policy after the NIE leaking...

Posted by: zAmboni on September 26, 2006 05:15 PM

Could these concerns apply not only to football strategy but also to political strategy?

Dem. strategests certainly do act like the kinds of people who have less knowledge/skill/experience in competative sports than even I do -- and I have very little such experience. Let's just put it -- the coach types are right: you do learn certain life lessons in sports. And I've sufferred from not learning them as soon as more sports oriented folk have ... and it seems much of the Dem. leadership have yet to learn some of those lessons ...

Posted by: DAS on September 26, 2006 05:16 PM

You and your numbers. The best reason to go for it on fourth down is that it's more bad ass.

Posted by: ogged on September 26, 2006 05:26 PM

This decision would be affected by the quality of a particular team's defense, and I would not accept league-wide statistical analysis as dispositive.

IIRC, Chicago under Ditka made a living on punts.

Posted by: bob mcmanus on September 26, 2006 05:27 PM

"If, however, you plan on going for it on fourth down and the other team knows you're going to go for it then everything gets much harder to predict."

I'd have to run the numbers, but I'm 99% sure that a mixed strategy would be far more successful under a game theoretic model. A mixed strategy based on random iterations (going for it on 4th and 4 from your own 35, punting on 4th and 2 from midfield) would logically also cause far more confusion on 3rd downs...

Posted by: Dan Kahn on September 26, 2006 05:29 PM

Kevin Drum agrees. As do I. What makes coaches so risk averse?

Posted by: Al on September 26, 2006 05:30 PM

Bob,

Having a good D would seem to argue even more for going for it, the consequences of not making it are even less since your D can likely stop the other teams O anyway.

Posted by: Eric on September 26, 2006 05:30 PM

The urge to "pull a Farber" here is almost overwhelming . . .

Posted by: Jim Henley on September 26, 2006 05:44 PM

What makes coaches so risk averse?

I have a sneaking suspicion that coaches and other observers place more value on "field position" than they should. The reason I think this might be is that hardcore pass-oriented offenses, which when running smoothly can tear up yards much faster than "four yards and a cloud of dust," have changed the calculus, but people haven't caught up.

Posted by: dj moonbat on September 26, 2006 05:46 PM

Well, apropos of you del.icio.us link to Chait's hit piece on Notre Dame, it is pretty clear that Charlie Weis is way ahead of you. In four games so far this season, he has gone for it on 4th down ten times already, and although of few of those replaced risky field goal attempts, most of them (I would say 8 off the top of my head) replaced punts. He's a cerebral coach who has previously spoken about putting together databases of officiating crews calling tendencies, so he's likely taken a look at the numbers of going for it on 4th down.

As for why coaches don't do it more, I think it's fairly simple. Coaching is an extremely risk averse profession: but not only for the historically reason dj moonbat lays out ther, but also because it's not clear what games coaches might win, but the ones they lose tend to be quite glaring (poor clock management, overly conservative playcalling with big leads, and, yes, going for it on 4th down and not succeeding). Thus coaches have less incentive to maximizes wins as opposed to limit their exposure for losses. While the wins/losses will eventually get them fired, public perception of repeatedly blown calls will get them fire now. I would also note that the first adopters will face the gale force wins of stepping outside the socially approved punting. They won't be able to point to other coaches strategies as the excuse when a conversion inevitably fails.

So keep your eyes on Weis. He did this all last year, too, making use of extremely creative play calling (see the play action 4th and 1 play against Michigan State this past weekent), and gambles often. If coaching strategies surrounding punting change in the near future, he will certainly be pointed out as one of the leaders in the trend.

Posted by: Peter on September 26, 2006 05:54 PM

Psychologically I think that going for it on fourth down is a very powerful signal that a coach can send to his players. Basically you are showing that you have confidence in your offense to get the 3-yards. And frankly if you don't believe your players can get 3-yards on any play then you should probably just give up and walk off the field.

Posted by: djslippyb on September 26, 2006 05:59 PM

Eric at 5:30

I am refuted.

Posted by: bob mcmanus on September 26, 2006 06:00 PM

I'm baffled as to why any coach would ever want to "punt".

The minute one of your players kicks the ball with his foot, the official will blow his whistle and turn the ball over to the other basketball team. What purpose could this possibly serve?

Posted by: Petey on September 26, 2006 06:18 PM

Indeed, it will probably be a technical foul also, Petey.

Posted by: Al on September 26, 2006 06:24 PM

The author of THE HIDDEN GAME OF BASEBALL did a football book conluding that a football team should almost NEVER kick a field goal except in extreme circumstances (last drive of the game when you're down by 2 points, etc.) and particularly not inside the 20. Go for it always. When one team has possession on their own 20 it is 50-50 which team will score next (on average... not factoring in relative quality of the two teams). Having the ball on your own 10 is a losing proposition--the other team is likelier to score before you will. I don't know the implications for punting, but the 50-50 dynamic in the standard touchback position of starting on your 20 is interesting. Of course, the point of the field goal analysis is that field position is more important than people think, so it may suggest that punting at midfield is a BETTER idea than it seems since 25-40 net yards has a real value in points that may be higher than the value of going for it on 4th down. If you pin your opponant inside his 20 you are liklier to score than he is. If you go for it on 4th and three at mid field are you liklier to score next? So I'd guess that you always go for in field goal range and very seldom go for it outside field goal range.

Posted by: cf on September 26, 2006 07:18 PM

Pete Carroll almost never punts. (Indeed, rather than declaring Charlie Weis a genius, Notre Dame fans should admit that he's just copying the strategy of coach of the school's hated rival, USC.)

And in the pros, Bill Belichick almost never punts.

That alone should tell you something.

Posted by: Dilan Esper on September 26, 2006 07:48 PM

Worrying about "field position" is the sports equivalent of targeting "swing voters."

Posted by: dj moonbat on September 26, 2006 08:11 PM

I read an article about inner city high schools in D.C. that almost never punt or attempt field goals or extra points because they can't get anyone to practice kicking. Touching the ball with your foot is for wimps, apparently.

These schools would make a good test case for economist Romer's theory that almost never punting is smarter. Maybe they do better than suburban schools with soccer-trained field goal experts. Or maybe not.

Posted by: Steve Sailer on September 26, 2006 08:15 PM

Stanford economist David Romer did a study of 20,000 NFL plays and concluded that NFL teams should go for it more on fourth down, including going for it on 4th and 2 at their own 10 yard line (not the other team's 10, their own 10!).

Unfortunately, Romer's study is pretty close to worthless because he makes a catastrophically bad assumption. Romer writes on p. 4 of his PDF:

"Decisions to go for it on fourth down (that is, not to kick) are sufficiently rare, however, that they cannot be used to estimate the value of trying for a first down or touchdown. I therefore use the outcomes of third down plays instead."

In other words, he didn't actually look at whether or not teams make it on fourth down. What he looked at was whether they make it on third down.

But any football fan can realize the big difference between, say, third and two and fourth and two. It's easier to pick up, say, at least two yards on third down than on fourth down, just as it's easier to pick up at least two yards on first down than on third down.

Why? Because the lower the down, the more tries you have left to get a first down, so the safer it is to try a risky play now for a long gain. If on third and two you try to throw a long pass into the end zone for a touchdown, but it falls incomplete, well you still have fourth down. But on fourth down, the penalty for failure is severe -- you turn the ball over to the other team. So, you'll probably run a conservative play to grind out the needed yardage and not much more. Knowing that, on lower downs, the defense tends to play back to prevent giving up a touchdown or long gain.

This is a good example of what's wrong with the freakonomics fad -- academic economists are rewarded for building elaborate econometric models, but they aren't rewarded for performing simple reality checks on their own elaborate models.

Posted by: Steve Sailer on September 26, 2006 08:24 PM

If the analysis shows that you can accept the penalty for failure on 4th down if it occurs at the rate of 3rd down plays, then you should in fact play 4th down with the 3rd down playcalling strategy. If you become more conservative on 4th down, constraining your choices and the defense can predict this, you're choosing a suboptimal strategy. Why would any coach acting rationally enough to go for it on 4th down then act irrationally in constraining his play choice? At least, there's no reason the model should assume that. So, I don't see the problem.

Posted by: Larry on September 26, 2006 08:59 PM

I think that's missing one factor - the defense may play 4th down differently than it plays third down. (Not to mention that the crowd may react with more, um, vigor on 4th down.)

Posted by: Al on September 26, 2006 09:04 PM

There are two things in a football game that bother me to no end. They are (1) punting from inside the opponent's 40 yard line and (2) running a pass play on 3rd and less than three yards to go, failing, and then going for it on fourth down. If you've decided that you're going to take two tries to make a first down and you have less than three yards to go, I'd guess that your probability of success increases significantly if the first of those two plays is a run. I think if most coaches thought more than 30 seconds into the future, they'd realize this.

Posted by: bill on September 26, 2006 09:04 PM

Think about it.

Of course you'd be more conservative -- for rational reasons -- on 4th down play calling than on 3rd down play calling. The penalty for an incompletion on 4th down is the opponents gets the ball right here. The penalty for an incompletion on 3rd down is that your opponents either get the ball about, oh, 38 yards downfield or you try it again on 4th down.

This should not be a new concept to economists -- it's called risk vs. reward. The higher the risk, the higher the expected reward needs to be to make it worth doing.

Posted by: Steve Sailer on September 26, 2006 09:09 PM

The Detroit Lions and the Oakland Raiders should both seriously consider cutting their punters loose and trying the "never punt" tactic this year. Those teams have nothing to lose and everything to gain - they could add an additional productiver player to the roster and their offenses would get a little more practice and padded stats with those extra 4th down plays. Hell, the curiosity factor alone would at least keep fans in their seats and help draw better TV ratings than your normal 2-12 team gets.

Posted by: vanya on September 26, 2006 09:46 PM

I mostly agree, but I'm curious if someone has run the numbers: if you adopt a strategy of usually going for it on 4th down (or even every other 4th down), how many extra snaps per season does that involve your QB taking, and what does that do to your chances of losing your QB with a game- or season-ending injury?

First rate quarterbacks are expensive. (So, for that matter, are running backs, wide receivers and tight ends.) I can understand coaches and owners being conservative in how much they play them.

Posted by: Doctor Memory on September 26, 2006 10:03 PM

Yes, I can understand that the penalty for failure is higher on 4th down. However, the analysis shows that penalty isn't high enough to deter acccepting the failure rate of the normal 3rd down strategy. You can fail at that rate and still gain an advantage with the first downs being made. Therefore, you should only make playcalling strategy changes that would increase your success rate. Becoming more conservative and more predictable doesn't do that, so you shouldn't do it. And if there is a way to increase your success rate, then Romer's model isn't aggressive enough.

It is true that the reward for success on the defensive side increases symmetrically, and thus the defense might be willing to try increasing their success rate at the expense of allowing a few more big plays, but this would point towards being even MORE aggressive with the playcalling on 4th down to take advantage of the extra big plays you'd get.

So, while its true thta 3rd down is not the same as 4th down, I don't see how there's a way in which that leads to an error that changes the conclusions of the paper.

Posted by: Larry on September 26, 2006 10:16 PM

What Larry and Professor Romer overlook is that the chance of making the needed yardage for a first down is, ceteris paribus, lower on 4th down than on 3rd down because the defense knows that the offense faces an incentive to call a more conservative play, so the defense can play more aggressively on 4th down to stop the short gain because they have less to fear being burned for a long gain or touchdown.

To salvage some utility from his study, what Romer should do is take his calculations and say to NFL coaches, "All right, I admit it, I don't know anything about the chance of making a first down on 4th down. Obviously, my methodology of looking at 3rd down plays is useless for understanding the chances of making it on 4th down, except probably near the goal line. However, here are the expected returns in all situations of making it versus not making it. Then, you football coaches should take _your_ estimates of the percentage chance of making it on different 4th down situations, which are obviously better than mine, and multiply it by my estimate of the returns of making it, which are pretty good, and the combined result of our efforts will be useful information."

A little more humility would increase the utility of the economics profession.

Posted by: Steve Sailer on September 27, 2006 12:07 AM

I think that people are way underestimating defences in these situations. D has several things going for them on the 4th down: it is a all or nothing down that allows you to immediately get the ball on the same spot. 2. That, in turn, increases the ferocity of the players. 3. These are the players who are bigger and stronger (and much tougher) than offensive players, simply because that is what it takes to play D in the NFL.

Yet, i am a big proponent of going for it on the fourth down ONLY when it is on the opp. side of the field in the NOMAN zone (40-30 yard line). The problem that we encounter is that the coaches get too conservative on this down and run their RB's into defenses (Shottenheimer and Edwards in the playoffs 2 years ago comes to mind. They both had hall of fame RB's and all they needed was a playaction pass to win their respective games against the Jets, and later the Jets against the Steelers. What about Pats v. Colts, where the Colts had 1&goal on the one and ran EJames 4 straight times) These coaches go into a shell and become predictable. They do not want to put the ball in the air, and that inevitably leads to a turnover on downs. D's know that and become overly agressive on fourth down, coming with big blitz packages.

Posted by: brooklyn on September 27, 2006 01:15 AM

Steve Sailer just doesn't understand the paper, nor does he understand the arguments Romer explicitly makes for why using 3rd down makes sense.

Larry, on the other hand, makes a lot of sense.

Romer's paper is really pretty good, if you don't mind a little math.

Posted by: ed on September 27, 2006 01:18 AM

the chance of making the needed yardage for a first down is, ceteris paribus, lower on 4th down than on 3rd down because the defense knows that the offense faces an incentive to call a more conservative play

No, on 4th, one would have an incentive NOT to call a conservative play, at least once one decided not to punt.

Posted by: dj moonbat on September 27, 2006 01:30 AM

Personally, I tend to agree with economist David Romer that NFL coaches are too conservative on fourth down, but that doesn't mean Romer's methodolody is useful for demonstrating that theory. It is possible, strange as it may seem, that Bill Walsh and Bill Belichick know more about football play-calling than Romer and I do.

I've read Romer's defense of his using data from third down to assess the chance of making it on fourth down, and it's simply a weak rationalization, an attempt to band-aid over a fundamental flaw in his study.

Here's a simple way to understand why the chance of making it on fourth down and x yards to go is not as good as the chance of making it on third down and x yards to go.

On second and one, as is well known, the offense can afford to throw a long (i.e., low percentage) pass because if it is incomplete, they simply face third and one. So, on second and one, the defense must hang back to defend against the bomb. In turn, that means on second and one that it's easy for the offense to make the first down by calling a conservative running play.

On third and one, the defense can stack the line a little more, because the cost of a long incompletion (having to punt) is greater (although it's not disastrous like turning the ball over is). So, it's tougher to make just one yard.

Similarly, on fourth and one, the defense can stack the line a lot, because it knows that throwing a long low percentage bomb is highly risky for the offense, so it's even tougher for the offense to make the needed yard.

Posted by: Steve Sailer on September 27, 2006 03:33 AM

Okay, I'll praise the Poodle like I should. Yes, USC went for it on 4th down thirty times last year. A pretty impressive clip, with a number of those attempts coming against the Irish. Belichik also is noted for going for it. Between the best coach in the NFL and two of the best coaches in college adopting a punt more infrequently strategy, I think we may well be witnessing the early adopters whose success will eventually change the punting norms.

I think Steve is right, however, that simply assuming that looking a 3rd down success rates is the proper route is extremely dubious. Since the average punt is going to net nearly forty yards, the defense has a very high incentive simply to prevent the first down. Even with an offensive coordinator who was willing to not become more conservative in play calling in 4th down situations, the fact that the defenses would adjust their strategies to focus narrowly on preventing the short gain would ensure that the conversion rate would in fact drop. Just that one stop is the equivalent of a posssesion plus forty yard gain for the defense.

Posted by: Peter on September 27, 2006 09:44 AM

No, on 4th, one would have an incentive NOT to call a conservative play

This is exactly right; Steve is exactly wrong.

Because the penalty for failure is higher, the incentive is to call a LESS conservative play. A more conservative play is more likely to produce a gain but with yardage insufficient to make the first down, while a less conservative play would be more likely to produce the necessary yardage (while also being more likely to be a complete failure and produce no yards at all).

An example: 4th and 3 at your own 40. What do you call? If it were 3rd and 3 and you would punt on 4th, you could call a running play. However, a running play is more likely than a passing play to make 1 or 2 yards (a positive gain but insufficient for a 1st down). On 4th down, though, you likely wouldn't call such a play - you'd rather call a pass, which is more likely to get the 3 yards if successful, but also more likely to result in a sack, interception, or no-gain (due to an incompletion).

Nonetheless, the overall point that Steve is making - that current 3rd down results may not be a good proxy for hypothetical 4th down plays - I think is valid.

Posted by: Al on September 27, 2006 10:01 AM

The biggest flaw in the study is that results in football are highly contingent on the makeup of your team and the team you're playing. Is your punter an ace at landing coffin-corner kicks? How confident are you in the ability of your defense to stop the other team if it gets the ball on your 40? How good is the placekicker on the other team? If you give the ball to Philly and David Akers on your own 30 you've just given Philly a minimum of 3 points. On the other hand if you're playing the Jets you might consider that strategy. If the Pats had gone with a no punt strategy against Denver on Sunday they probably would have lost 34-0 because they could not get a consistent running game or a passing game going. Looking at averages over the course of many seasons in football is meaningless when judging what to do in a particular situation. Maybe the average NFL play gains 5 yards, but if I'm Pittsburgh with a wounded Rothlisberger facing Jacksonville suddenly those odds aren't looking so great.

Posted by: vanya on September 27, 2006 12:17 PM

Steve Sailer:

Reading your posts is kind of amusing because your description of the situation is sound, but your conclusion is just wrong and you're just not paying attention to what other people are saying.

If I have a play-calling strategy on ANY DOWN that yields a certain percentage of first downs, I can use the EXACT SAME strategy on ANY OTHER DOWN. And as the defense adjusts to that strategy it will yield the exact same conversion percentage.

For example: we throw it long sometimes on 3rd down. This is for two reasons: it keeps the defense honest and it allows for the possibility of a big play. Now the defense adjusts and when we run it, its a little easier to make it. If this yields a higher conversion percentage than just running it every single time- then you do the SAME THING on 4th- you keep the defense honest by throwing downfield on 4th down from time to time.

Now, teams usually don't throw downfield on 4th down very often and the reason why may be that you don't actually increase your overall conversion percentage by going long from time to time. The incomplete passes outweigh the benefit of keeping the defense honest. Whether or not that's true is an open question. But the upshot is that we should be able to find a play calling strategy on 4th down that yields at least as good of a conversion percentage as on 3rd.

There is only one complication here- defenses may refuse to adjust their strategy based on your play-calling. Maybe they'd rather get more aggressive about going for the stop and be willing to risk giving up a big play on 4th down even though you do occassionally throw downfield. I'm not sure if this is rational or if it needs to be considered, but at least its there.

Posted by: mpowell on September 27, 2006 12:23 PM

Steve,

I don't think the data from high schools would be usefull. One factor in the NFL is that talent level is really not that different. Take the worst team (Houston? Oakland?) and one of the best teams (Colts? Seahawks?) and the raw talent isn't that far apart. A lot closer than the best College IA teams and the worst. And the talent gap in highschools can be off the charts.

Posted by: Eric on September 27, 2006 01:29 PM

"If I have a play-calling strategy on ANY DOWN that yields a certain percentage of first downs, I can use the EXACT SAME strategy on ANY OTHER DOWN. And as the defense adjusts to that strategy it will yield the exact same conversion percentage."

This is like saying a 30 year old and a 60 year old should have the exact same strategy for investing for retirement. No, the 50 year old should invest in risker assets with higher expected returns because he has some time to recover from bad luck before he retires. The 60 year old needs to invest more in lower risk, lower return assets because he doesn't have time to recover from a bad outcome. The 50 year old is like a football team on 3rd down and the 60 year old is like a football team on 4th down.

Romer's mistake -- using 3rd down data to guess about 4th down -- is the equivalent of using data about the investment success of 50 year olds to advise 60 year olds. Economists wouldn't make that mistake, but they blunder into the equivalent mistake when they start freakonomizing.

Posted by: Steve Sailer on September 27, 2006 06:05 PM

I agree that the CW is that coaches would be more conservative on 4th down because the risk is scarier. But, the point of the Romer analysis is that the risk is, in fact, not as scary as coaches think it is. And the chances of obtaining the reward are higher than they think. If they use the correct playcalling strategy on 4th down.

I don't want to ignore Steve's point, which is there's clearly a difference between 1st down and 3rd down, so we should extend that obvious truth to a difference between 3rd and 4th down. There's a change in the risk-reward calculation. That's true and it isn't just limited to the decision of whether to go for it, it extends to the playcalling choice as well for both offense and defense. It isn't obvious to me how the defense can make the offense do worse on 4th down that they do on 3rd down. In order for Steve's objection to be right, you'd have to be able to find a defensive strategy that materially decreases the offense's success probability. I think this is unlikely. Consider goal line situations where the defense's reward is enormous (4 points) for a stop. This is even bigger than the reward for 30-40 yards of field position we're discussing here. Even on 3rd and goal, the defense usually is at a strong disadvantage. So, I think the conclusions here are sound.

BTW, what the heck does freakonomics have to do with anything here?

Posted by: Larry on September 27, 2006 07:52 PM

The best response to Steve Sailer's concerns are given by Romer himself. Here's a lengthy quote from section IV of the paper:

The analysis uses the outcomes of third-down plays to gauge what would happen if teams went for it on fourth down. There are two ways to investigate whether this is likely to introduce important bias. The first is to consider how teams’ incentives are likely to affect outcomes on fourth downs relative to third downs. The second is to directly compare outcomes on the two downs.

To consider incentives, note that the relative payoffs to different outcomes are different on fourth down than on third down. In particular, the benefit from a long gain relative to just making a first down is smaller on fourth down. As a result, both the offense and defense will behave differently: the offense will be willing to lower its chances of making a long gain in order to increase its chances of just making a first down, while the defense will be willing to do the reverse.

It follows that one would expect the direction of the bias from using third-down plays to depend on which team has more influence on the distribution of outcomes. For example, consider the extreme case where the offense always calls the same play but the defense can adjust its behavior. In this case, the defense can do at least as well as it would if the distribution of outcomes on fourth downs were the same as on third downs, and it may be able to do better. Thus using third downs to gauge what would happen on fourth downs would lead to overestimates of the value of going for it. Similarly, if only the offense can influence the distribution of outcomes, using third downs would lead to underestimates of the value of going for it. Since it seems unlikely that the defense has substantially more scope than the offense to affect the distribution of outcomes, this suggests that the use of third downs is unlikely to lead to substantial overestimates
of the value of going for it.

More importantly, the relative payoffs to different outcomes do not differ greatly between third and fourth downs. This is clearest for cases where the team has third and goal or fourth and goal. To a first approximation, on either down the offense will try to maximize its chances of a touchdown and the defense will try to minimize it. Thus both sides’ behavior on fourth down should be essentially the same as on third down. But even away from the goal line, the relative payoffs to different outcomes are similar on third and fourth down. For example, consider a team that is on its 30 and needs 2 yards for a first down. On third down (under the realistic assumption that the team will punt if it fails to make a first down), the benefit of gaining 15 yards rather than none is 1.4 times as large as the benefit of gaining 2 yards rather than none. On fourth down, the benefit of gaining 15 yards rather than none is 1.2 times as large as the benefit of gaining 2 yards rather than none. Thus, one would not expect teams to behave very differently on the two downs. As a result, any bias from the use of third-down plays is likely to be small.

The second approach to investigating the appropriateness of using the outcomes of thirddown plays is to examine how closely outcomes on fourth downs resemble those on third downs. In particular, one can compare the realized values of plays where teams went for it on fourth downs (that is, the immediate points scored plus the value of the resulting field position) with what one would expect based on the analysis of third downs.

This comparison is potentially problematic, however, for two reasons. First, the sample size is small. As described above, teams went for it only 118 times in the sample, whereas there are 4733 third-down plays. Second, times when teams choose to go for it are likely to be unusual: the teams may know that they are particularly likely to succeed, or they may be desperate.

To increase the sample without bringing in fourth-down attempts that are likely to be especially unusual, I expand the sample to include the entire game except for the last two minutes of each half (and overtimes). This increases the sample to 1338 plays. And as a partial remedy for the second problem, I experiment with controlling for the amount the team with the ball is trailing by and the amount it is favored by.

The results suggest that fourth downs are virtually indistinguishable from third downs. The mean of the difference between the realized value of the fourth-down attempts and what is predicted by the analysis of third downs is 0.006 (with a standard error of 0.7), which is essentially zero. When controls for the prior point spread and the current point differential are included, the coefficient falls to -0.042 and remains highly insignificant. The point estimate corresponds to the probability of success being one percentage point lower on fourth downs than on third downs, which would have almost no impact on the analysis.

Posted by: ed on September 28, 2006 02:00 AM

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