First, imagine that you are the coach of one of last night’s Super Bowl teams. It’s the second quarter, the score is tied, and your team faces fourth and one on your own 45-yard line. Do you punt, or do you go for it? Second, pretend that you are the general manager of a middle-income professional baseball team. This off-season, you have the opportunity to trade for either the New York Yankees’ Alfonso Soriano, or the San Diego Padres’ Brian Giles. Last year, Soriano hit more home runs, drove in more runs, and stole (many) more bases than Giles, but Giles walked much more often than Soriano. Which player would you choose?

At present, almost every football coach would instruct his team to punt in the above scenario, and almost every baseball general manager would trade for the Yankees’ speedy, power-hitting second baseman. But they would all be wrong. Football statistics (highlighted in yesterday’s New York Times) conclusively indicate that, on fourth downs around midfield, “the potential benefit of keeping the drive going outweighs the cost of giving the opponents good field position.” Football coaches, adhering to the rule of thumb that you should only go for it on fourth down when very close to the opponent’s goal line, or under dire late-game circumstances, therefore routinely miss easy chances to improve their teams’ odds of victory. Baseball general managers, similarly, are often overawed by eye-catching home run, RBI, and stolen base numbers, as well as by players (like Soriano) that fit their mental image of what a baseball star should look like. As a result, they end up neglecting the humble base-on-balls, even though a player’s ability to walk frequently and strike out rarely — an attribute Giles possesses in spades — is the single best indicator of future superstardom.

Over the last few years, a tiny minority of baseball and football teams have begun exploiting these (and other) inefficiencies in the sports “market.” The cash-strapped Oakland A’s, most famously, have made the acquisition of hitters with high on-base percentages and pitchers who produce disproportionate numbers of ground outs (another undervalued ability), the central tenet of how they construct their team. Despite one of the lowest payrolls in baseball, this approach has yielded three consecutive playoff appearances for the A’s — and by far the best dollars spent to games won ratio in the league. In football, no team has yet plumbed the statistical depths to the same extent as the A’s. But the New England Patriots, winners of two of the last three Super Bowls despite a roster nearly bereft of stars, ran in short-yardage situations more than any other team in football (a better option, statistically speaking, than passing), attempted the fewest two-point conversions of any team (another quantitatively advantageous move) — and, in the AFC championship game two weeks ago, shocked analysts by going for a midfield fourth down on the very first drive of the game. Coincidence? Almost certainly not. More likely, Bill Belichick and his Patriots have stolen a step on the competition by discovering, and ruthlessly taking advantage of, deviations in the football world from perfect rationality.

The recent success of statistically oriented, hyper-rational sports teams raises two fascinating questions. First, in what other fields of human interaction could rigorous cost-benefit analysis also have enormous and unexpected impacts? It is quite possible that businessmen routinely overpay for companies that have enjoyed temporary spikes in their stock price, that plaintiffs’ lawyers settle for less than they should when facing powerful defendants, or politicians’ responses to events overlook the lessons that could be gleaned from past experience. In these areas (and many others), I expect that a clever young thinker, armed with nothing more than reams of data, a solid grasp of statistics, and a spark of creativity, could turn the world upside down with the inefficiencies and irrationalities that she would find.

Second, once our bright young thing has identified and publicized some example of irrational decision-making, how long does it take the market to eliminate that inefficiency? The examples of the A’s and Patriots suggest that, just as they were blind to the inefficiency in the first place, most competitors in a market are also slow to change their less-than-ideal behavior even when confronted with evidence of its inadequacy. Though it has been several years since the A’s adopted their player-selection methodology, only two teams (the Boston Red Sox and the Toronto Blue Jays) have followed their lead, and no football team currently comes close to the Patriots’ statistical savvy. What this means, then, is that the rewards for discovering a decision-making flaw in sports (or, presumably, business or law or politics) are even greater than they should be. Imitation may be the highest form of flattery — but this is a maxim that most competitors seem to have forgotten.