In today’s Slate, Tim Harford writes about using game theory to analyze the optimal strategies for strikers and goalies in a penalty kick situation.

In soccer, penalty kicks pit the goalkeeper against a lone striker in a mentally demanding contest. Once the penalty-taker strikes the ball, it takes 0.3 seconds to hit the back of the net—unless the goalkeeper can somehow get his body in the way. That is simply not enough time for the keeper to pick out the trajectory of the ball and intercept it. He must guess where the striker will shoot and move just as the ball is being struck. A keeper who does not guess correctly has no chance.

Both striker and keeper must make subtle decisions. Let’s say a right-footed striker always shoots to the right. The keeper will always anticipate the shot and the striker would be better off occasionally shooting to the left—because even with a weaker shot it is best to shoot where the goalie isn’t. In contrast, if the striker chooses a side by tossing a coin, the keeper will always dive to the striker’s left: Since he can’t guess where the ball will go, best to go where the shot will be weak if it does come. But then the striker should start favoring his stronger side again.

So, what to do? The answer comes from a wartime collaboration between economist Oskar Morgenstern and mathematician John von Neumann. They produced a “theory of games,” which mathematically analyzed situations of strategic interaction—that is, any situation where participants have to take into account the other side’s responses. A free throw in basketball is not a strategic interaction, but a soccer penalty is. A “game” is a mathematical description of how all the possible payoffs to the different players vary with their different strategies—so if the goalkeeper jumps to his left while the striker shoots to the keeper’s right, the striker will get a high payoff and the goalkeeper will get a low one.

In fact, at least one economist has recently studied the strategies players use in penalty kicks and found them to be nearly perfect in a game-theoretic sense. In this complex subgame of anticipation, feigned signals, and reaction time, top soccer players are extremely skilled at maximizing their chances of scoring a goal.

Ignacio Palacios-Huerta, an economist at Brown University, found that individual strikers and keepers were, in fact, master strategists. Out of 42 top players whom Palacios-Huerta studied, only three departed from game theory’s recommendations—in retrospect, they succeeded more often on one side than the other and would have been better altering the balance between their strategies. Professionals such as the French superstar Zinédine Zidane and Italy’s goalkeeper Gianluigi Buffon are apparently superb economists: Their strategies are absolutely unpredictable, and, as the theory demands, they are equally successful no matter what they do, indicating that they have found the perfect balance among the different options. These geniuses do not just think with their feet.

Behavioral Finance researcher (and Columbia Business School Ph.D.) Meir Statman uses the stock portfolio that Martha Stewart divulged during the course of her 2004 trial to illustrate the types of cognitive biases that so often plague investors, even those as rich and powerful as Martha. Between June 30, 2000 and December 20, 2001, Martha’s NASDAQ-heavy portfolio lost 46% of its value. In addition, 23 of her 36 stock positions at that time were losers, together totalling over a million dollars in paper losses. Just before she sold the shares of ImClone Systems that got her into hot water, she unloaded 22 of those 23 losing positions, sending this note to a friend:

Just took lots of huge losses to offset some gains, made my stomach turn.

Why is it that realizing what had previously been only a paper loss is so painful for investors? Shouldn’t it be the declining market price that is most painful, not simply the sale that realizes our loss? This bias hurts the performance of the portfolios of many investors. We are too slow to sell losers, letting money languish in a bad investment instead of selling it off and putting the money to more productive use. Financial advisors employ some psychological tricks to try and soften the pain of these realized losses. One is the well-known strategy of selling off losers in December for tax purposes. A sale that would be framed as an investment loss in November can be re-framed as simply a tax deducation if sold in December. Another technique is to “swap assets” by selling the losing position and immediately using the proceeds to buy into a new position.

Normal investors like swaps because swaps blur mental accounts and distract their attention from the fact that they are realizing losses. Consider the mental accounting benefits of swaps recommended by Gross in his manual for brokers: “The two separate transactions (moving out of the loss and moving into a new position) are made to flow together by the magic words ‘transfer your assets.’ The prospect thought he was making a single decision, switching one investment into another. He was not being asked to think in terms of selling XYZ…”

What can investors do to avoid the trap of holding losing positions too long? Statman proposes one such strategy — “loss harvesting”:

…a rule that mandates loss harvesting at the end of every quarter makes it easier to realize losses because it makes loss realization automatic. (Note also how the term “harvesting” creates a positive frame. Harvesting connotes sweet fruit, not bitter losses.)

Read more: Martha Stewart’s Lessons in Behavioral Finance, by Meir Statman

As followup to last week’s post on “the management myth”, here’s an excerpt from a New York Times article on the value of an Ivy League MBA. There’s little doubt that an Ivy League MBA earns a premium in the marketplace, but the question remains: is that premium due to the education itself, or to the selection bias of top business schools only accepting candidates who would earn a similar premium with or without the added education?

“The real value of an Ivy League business degree is arguably not the education itself, but the screening of intelligence, drive and past accomplishments that the schools do,” said Ben Dattner, founding principal of Dattner Consulting in New York. “Just like with undergraduate degrees, if you’re smart enough to get into a top-tier school, you’re likely to inspire confidence.”

Agree or disagree?

Previously: The Management Myth

Nassim Taleb, one of the more colorful, controversial, and cosmopolitan commentators about the science and philosophy of uncertainty, has started a new blog. This is not to be confused with the notebook on his site which he takes pains to note is “not a blog“.

Taleb’s most recent notebook entry on the logic of prediction errors has some interesting observations about our perception of “conditional expectations” and randomness:

One main life expectancy is from Mediocristan, i.e. is subjected to mild randomness. In a developed country a newborn female is expected to die at around 79, according the insurance tables. When she reaches her 79th birthday, her life expectancy, assuming that she is in typical health, is another 10 years. At the age of 90, she will have another 4.7 years to go. At the age of 100, 2 ½ years. At the age of 119 , if she lives miraculously that long, she will have about nine months left. As she lives beyond the expected date of death, the number of additional years to go decreases. This is the major property of random variables related to the bell-curve. The odds of a large number is small, so the conditional expectation of additional days drops.

With scalable variables, the ones from Extremistan that we encounter in real life, you will witness the exact opposite effect. Say a project is expected to terminate in 79 days, the same expectation in days as the newborn female has in years. But the errors are scalable, i.e. power-law distributed. On the 79th days, if the project is not completed, it will be expected to take another 25 days to completion. But on the 90th day, if the project is not completed, it will have about 58 days to go. On the 100th, it will have 89 days to go. On the 119th , it will have an extra 149 days. On day 600, if the project is not finished, you will be expected to need to wait an extra 1590 days. As you see the longer you go, the longer you are expected to wait.

This subtle, but extremely consequential property of scalable randomness is unusually counterintuitive. I believe that this is the core reason for our missing in our forecasts as we do not take into account the logic of the large deviations from the norm. The distribution is Mandelbrotian.

This idea can illustrate many phenomena; it applies to the completion date of your next opera house, the time a refugee is expected to wait until he can finally return home, or the day when the next war will end.

In the June 2006 issue of the Atlantic Monthly, Matthew Stewart argues that the bulk of management theory is inane, and that students of management would be better served by studying philosophy than by getting an MBA.

During the seven years that I worked as a management consultant, I spent a lot of time trying to look older than I was. I became pretty good at furrowing my brow and putting on somber expressions. Those who saw through my disguise assumed I made up for my youth with a fabulous education in management. They were wrong about that. I don’t have an M.B.A. I have a doctoral degree in philosophy—nineteenth-century German philosophy, to be precise. Before I took a job telling managers of large corporations things that they arguably should have known already, my work experience was limited to part-time gigs tutoring surly undergraduates in the ways of Hegel and Nietzsche and to a handful of summer jobs, mostly in the less appetizing ends of the fast-food industry.

The strange thing about my utter lack of education in management was that it didn’t seem to matter. As a principal and founding partner of a consulting firm that eventually grew to 600 employees, I interviewed, hired, and worked alongside hundreds of business-school graduates, and the impression I formed of the M.B.A. experience was that it involved taking two years out of your life and going deeply into debt, all for the sake of learning how to keep a straight face while using phrases like “out-of-the-box thinking,” “win-win situation,” and “core competencies.” When it came to picking teammates, I generally held out higher hopes for those individuals who had used their university years to learn about something other than business administration.

After I left the consulting business, in a reversal of the usual order of things, I decided to check out the management literature. Partly, I wanted to “process” my own experience and find out what I had missed in skipping business school. Partly, I had a lot of time on my hands. As I plowed through tomes on competitive strategy, business process re-engineering, and the like, not once did I catch myself thinking, Damn! If only I had known this sooner! Instead, I found myself thinking things I never thought I’d think, like, I’d rather be reading Heidegger! It was a disturbing experience. It thickened the mystery around the question that had nagged me from the start of my business career: Why does management education exist?

There is no doubt that many books on management bear an uncanny and uncomfortable similarity to those found on the self-help shelves. But to extrapolate from that observation to a claim that management theory is useless and a business education is a waste of time is certainly a case of throwing the baby out with the proverbial bath water. Likewise, his argument that studying philosophy is a more effective use of one’s time than going to business school isn’t really explained, beyond the fact that Stewart himself studied philosophy at Oxford and went on to become a founding partner of the consulting firm Mitchell Madison. “It worked for me” does not make for a compelling argument.

Stewart does raise one interesting and controversial point, however. Do the elite business school programs really create better leaders and entrepreneurs through the education they provide, or do they simply cherry pick the students who are already most able — students who are likely to be successful with or without an ivy league diploma? Stewart claims the latter, and goes on to argue that MBA admission policies are really just an extension of the corporate recruiting processes of prestigious firms.

For companies, M.B.A. programs can be a way to outsource recruiting. Marvin Bower, McKinsey’s managing director from 1950 to 1967, was the first to understand this fact, and he built a legendary company around it. Through careful cultivation of the deans and judicious philanthropy, Bower secured a quasi-monopoly on Baker Scholars (the handful of top students at the Harvard Business School). Bower was not so foolish as to imagine that these scholars were of interest on account of the education they received. Rather, they were valuable because they were among the smartest, most ambitious, and best-connected individuals of their generation. Harvard had done him the favor of scouring the landscape, attracting and screening vast numbers of applicants, further testing those who matriculated, and then serving up the best and the brightest for Bower’s delectation.

Follow up on this question later…

Read more: The Management Myth