Football, Statistics, and Agency Problems

The most interesting part of Monday’s post on TARP may have been this little football example:

In honor of the changing seasons, imagine it’s the first quarter of a football game and you have fourth-and-one at the other team’s 40-yard line. Anyone who studies football statistics will say you should go for it; it’s not even close. (Some people have run the numbers and said that a football team should never – that’s right, never – kick a punt.) If the offense fails to make it, the announcer, and the commentators the next day, will all say that it was a bad decision. That’s completely wrong. It was a good decision; it just didn’t work out.

One of my friends was particularly intrigued by the theory that a football team should never punt. I recall reading this somewhere, but I couldn’t find it actually demonstrated anywhere, although this high school football team implemented the strategy – and won the state championship. That article cites “Do Firms Maximize? Evidence from Professional Football” by David Romer, who analyzes the punting question in detail.

He calculates the point value of a first down at any point on the field, and from that the point value of the “kicking” and “going for it” options at any point on the field; the point value of the punt option is based on the opponent’s expected field position, while the point values of the field goal and go for it options are based on your expected points and the expected resulting field position.

The conclusion (PDF p. 14) is that over most of the field you should go for it if you have four or fewer yards to go; there is a big spike around the opponent’s 33-yard line where you should go for it even on fourth and nine, because the net field position benefit of punting is low and the expected point value of attempting a field goal is low.

The implication, of course, is that football teams don’t maximize. Romer concedes that making the right decision on fourth down would lead to about one more win every three years, and this is probably outweighed by the asymmetric returns: you are more likely to be penalized (as a coach) if you go against convention and are wrong than if you follow convention, since the fans (and the owners) are more likely to notice departures from convention. So the incentives of football coaches are not simply to maximize points, but also to maintain their reputations.

It probably wouldn’t be too hard to come up with a banking analogy at this point, but I won’t beat a dead horse.

Update: Commenter Ian M. helpfully links to this analysis of the “never punt” strategy. Taunter also says that Gregg Easterbrook (Tuesday Morning Quarterback at ESPN) has been advocating this strategy.

By James Kwak

31 responses to “Football, Statistics, and Agency Problems

  1. What am I missing here? In the paper they studied the history of 700 hundred games in which the always-punt strategy was never used. If a team did use this strategy, surely everyone would notice within the first 10 or 20 games. The other teams would react accordingly and the strategy would result in a net disadvantage, wouldn’t it?

    In any case, please make the leap to banking. The analogy doesn’t translate for me.

  2. Eh, not sure where I got the “700” number.

    “Play-by-play accounts of virtually all regular-season NFL games for the 1998, 1999, and 2000 seasons were downloaded from the NFL Web site, nfl.com. Since I focus on strategy in the first quarter, I use data only
    from first quarters to estimate the V’s. These data yield 11,112 first- quarter situations.”

    Same issues though.

  3. James,

    While I admire Romer’s work in proving that technological innovation is endogenous, he– and all economists– should stay away from trying to apply their hokum to sports unless and until they are willing to accept that their definition of utility is insufficient to encompass everything that football players and fans care about. Football is not just science. It is combat. It is drama. Momentum matters.

    There’s a reason why all of the economics conferences worldwide in a year probably don’t pull in as much profit as a single Dallas Cowboys game: neoclassical economics assumes that monetary value is the ONLY value considered in the utility analysis. Everybody but economists know that isn’t true, and even most economists admit it in their heart of hearts.

    Another way to discuss all of this is what, precisely, are firms trying to maximize? The assumption that you seem to make from Romer’s strawman is that coaches care more about their reputations than winning, but we all know that a coach’s reputation is his record. In my time as an executive of a public company, I recognized that putting together a winning team meant creating a reputation that my team could rely on both to chart a positive course for them and to protect them from my mistakes. In other words, the only reputation I cared about as coach was the reputation I had with my players. If the players stop believing in the coach, the team will fail. A coach can’t win without his team, and without a winning record, what reputation does a coach have?

  4. Billy,

    You’re not the only one. I don’t get the analogy, either, particularly when many public CEOs have the reputation of being serial failures, at least from a shareholder perspective (I’m thinking of the guy who went from Home Depot to Chrysler than lost his job while getting a platinum ruby-encrusted parachute with helium boost). From a management/board perspective, however, they may well be best of breed winners.

  5. Perhaps the connection is as simple as this: CEOs, like coaches, don’t always go all out to win. Sometimes they’re just trying to keep their jobs.

  6. Absolutely. A slightly different example that’s stuck in my head is that of the late Roland Arnall. He made subprime lending a science, became a multi-billionaire, had the company pay a fine, and then was awarded an ambassadorship to the Netherlands. All that’s left of the company and many of the people he lent to, is dust. What’s the point of walking the earth if that’s the kind of legacy you know you’re going to leave?

  7. I have never worked for a CEO that worried about keeping his job, so I reject that generalization as false, which is not say that it is not often true.

    I think the “Agency Problems” mentioned in the title may give us a clue as to James’ intent. The agency problem refers generally to the conflict between the interests of the principal and the agent, and the tendency of the agent, in some situations, to put his own interests first. While I think that is a real phenomenon, I don’t think it is ubiquitous. John Bogle has written some good stuff on this topic, and I’m proud to say that the companies I worked for were not afflicted with that problem.

    I strongly believe, however, that what it means to “win” in a public company is a lot different than what it means to “win” in a private company. Between the demand for quarter-to-quarter earnings growth, the expectation of steady-as-she-goes change, and the effect of GAAP accounting and SOx compliance on decision-making, public company CEOs face a very different utility analysis than private company CEOs, which changes what it means to “go all out to win.”

  8. Billy,

    The point for the people who hired Arnall and made their money before what he created turned to dust is that Arnall made them a lot of money. The point for Arnall is that he made a lot of money.

    Personally, I think you can make a lot of money for your investors and for yourself while creating a sustainable business. It’s a bit harder, but I’ve seen it done, and I certainly plan to do so.

    That being said, the world tends to divide itself into people that believe either that (1) mankind is inherently good or (2) mankind is inherently evil. I’m a pragmatist that believes that people who believe that people are inherently good are relatively idealistic and people who believe that people are inherently evil are relatively mercenary. Therefore, I try to align myself with fellow pragmatic idealists who know that we can’t avoid working with mercenaries and plan accordingly.

  9. For a little more depth on the football punting analysis, see William Krasker’s football commentary blog, where he includes what he refers to as “go for it” tables.

    Available at:

    http://www.footballcommentary.com/goforittables.htm

  10. If I’m ever fortunate enough to meet Barry Switzer in my life, I’ll ask him. There is no one on God’s green earth better to ask about tough 4th and 1 decisions. Barry made a lot of tough 4th down calls in his life. And Oklahomans will always love him for it. Oklahomans know the REAL Barry Switzer. Wish I could share Jack Daniels on the rocks with Coach someday!!! We love you coach!!!

  11. Off topic (for the most part):

    Back to the world where spooks meet economics meet PR for a moment. Mark Thoma points to this post at:

    http://www.creditwritedowns.com/2009/09/weakest-employment-market-since-the-great-depression.html

    Note the PR savvy and the quick rise to the top of the econ blog heap reminiscent of some other blogs we know:

    “The site has quickly become one of the highest-ranked economics and finance sites on the Internet (now in the top 20 by traffic and ranked one of the best finance blogs on the Internet by finance resource Business Pundit). Posts by its authors have been featured in the mainstream media in the Guardian Newspaper, Reuters and the Chicago Sun Times as well as on big-name finance sites like the Financial Times, Seeking Alpha, the Prudent Bear and RGE Monitor. Edward Harrison also contributes guest posts at Naked Capitalism and has appeared on the BBC World Service and Fox News.”

    http://www.creditwritedowns.com/2009/09/weakest-employment-market-since-the-great-depression.html

    The author of record:

    http://seekingalpha.com/author/edward-harrison
    (Yes Raven, I know what you want to say, but you’re wrong)

    So getting back to the thesis that economists, and, or people that look like economists sometimes, are being used as propogandists — it makes sense to use ex-spooks or current spooks because they are already filtered for their talent and trained to lie. If they haven’t done a doctorate in econ already, send them through a quickie MBA program to give them facility with most of the lingo and then set them loose on the blogs. They know how to “build credibility,” “mount operations,” use the “limited hangout,” “deniability,” “cutouts,” and how to discredit and compromise opponents.

    So how does that post fit into the current message that the Mighty Wurlitzer is pumping out? It seems like a reasonably reasoned argument that things are really not all that bad. Why is the widespread message in the media that things are not all that bad? See Yves Smith’s recent post. To decelerate the crash? Is that the whole story?

  12. Gregg Easterbrook (Tuesday Morning Quarterback at ESPN) has been advocating this for years, and has probably done the best job advocating it. There are some wrinkles you are leaving out – clock/score and the importance of the other team’s field goal kicker – but as a general rule, teams wildly over-punt. Ted K’s reaction is common but ill-supported; far from being a “tough” call, going for it is generally the expected value-positive strategy. It’s only tough because it is unconventional and, crucially, because the failures are so much more visible than the successes.

    As for the parallels, there are many, but two bear specific mention in my mind:

    (a) Better to fail conventionally than succeed unconventionally. Suppose you recognized the problems in the mortgage market in 2003. Classical economic theory suggests you would short the sector, profit, and in so doing drive the market to equilibrium. But if you went short when everyone was minting money, you got fired by the end of 2005. By the time the bubble hit its late stages, natural selection had created an unusually optimistic group of participants. Furthermore, these participants – the guys who made money in 2006 and lost it in 2008 – all kept their jobs, because how could you hold them responsible for a mistake “everyone” made?

    (b) Sample sizes are almost always too small to make a meaningful assessment of individual talent. Bill Belichick is arguably the most successful coach in football history (as well as the closest anyone in the real game comes to Romer’s analysis). In his first head coaching job he went 36-44, was fired, and spent five years as an assistant before getting another opportunity. If you dig enough into most famous investors’ track record, you will find that a few deals made their careers. If Sears and Autozone had gone down and then up, instead of up and then down (ending at the same place), Eddie Lampert would be an anonymous failed fund manager.

    http://tauntermedia.com/2009/06/22/volatility/

  13. How interesting. I have not seen too much of your football in my life and it is so comforting for me to read that I was not totally off the wall when sometimes I just could not for the life of me understand… “why don’t they go for it?”. David Romer, thanks.

    From an article that I titled “Roping in the herd” and published in the Daily Journal in 1997 (no web sorry) I extract the following two paragraphs that describe another quite similar decision making process: –

    As an example, I can go back to the period just after Venezuela abandoned exchange stability (February 1983). I watched with surprise as the treasurers of large multinational companies blithely signed contracts that insured future exchange rates at such incredible costs that they seemed outright irrational. The premium paid easily surpassed the possible exchange losses that would be caused by reasonably predictable devaluations.

    When I tried to get to the bottom of this madness (frequently assisted by a shot of whisky), I invariably would receive the following explanation: “We actually have two accounting registries. In the first we register the exchange earnings or losses per se. In the second we register the cost of the insurance premiums to cover exchange risks. Our head office has become so sensitive to exchange risk that it doesn’t add both accounts to analyze the total net results. On the contrary, even if I save the company a fortune by not contracting this cover, but incur in so much as one cent in exchange losses, I would be handed my pink slip in a flash.” end of quote.

    Anyone wants to read the full article (which has to do with capital controls in small economies) you can find it here http://perkurowski.blogspot.com/1997/12/roping-in-herd.html

  14. Having played high school football on a team which punted on seventy or eighty percent of its possessions, I suggest that it matters whether or not you have an offensive line which can move forward, a back who can hit the holes, a quarterback who can hit receivers, or receivers who can catch his passes. Our team had very little help in any of these areas, but still managed to win nearly half its gaems, due in no small part to having the league’s best punter, who happened to be me. This suggests one of the problems with statistics based decisions: the results achieved by others in the past may be less relevant in your particular case than the actual facts of that case. This was the problem with using Mike Milkin’s junk bond research as a basis for the creation of a junk bond industry. His statistics on fallen angels didn’t apply to securities that were junk on the day of birth. He did okay for a while though.

  15. http://www.footballoutsiders.com/stat-analysis/2006/never-punting

    This is probably the type of analysis you were looking for.

  16. I believe most studies show that perceived momentum is actually a cognitive fallacy.

    If the most important asset to a coach is his record, then why don’t coaches make decisions that maximize their chance of winning? Or is your argument that the momentum factor outweighs the rest of Romer’s analysis?

  17. Teams should not punt … especially if playing in the new Cowboys stadium, as they’d hit the new wizz-bang giant TC screen!

  18. I won’t claim to be expert, but how much of the advantage to never punting is tied up in the idea that the opposing team won’t expect this? In other words, its a lot like other offensive strategies in that one must demonstrate both an ability and a willingness to execute diverse options.

  19. I think the problem is that there are various types of CEO’s and management teams out there, both at private and public companies with various motivations. There are a few old school owner-operators who depend on conventional wisdom, and those who attempt some level of innovation in an attempt to maximize their chances. There are CEO’s and management teams who go in and go for maximum short term returns. There are those who sit in place for years, knowing that their strategies will lead to an explosion down the line. Mix and match.

  20. James,

    My intent was not to make an argument about momentum. I was merely providing momentum as an example of the types of other considerations that a coach has to consider when making decisions in a game.

    My real argument is that I don’t accept the premise that a coach’s most important asset is his record, and that long-run statistics don’t matter much in the heat of the game. If a coach’s record was all that mattered to future employers, team owners would not bother with interviewing candidates, they’d just look at the stats and go with the candidate with the best record. If a coach’s record was all that mattered to players in a game, you’d never see tirades or dejected looks on the sidelines, but you do.

    My problem with Romer’s analysis is that it starts with a false premise that entirely ignores the real metrics by which coaches are measured, instead boiling it all down to a single metric of dubious value. Economists do this all the time, assuming away things they don’t know how to measure as exogenous to their models. By doing so, they often reach conclusions that are fundamentally wrong in the real world but fit their models quite nicely. In Romer’s case, by focusing on a single metric of success and assuming away other metrics, he is unable to reliably assess whether football coaches maximize or not. Coaches have to balance a lot of factors in a game just to get a win, and Romer’s statistical analysis cannot capture the complexity of the problem.

    While perceived momentum may be a cognitive fallacy in the virtual world constructed by behavioral economists to test whether there’s any such thing as a “hot hand,” it is something that you have to contend with in the real world. People are emotional, and when you manage them or lead them, you have to deal with their emotions. Those emotions can and do affect the outcomes of football games.

    A coach has to manage those emotions in the short run to better ensure his team executes successfully to the best of its ability. A coach following Romer’s suggested approach would quickly have a demoralized team that would wind up with a worse record than Romer assumes. How would a coach motivate his team when following Romer’s recommendations: “Hey, fellas, cheer up, we will wind up with one more win every three years through this strategy.” Quite the pep talk, particularly when a lot of the players won’t be on the team after any given season.

  21. There is also speculation that going for it on fourth nearly all the time would impact defenses on third down and short situations since the offense would not feel compelled to limit the play selection to those perceived to have a high chance of picking up the needed short yardage. The thinking is that it may be easier to get the 2 yard run because the defense has to legitimately defend the 40-yard pass play. I don’t believe it myself, since the defense has to key off the offensive spread anyway. Now it would be cool if the 4th down and 2 play was the 40 yard pass!

  22. That is hard to believe. The same logic would say that coaches need to yell, for example – many will justify their displays of emotion on motivational grounds – yet Tony Dungy has managed to win without doing so. If anything, the Conventional Wisdom is that a coach who goes on fourth is “challenging his team” and “showing confidence”.

    If you told a team of professional players before the season begins “I expect you to play four-down series on offense, because that’s going to give us a better chance of winning, and I need you to play through the conversions that fail” even the low-Wonderlic guys who populate the team should be able to appreciate it. These are guys who have to keep playing after red zone turnovers or kick returns for touchdowns.

  23. Bald Man didn’t make a generalization so I’m not sure what your’re rejecting. Chrome dome said “. . . don’t always. . .”, hardly a “generalization.” You’re like one of those crazy dudes in a town hall arguing against a position that no one holds. The comments on Baseline Scenario are among the best on the web; please, let’s keep it that way.

  24. “It’s no trick to make a lot of money if all you want to do is make a lot of money.” – Bernstein in “Citizen Kane”

  25. @Taunter,

    Since you weren’t able to respond to anything else I said before the pep talk analogy, I suppose I should have quit while I was ahead. :-)

    The bottom line is that Romer’s “analysis” is actually an overly simplistic model that, like most neoclassical economic models, assumes that only one type of value is to be considered in a utility analysis. The fact is that each and every one of us when making a decision balances several different types of value to determine what we think is the overall best outcome. Determining what’s in your own best interest is not limited to considering what yields the highest immediate monetary reward. (Sometimes I wish we still had some Institutionalists like Myrdal and John Kenneth Galbraith kicking around so this common sense concept wouldn’t seem so foreign to everyone.)

    Additionally, there simply is no basis for believing that Romer’s analysis would have any validity in the real world, where the probabilities change dynamically based on things like personnel, weather conditions, and the physical and emotional state of your players. These are things that the coach has to deal with and balance in real time with his players and not some statistically averaged ideal.

  26. Jame Kwak: “I believe that most studies show that perceived momentum is actually a cognitive fallacy.”

    I think that most studies show that streaks are not more likely than random. That has little relation to team momentum, which has to do with esprit, and is not a question so much of perception as creation.

  27. No. There is a very big difference between which play to call – a situation where the mixed strategy makes sense – and the decision to call an offensive play or punt.

    The decision to go for it (excepting fake punt situations) is known to the defense. But it is known to the defense on second down as well. If the expected value of a play from scrimmage on an early down – when the defense surely expects a play – is slightly more than three yards, it seems logical to expect that the very same situation holds on fourth down with everything else held constant.

    Clearly, there is variance around that expected value. There is a nonzero probability of the play going for a loss. The argument Romer and Easterbrook and others make is that the probability of getting fewer than one yard on a play from scrimmage is fairly small. Remember, there is no rule that says the only way to go for it is to line up heavy and run between the tackles…

    You still need to calculate the expected value of both a new set of downs for yourself and the field position gain from punting. This is the limited area where it would appear Scot and I agree. With an incredible tailwind you should be more aggressive about going for it (you need fewer yards to kick a field goal,the opponent needs more yards to kick a field goal against you) than with an incredible headwind.

    All that being said, the guys who play on Sunday punt too much. It is driven by the desire to avoid criticism. It is the same reason coaches focus on keeping the point spread close in losing efforts, or are so dedicated to avoiding being shut out. Last season the St. Louis Rams were trailing the New York Jets 40-0 with 9:56 remaining in the third quarter. They had fourth and seven on the Jets’ 19-yard line. They kicked a field goal.

    To tie the game they would have needed five touchdowns and five two-point conversions. The field goal didn’t do them much good in the quest for forty points in twenty-five minutes. But it did prevent Jim Haslett from needing to endure a week of talk radio discussion of being shut out. Indeed, he pulled the same stunt two weeks later against the Bears, kicking a field goal to pull to 21-3.

  28. Scot,

    Regarding this quote from your post above: “The fact is that each and every one of us when making a decision balances several different types of value to determine what we think is the overall best outcome.”

    Based on my life experiences of more years than I’d like to publish, I agree with you.

  29. Dear sir
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