Was Bill Belichick’s decision’s to go for a fourth and two conversion at his own 28 with 2 minutes left in the game against the Colts a boneheaded move?

There’s already been a lot of Monday morning quarterbacking by media talking heads (here, here, here, and here) saying yes. The stat gurus at Advanced NFL Stats say no, prompting this response from a commenter:

“Well, he went for it and it didn’t work. Then his team lost a game it was winning by six points with two minutes left.  We don’t need any more proof then that to know it was a dumb decision, no matter what any stat geeks claim.  This isn’t calculus calls. This is the NFL.”

The Nudge blog thinks there was nothing crazy or boneheaded about Belichick’s decision. Sure, it was a close call, but all the Monday morning quarterbacks are suffering from a condition known as the hindsight bias – because something happened means that something was always destined to happen.

Where were all these critics when Belichick successfully went for it on fourth and 1 from his own 24 against the Falcons last month?

Here is the Advanced NFL Stats analysis that we find convincing. Warning: if you are not a football fan, stop reading here.

With 2:00 left and the Colts with only one timeout, a successful conversion wins the game for all practical purposes. A 4th and 2 conversion would be successful 60% of the time. Historically, in a situation with 2:00 left and needing a TD to either win or tie, teams get the TD 53% of the time from that field position. The total WP (winning percentage) for the 4th down conversion attempt would therefore be:

(0.60 * 1) + (0.40 * (1-0.53)) = 0.79 WP

A punt from the 28 typically nets 38 yards, starting the Colts at their own 34. Teams historically get the TD 30% of the time in that situation. So the punt gives the Pats about a 0.70 WP.

Statistically, the better decision would be to go for it, and by a good amount. However, these numbers are baselines for the league as a whole. You’d have to expect the Colts had a better than a 30% chance of scoring from their 34, and an accordingly higher chance to score from the Pats’ 28. But any adjustment in their likelihood of scoring from either field position increases the advantage of going for it. You can play with the numbers any way you like, but it’s pretty hard to come up with a realistic combination of numbers that make punting the better option. At best, you could make it a wash.

For those who are curious, .60 is the probability of succeeding on fourth down and .53 is the probability the Colts will score a touchdown given a Patriot’s punt plus any increase in the probability of a Colts’ touchdown given that the Patriots don’t convert on fourth down.

Here’s another way to look at the decision with an additional probability assumption.

Let y = the probability the Colts score a TD, given that the Pats punt. The Advanced NFL stats equation calls y the winning percentage.

Let x = the increase in the probability that the Colts score a TD, given that the Pats do not convert.

0.6 + 0.4 (1-(y + x)) > (1-y).

Rearranging terms, x < 1.5 y.

Suppose the Colts probability of scoring would have been 0 if they took the ball over on their own goal line, and 1 if they take over on the Pats’ goal line. This basically means the Colts would definitely not score a touchdown if they had to go the length of the field, and would definitely score if they got to start at the Patriot’s 1-yard line. Suppose also that this probability increases linearly with field position. That means x is the net yardage of the punt (divided by 100), and y = .70 – x. (.7 is the probability of scoring when taking over on the opponents’ 30.)

Plugging terms into the algebraic condition x <1.5 y produces x < .42. So Belichick should punt if the expected net yardage of the punt is more than 42 yards. Guess what New England punter Chris Hanson’s lifetime indoor punting average is? 42.9 yards. His 2009 average is 39.6 yards.

Belichick’s critics treat the Colts’ touchdown as an inevitability. But the probability of a Colts’ touchdown was not 1. The New England defense could have held them to a field goal and still won the game.

Hat tip to Thomas Hubbard to whom all hate mail should be sent.

Addendum: For more on fourth down conversion calculations by Berkeley economist David Romer check out his paper, “Do Firms Maximize, Evidence from Professional Football.”

Richard Thaler’s latest Economic View column ponders the attraction of penny auction sites like Swoopo.com that let people bid for merchandise in one cent increments, while charging them lots of cents for the right to place a bid. In the end, the winner gets a great deal, $20 for a laptop or $15 for an iPod, with the rest of the item’s cost (plus the auction site’s profits) paid for by losing bidders. Consumer electronics aren’t the only items Swoopo has put up for bid.

Swoopo has even sold cash using this format — specifically, checks for $1,000. My colleague Emir Kamenica and I looked at 26 such auctions we found in a data set posted on the Swoopo Web site. For each of these, the average revenue to Swoopo was $2,452. Winning bidders also did well: Of the winners, all but two made money even after accounting for the cost of their bids, with an average profit of $658. Still, the important point to remember is that, collectively, bidders are losing money. Only the lucky last bidder is a winner.

Swoopo also has put up blocks of bids for auction. Since these bids cost Swoopo nothing, every penny earned is pure profit. One recent auction for 50 bids ended with a winning bid of $.60.

Sixty cents also happens to be the amount Swoopo.com charges people for each bid placed. As Thaler observes, it wouldn’t be hard for smaller competitors to come in and undercut Swoopo’s price. On the Times web page for Thaler’s column, three of Swoopo.com’s lesser known competitors are advertising through Google’s web ads. None of them seem to be competing with Swoopo on price: BidRodeo ($.70 per bid); Bidfire($1 per bid); BidCactus ($.75 per bid). Hard to imagine what else they are competing with Swoopo on. Free shipping? Strange, indeed.

Based on the scientific literature, we know that people who seek out and use calorie information are likely to be different from other eaters in many ways, including their motivation to cut calories. Sure, it’s possible that some people who looked at the information were persuaded to consume fewer calories, but it is equally plausible that those who were intending to order lower-calorie meals were more likely to seek out the calorie information.

By helping consumers make more informed decisions, calorie posting may be desirable even if it fails to reduce calorie intake. But effective policies to deal with obesity will need to involve much more than posting calories. People eat too much because calorie-dense foods are convenient and cheap, with large portion sizes priced to encourage overeating.

That’s Julie S. Downs, George Loewenstein, and Jessica Wisdom on the effectiveness of calorie posting nudges.

Wharton’s Kevin Volpp thinks a revised menu design might be a better nudge.

Incentivizing convenience of ordering low calorie food, by clustering these options together at the top of the menu, seems to have a significant impact. This indicates that traditional measures of informational provision are not always sufficient to motivate changes in unhealthy behavior.

The Federal Reserve will prohibit banks from charging overdraft fees on automated teller machines or debit cards, unless a customer has agreed to pay extra charges for exceeding account balances. Financial companies will have to explain overdraft programs and fees, as well as choices available to consumers, the Fed said today in a statement announcing a rule that takes effect next year.

The rule comes after Fed research indicated that consumers don’t like to be automatically enrolled in overdraft protection programs. Of course, most consumers don’t even know they’ve been enrolled until they get hit with a fee after overdrawing their accounts. More at Bloomberg.

(Hat tip: Mort Goldman.)

Addendum: The new default rule won’t apply to old fashioned checks or regularly recurring debits from checking accounts. As more and more people pay their cable, phone, and utility bills automatically and electronically, a new round of debate about the default rule may still be ahead.

1) Atlanta is testing out an incentivized recycling program where residents can earn and exchange points for “rewards, gift cards, groceries, and products” with participating retailers. (Hat tip: Mike Erskine)

2a) Rewarding first-graders for eating fruits and vegetables with small prizes.

2b) “‘If you want to know if an urban environment supports cycling, you can forget about all the detailed ‘bikeability indexes’—just measure the proportion of cyclists who are female,’ says Jan Garrard, a senior lecturer at Deakin University in Melbourne, Australia, and author of several studies on biking and gender differences.” From Scientific American.

(Hat tips: Christopher Daggett)

3) A scale that tells the world how much you weigh via Twitter. (Hat tip: Justin Holz)

4) Photos of calorie counting nudges at Freakonomics.

1) They both pay a price for their procrastination. American workers pay when it comes to planning and saving for their retirements; Kenyan farmers pay when it comes to planning and purchasing fertilizer for their harvests.

2) They both love free shipping.

In a working paper titled “Nudging Farmers to Use Fertilizer: Theory and Experimental Evidence from Kenya,” three economists from MIT, Harvard, and the University of California-Santa Cruz weigh in on a contentious policymaking debate with some interesting findings. Many policymakers consider fertilizer subsidies to be a standard tool for boosting agricultural productivity and economic growth in developing countries. Many economists criticize these subsidies as inefficient mechanisms, which are instead used to line politicians’ pockets and keep them in power. If Kenyan farmers behaved like econs, the economists’ argument goes, they would be able to figure out the exact amount of fertilizer necessary for generating more crops and more profits, all without the need for any subsidies. After all, it’s hardly a secret that fertilizer yields more crops, and since it can be bought and sold in almost any amount, farmers should easily be able to purchase the exact amount necessary for their plot of land.

But it turns out that most farmers behave like humans–71 percent of them according to the paper–by thinking they’ll buy fertilizer, which they’ll absolutely, positively buy…tomorrow. They overestimate their patience and planning talents, waiting until the last possible moment to buy fertilizer and ending up with not much of any. It is possible, authors Esther Duflo, Michael Kremer, and Jonathan Robinson say, that large subsidies could spur fertilizer purchases, but it is also possible that these subsidies could lead to wasted purchases, extra transaction costs, and fertilizer overuse among impatient buyers. (The consequences of saving too much seem less damaging than buying or using too much fertilizer.)

What if there was a commitment strategy that could help farmers use fertilizer more efficiently and boost crop yields?

Working with a non-government organization called International Child Support, the economists developed a plan to offer small, limited-time discounts right after the harvest when farmers have extra money from recent sales. The simplest form of the discount wasn’t much of a discount. Farmers were offered a voucher allowing them to pay full price for the fertilizer and get free delivery at a date of their choosing. But free delivery is a powerful incentive for a farmer who typically has to spend time and money going to town to purchase fertilizer. Farmers were also given the option to commit to these discounts before the harvest. The program could have offered discounts at different points during the harvest season, but the economists thought that earlier discounts would not need to be as big as later discounts in order to spur purchases. They tested the idea against a standard 50 percent subsidy and simple reminders about the importance of fertilizer (without discounts). Neither performed as well as the nudge. Simply offering free delivery early in the season increased actual fertilizer use by 46 to 60 percent, a bigger boost than with a half-off subsidy offered later in the season.

The Kenyan farmers example may offer some ideas for banks here in the U.S., which could certainly benefit from a healthier deposit base. There are many commitment strategies for saving – Save More Tomorrow being the favorite one from Nudge. The savings nudge with the closest resemblance to the fertilizer nudge is a debit card loaded with your tax refund. Aimed at Americans without bank accounts, the card provides a way to put cash aside without paying huge check cashing fees. Perhaps some marketing campaigns for special savings accounts or certificates of deposit with slightly higher interest rates could be offered around New Years Day, when people are always trying to make commitments, or tax day, when people have a few extra dollars in their wallet.

Of course, the real lesson from this nudge may be the power of free shipping. Would Americans accept lower interest rates or commit to locking up their money for longer periods if banks offered to pay the shipping costs (up to some amount) on their DVD and book purchases for the year?

Interested readers can find a full copy of the June version of the paper can be found here. A gated copy of the August version can be found here.

Question: Who decides what the best outcome is?
Thaler: Well, there’s the question. Clearly it’s not Richard Thaler and Cass Sunstein. One criticism I frequently hear is that we think we know what’s best for people and this is elitist thinking. I think in many situations, it is pretty easy for the choice architect to have a good idea what choices people would really prefer. I think if we go back to default options in the open enrollment period, do we think that people who forget to enroll are going to want no healthcare? Probably not. So it’s not that we think we know what’s best for them. It’s that we have a pretty good idea of what they would want the default to be if they were the choice architect. Sure, there may be some tough cases, but I think most of us would rather be healthier. We’d rather have our kids be well educated. We would rather not starve in retirement. We would rather not wake up some morning and have our mortgage doubled because of some term that was buried in the fine print. So I think we can make a lot of progress without much controversy. And there will be a few cases where it’s harder, and that’s what the politicians are elected to deal with.

Question: How do politicians sort out those hard cases amid conflicting interests?
Thaler: It’s difficult. I want to emphasize that we don’t envision a larger role for government. Government has to make decisions. They have to nudge. So why not do it effectively and transparently? And if we don’t like the way the government is doing it, then throw the bums out and elect somebody who will do a better job.

For more of the wide-ranging interview, check out the latest special behavioral issue of the Yale School of Management’s journal Qn.

Establishing a value added tax (VAT) in the United States is a topic of considerable debate and controversy. Such a tax, which would add a fixed percentage to every product or service, is standard in many European countries. There has been discussion about whether to add a VAT on top of existing taxes, or whether to reduce income taxes and offset the revenue losses with a VAT. Ted Gayer, Co-Director of Brooking’s Economic Studies, wonders what the behavioral implications of such a tax would be.

Traditionally, economists view the structure and application of a tax as unimportant. All that matters is the change in relative prices. But (economists Raj Chetty, Adam) Looney, and (Kory) Kroft find that structure and application do matter. For example, they find that consumers are less likely to buy an item if a sales tax is explicitly listed on the product than if the same tax is instead added at check-out.

The economists’ argument stems from a recent American Economic Review paper of a field experiment in a grocery store that varied the displayed prices of alcohol (gated copy here). The VAT raises interesting questions for policymakers who might be able to manipulate the salience of taxes in ways that would bring in more tax revenue, but potentially harm consumers. Check out the link to Brookings (Hat tip: Amol Agrawal).

Frequent Nudge blog readers might have watched Rory Sutherland’s TED talk about the intangible “perceived value” that advertising adds to products. Sutherland cites some historical examples of counter intuitive ways to change behaviors. For instance, the King of Prussia wanted his subjects to eat potatoes so he ordered people to eat them. Complete failure. Undeterred, he got the idea to restrict potato consumption to the royal family and set up a special King’s potato garden. Suddenly everyone wanted one.

A version of this strategy is alive and well on the University of Texas football team. Football fans often refer to three phases of the game – offense, defense, and special teams. Of these, special teams is the ugly duckling. Typically, special teams players aren’t offensive or defensive starters, special teams plays are after thoughts for most fans because scoring is so rare, and special teams skills involve a lot of unglamorous “dirty work” like blocking and tackling. Nevertheless, great special teams play can be a huge advantage for teams through turnovers, touchdowns, field position, and momentum swings (plenty of economists don’t buy the momentum swings argument).

Noting the importance and structural problems associated with special teams units, Duane Akina, the special teams coach of the Longhorns since 2001, has added a ton of “perceived value” to the forgotten phase. In a fascinating piece in today’s Austin American-Statesman, Alan Trubow reports on changes Akina has made:

1) He convinced many of the Longhorn’s superstars to play special teams. Superstar 0 was wide receiver Roy Williams, the seventh pick in the 2004 NFL draft, who now plays for the Dallas Cowboys. This year, star wide receiver Jordan Shipley returns punts.

2) He created a point system like to the one used by Marriott hotels in which players earn points for making certain plays, which lead to special perks like membership in “block party,” “gold,” and “diamond” clubs.

3) He kept the clubs exclusive. Subjectively, of course.

“I can’t tell you too much about the block party because it’s a team thing. Really you have to be a member of the block party to understand it,” said Akina, who came up with the idea in 2003 or 2004.

Quarterback Colt McCoy, the biggest superstar on this year’s team, has supposedly lobbied for a membership.

“I’ve tried and I’ve tried to get on that unit,” Texas quarterback Colt McCoy said. “When I’m walking by their office on the way to the offense I always stop and say, ‘Hey, I’m ready. I’m here. (No.) 12 is always ready.’ You walk by there and they’re all happy, yelling and excited. You just want to be a part of it.”

But despite being a Heisman Trophy runner-up, McCoy’s not welcome as a member of the block party.

“The rules are strict,” (special teams member) Curtis Brown said. “You only get in if you earn your way in. That’s just the way it is. We’ve got to keep it that way. If we didn’t, everybody would be a member.”

The result: Texas’ special teams have blocked 45 punts since 2002, the second most in the nation, including three this season. They have also scored six touchdowns in 2009, and have the highest kickoff return average (31 yards) of all FBS teams.