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Authors: Tobias Moskowitz

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Leave a player with five fouls in the game and what happens? The average player with five fouls will pick up his sixth and foul out of the game only 21 percent of the time. A star is even less likely to pick up a sixth foul (only 16 percent of the time once he receives his fifth foul; remember “Whistle Swallowing”?). Thus, leaving a player in the game with five fouls hardly guarantees that he’ll foul out.

Bottom line: An NBA coach is much better off leaving a star player with five fouls in a game. By our numbers, coaches are routinely giving up about 0.5 points per game by sitting a star player in foul trouble (and that doesn’t include the minutes he might have sat on the bench with three fouls in the first half). That may not seem like much, but in a close game, in which these situations often occur, it could mean the difference between winning and losing. We estimate that leaving a player in with five fouls instead of benching him improves the chances of winning by about 12 percent. Over the course of a season, this can mean an extra couple of wins. Yes, a player may foul out of a game, but benching the player
ensures
that he’s out of the game. As
Jeff Van Gundy, former coach of the Houston Rockets and New York Knicks and current television announcer, once put it on the air, “I think
coaches
sometimes foul their players out.”

So why don’t NBA coaches let their players—particularly their stars—keep playing when they have a lot of fouls? Again, loss aversion and incentives. If you lose the game by following convention and sitting your player down, you escape the blame. But if you play him and he happens to foul out and the team loses, you
guarantee yourself a heaping ration of grief on sports talk radio, in columns, and over the blogosphere even though the numbers strongly argue in favor of leaving the player in the game. As with punting on fourth down, coaches are willing to give up significant gains to mitigate the small chance of personal losses. Presented with this evidence, one NBA coach maintained that he was still going to remove a player when he picked up his fifth foul late in the game. Why? “Because,” he said, “my kids go to school here!”

Another example of
loss aversion is seen in
baseball. Game after game, the same scene plays out with almost numbing familiarity: It’s the ninth inning, the manager for the winning team summons the liveliest arm in the bullpen, the PA system cranks up ominous music—Metallica’s “Enter Sandman” more often than not—and out trots Mariano Rivera, the Yankees’ peerless relief pitcher, or his equivalent, to record the save. Why? Because conventional baseball wisdom dictates that managers use their best relief pitchers at the
end
of games to preserve victories. The presumption: This is the most important part of the game, with the greatest impact on the outcome. Not for nothing are these pitchers called closers.

But where is it written that a closer must close? What if the most important moment in the game, when the outcome is most likely to be affected, occurs earlier? Might it not make more sense to summon Rivera or Boston Red Sox closer Jonathan Papelbon when the game is tied in the sixth inning and there are runners on base? Wouldn’t they be more valuable at this juncture than they are when they usually report to work: the ninth inning when their team is ahead?

Yet you almost never see a manager use his bullpen ace before the eighth inning. Why? Because, again, what manager wants to subject himself to the inevitable roasting if this strategy fails? If your closer isn’t available to seal the game and you happen to lose … well, managers have been fired for lesser offenses. (Keep in mind, too, that closers like to accumulate “saves”—which occur
if they are the last one pitching—since saves translate into dollars in the free agent market.)

Even in
hockey, one can see
loss aversion affecting coaching strategy. “
Pulling the goalie” and putting another potential goal scorer on the ice near the end of a game when your team is losing decidedly improves your chances of scoring a goal and tying the game, but it also increases the risk that with the net empty, an opponent will score first and put the game out of reach. We found that NHL teams pull their goalies too late (on average with only 1:08 left in the game when down by one goal and with 1:30 left when down by two goals). By our calculations, pulling the goalie one minute or even two minutes earlier would increase the chances of tying the game from 11.6 percent to 17.6 percent. Over the course of a season that would mean almost an extra win per year. Why do teams wait so long to pull the goalie? Coaches are so averse to the potential loss of an empty-net goal—and the ridicule and potential job loss that accompany it—that they wait until the last possible moment, which actually reduces their chances of winning.

When
do
we see coaches take risks? Well, when do we take risks in everyday life? Usually when there’s little or nothing to lose. You’re less likely to be loss-averse when you
expect
to lose. Think of your buddy in Vegas who’s getting crushed at the tables. Already down $1,000, he’ll take uncharacteristic risks, doubling down when he might otherwise fold, in hopes of winning it back. How many times have you gotten lost driving the back roads and taken a few turns based on intuition rather than consult your map or GPS? “Hey, why not? I’m lost already.” For that matter, how many schlubs have overreached around the time of last call, figuring that if they get shot down, they’re no worse for it?

Coaches are subject to the same thinking: In the face of desperation, or a nearly certain loss, they’ll adopt an unconventional strategy. They’ll go for it on fourth down when their team is trailing late in the game. They’ll pull the goalie with a minute left. They’ll break the rotation and use their ace pitcher in the seventh game of a World Series. Why not?

Consider how the forward pass became a part of football. It was
legalized in 1906 but hardly ever deployed until 1913, seven years later, when a small, obscure Midwestern school, Notre Dame, had to travel east to face mighty Army, a heavily favored powerhouse. With little to lose, the Fighting Irish coach,
Jesse Harper, decided to employ this risky, newfangled strategy by using his quarterback, Charlie “Gus” Dorais, and his end, a kid named
Knute Rockne. The summer before, Dorais and Rockne had been lifeguards on a Lake Erie beach near Sandusky, Ohio, who passed the time throwing a football back and forth. The Army players were stunned as the Irish threw for 243 yards, which was unheard of at the time. Notre Dame won easily, 35–13. After that, the Irish no longer resided in college football obscurity, Dorais and Rockne became one of the first and best passing tandems of all time, and the forward pass was here to stay. Dorais and Rockne would both go on to become revered Hall of Fame coaches, in large part because they continued deploying their passing tactics at the coaching level.

In the rare instances when coaches in sports embrace risk systematically—not in the face of desperation but as a rule—there is a common characteristic. It has nothing to do with birth order or brain type or level of education. Rather, those coaches are secure in their employment. If the experiment combusts, they have little to lose (i.e., their jobs).

Is it coincidence that New England Patriots coach
Bill Belichick opts to go for it on fourth down more often than any of his colleagues do? True, Belichick is a cerebral sort who understands risk aversion and probability as well as anyone, but he’s also won three Super Bowls since 2001 and has more job security than any other coach in the NFL. We noticed that before he became a coaching star, Belichick approached the game quite differently. In his first head coaching stint in the NFL, with Cleveland, Belichick amassed an unimpressive 45 percent winning percentage and had only one winning season in five years. In Cleveland, he never exhibited the penchant for risk-taking that he shows with the Patriots. Back when he commanded the Browns, he went for it on fourth down
only about one out of seven times. Since taking the helm at New England in 2000, Belichick has gone for it on fourth down a little more than one in four times.

But this tells only part of the story. In Cleveland, Belichick’s team trailed more often, and so many of the fourth downs he went for were in desperate situations—trailing near the end of the game. In New England, he had better teams and hence was ahead much more frequently, facing fewer “desperate” fourth-down situations. Looking only at fourth-down situations in the first three quarters with his team trailing by less than two touchdowns, we found that in Cleveland he went for it on fourth down only about one in nine times, but in New England he went for it about one out of four times in the same situations. Belichick was almost three times more likely to go for it on fourth down in New England than he was in Cleveland.

One could argue that having a better team in New England meant he was more likely to convert more fourth downs, which is why he chose to go for it more often. True, his Patriots converted more of their fourth-down attempts than his Browns did, but the differences weren’t big (59 percent versus 51 percent), certainly not three times larger. Plus, in Cleveland, since he attempted more “desperate” fourth downs, sometimes with more than ten yards to go, you’d expect the success rate to be lower. Controlling for the
same
yardage, Belichick’s Patriots were only slightly better than his Browns at succeeding on fourth down.

So what changed his appetite for risk? Belichick didn’t have great job security in Cleveland, as evidenced by his eventual dismissal in 1996. Even in New England the first couple of years, when his job was less certain, he remained conservative. Only after his teams had won multiple Super Bowls and he was hailed as “the smartest coach in football” did his risk-taking increase. His job security at that point wasn’t an issue.

But even a secure coach bucks convention at his own peril. In November 2009, the
Indianapolis Colts, undefeated at the time, hosted the New England Patriots. The latest installment in the NFL’s most textured rivalry, it was a Sunday night affair televised
on NBC. New England led comfortably for most of the game, but in the fourth quarter the wires of the Colts’ offense started to connect. Indianapolis scored a late touchdown to close the score to 34–28. The crowd noise at Lucas Oil Stadium reached earsplitting levels.

On the Patriots’ next possession, they moved the ball with deliberate slowness and faced fourth and two on their own 28-yard line. It was a compelling test case for risk management in the NFL. If the Patriots punted, it was a virtual certainty that Indianapolis would get the ball back, leaving
Peyton Manning slightly more than two minutes and two time-outs (one of their own and one from the two-minute warning) to move the ball 65 or 70 yards to score a touchdown—a feat he had achieved on many occasions, including the last time the two teams had met in Indianapolis.

If the Patriots went for it and converted, the game’s outcome would effectively be sealed. However, if the Patriots went for it and failed, they would give the Colts the ball inside their 30-yard line. So going for it would either end the game or—worst-case scenario—give the ball back to Manning and the Colts’ offense 35 to 40 yards closer than punting the ball would. If the Colts scored a touchdown quickly from that shorter distance, there might still be time for the Patriots to kick a game-winning field goal. There were other factors as well. The Patriots’ defense was visibly exhausted, and, thanks to injuries, two starters were missing from New England’s defensive secondary, another factor militating against punting. Watching the game at home in Arkansas, Kevin Kelley shouted at his television, hoping Belichick would have the “guts” (his word) to forsake punting.

Beyond gut intuition, the analytics also supported going for it. Crunching the numbers, the average NFL team converts on fourth and two about 60 percent of the time. If successful, the Patriots would almost assuredly win the game. If they failed and the Colts took over on the Pats’ 30-yard line with two minutes left and down by six points, the Patriots were still 67 percent likely to win the game. In other words, the Colts had only a one in three chance of actually scoring a touchdown from the Patriots’ 30, so
it was hardly as if the Patriots were conceding a touchdown if the fourth-down attempt failed. Alternatively, punting the ball would put the Colts at roughly their own 30, which gave the Patriots about a 79 percent chance of winning. There was, then, only a 12 percent difference in the probability of winning the game if the Patriots failed on fourth down versus if they punted the ball. And if they converted (which was 60 percent likely), the game would effectively be over. Adding everything up, going for it gave the Patriots an 81 percent chance to win the game versus a 72 percent chance if they punted.
*
Even tweaking these numbers by using different assumptions, you’d be hard-pressed to favor punting. At best, you could say it was a close call between punting and going for it; at worst, going for it dominated.

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