As the New Orleans Saints lined up to kick off the second half of Super Bowl XLIV, CBS Sports color commentator and former Super Bowl MVP Phil Simms was explaining why the Saints should have deferred getting the ball after winning the pregame coin toss. Simms suggested that the Saints, 4½-point underdogs to the Indianapolis Colts, would be in a better position were they not giving the ball to future Hall of Fame quarterback Peyton Manning, who already enjoyed a four-point lead and had had 30 minutes to study the Saints’ defensive strategy. Simms had barely finished this thought when Saints’ place kicker Thomas Morstead surprised everyone – the 153.4 million television viewers, the 74,059 fans in attendance, and most importantly the Indianapolis Colts – with an onside kick. The ball went 15 yards, bounced off the facemask of an unprepared Colt, and was recovered by the Saints, who took possession of the ball and marched 58 yards down the field to score a touchdown and gain their first lead of the game, 13-10. The Saints would go on to win the championship in an upset, 31-17.

Although Saints quarterback Drew Brees played an outstanding game and the defense was able to hold a dangerous Indianapolis team to only 17 points, Head Coach Sean Payton received the bulk of the credit for the win, in large part because of his daring call to open the second half. Onside kicks are considered risky plays and usually appear only when a team is desperate, near the end of a game. In fact the Saints’ play, code named “Ambush,” was the first onside kick attempted before the fourth quarter in Super Bowl history. And this is precisely why it worked. The Colts were completely surprised by Payton’s aggressive play call. Football is awash in historical statistics, and these probabilities guide coaches’ risk assessments and game planning. On that basis, didn’t Indianapolis Head Coach Jim Caldwell have zero reason to prepare his team for an onside kick, since the probability of the Saints’ ambush was zero (0 onside kicks ÷ 43 Super Bowl second halves)? But if the ambush’s probability was zero, then how did it happen? The answer is that our common notion of probability – as a ratio of the frequency of a given event to the total number of events – is poorly suited to the psychology of decision making in advance of a one-time-only situation. And this problem is not confined to football. Indeed, the same misunderstanding of probability plagues mainstream economics, which is stuck in a mathematical rut best suited to modeling dice rolls.

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