Scorecasting: The Hidden Influences Behind How Sports Are Played and Games Are Won

by L. Jon Wertheim

  The two researchers also tried to rule out all other potential explanations by controlling for the day of the tournament, how far off a golfer was from the leader board, how the previous holes were played, and what number hole was being played. None of those factors changed the tendency to putt differently for par than for a birdie.

  The authors estimated that when the average golfer overvalues individual holes at the expense of his overall score, it costs him one stroke for each 72-hole tournament he enters. That may not seem like much, but most golfers would kill to improve their game by one stroke. For a top golfer like Woods, this mismanaged risk has the potential to cost him more than $1 million in prize money each year.

  Tiger even appears to be aware of his loss aversion. As he told the New York Times, “Anytime you make big par putts, I think it’s more important to make those than birdie putts. You don’t ever want to drop a shot. The psychological difference between dropping a shot and making a birdie, I just think it’s bigger to make a par putt.”

  It’s somehow reassuring that Tiger is, at least in this respect, decidedly human. However, Pope has a point when he says: “If Tiger Woods is biased when he plays golf, what hope do the rest of us have?”

  This was thrown into sharp relief at the 2009 PGA Championship at the Hazeltine National Golf Club in Minnesota. Heading into the final round, Woods appeared to be cruising inexorably to still another Major championship. It wasn’t just that he was carving up the course and leading the pack, eight shots under par. His unlikely challenger, Yang Yong-eun, Americanized to Y. E. Yang, was unknown even to hard-core golf fans.

  Yang’s anonymity was such that television researchers and media members scrambled to find basic biographical info. It turned out he was the son of South Korean rice farmers and didn’t discover golf until he was 19. Until then, Yang had been an aspiring bodybuilder, but he injured his knee and channeled his frustrations at a local driving range. Teaching himself golf mostly by watching instructional videos, Yang was able to break par by his twenty-second birthday. Unfortunately, that was also the year he was required to show up for mandatory military duty. When his service ended, he returned to golf and slowly worked his way up the sports org chart, from the Korean regional tour to the Asian tour to qualifying school, eventually earning his card on the PGA Tour.

  Heading into 2009, Yang, then 37, was making a living but not much more. He had never won a PGA event and had posted only one top-ten finish. Even at Hazeltine, he was lucky to make the cut after shooting a shaky 73 in the first round. (Tiger had shot a 67.) Now here he was in a showdown against Tiger Woods for a Major. Even Yang admitted that his overarching goal was to not embarrass himself. “My heart nearly exploded from being so nervous,” he recalled.

  But under the principle of loss aversion, in the face of loss, we perform more aggressively. Sure enough, facing an almost certain loss, Yang could let it rip and play with devil-may-care abandon. Woods, by contrast, was facing an almost certain gain—a lead, an inexperienced challenger, and, above all perhaps, a 14-for-14 record of closing out Majors when leading after 54 holes. But in the face of gain, we perform conservatively, more concerned about “don’t-mess-this-up” defense than about “gotta-get-it-done” offense. In essence, the entire round was one big birdie putt for Woods.

  You may remember the remarkable outcome. Playing with a striking absence of aggression, Woods shot three shots above par, a score of 75 that included an astounding 33 putts. “I felt that with my lead, I erred on the side of caution most of the time,” Woods conceded. Yang, in contrast, played with what Sports Illustrated called “carefree alacrity.” He smiled, shrugged, and went for the pin every time. A stroke ahead on the eighteenth hole, Yang continued to play with a level of audacity that suggested that he still believed he was facing a loss. After a solid drive, he was 210 yards from the hole. On the approach, he used his hybrid club to try to loft the ball over a tree and onto the green. It was a shot as intrepid as it was difficult. And Yang nailed it, maneuvering the ball within eight feet of the hole. He putted out for a sensational birdie and won the tournament, becoming the first Asian to capture a Major championship in golf. And with the help of loss aversion, he’d humanized Tiger Woods.

  Not that golfers are unique. Look closely and you’ll see that virtually all athletes, just like the rest of us, are affected by loss aversion in one form or another. Imagine a pitcher jumping to an 0–2 count on a batter. The pitcher is probably thinking, I’m gonna get a strikeout here, or, at the very least, I’m gonna get this guy out, since he’s far ahead in the count. The pitcher has already accounted for the “gain” of an out. Then, after a few more pitches, the count is 3–2. Suddenly the pitcher is in danger of losing what he thought he had.

  Now imagine the same pitcher in a different situation. He throws three lousy pitches to the batter, and the count is 3–0. He’s likely to think: Damn, I’m gonna walk this guy. But then he steadies himself and throws a pair of strikes, or perhaps the batter fouls off two pitches, or the umpire gives him a couple of favorable calls. The count is now 3–2. Suddenly the prospect of an out takes on the dimension of an unexpected bonus.

  In a vacuum, the pitcher should handle the two situations identically, right? In both cases the count is 3–2, and how he arrived there—i.e., the purchase price—shouldn’t matter. The goal is simply to get the batter out, much as the goal of the golfer is to accumulate the lowest cumulative score over 18 holes or the goal of the retiree is to accumulate the fattest retirement portfolio. Intuitively, we might expect the pitcher starting 0–2—perhaps questioning his control after throwing three straight balls—to throw conservatively and the pitcher who started 3–0 but has thrown two straight strikes to be more aggressive.

  But that doesn’t account for loss aversion.

  Inspired by the golf study, we looked at three years of MLB Pitch f/x data (more than 2.5 million pitches) and accumulated all 3–2 counts that started off as either an 0–2 count (where the pitcher is now staring at a potential short-term loss: the loss of the out he thought he had) or a 3–0 count (where the pitcher is facing a short-term gain). We then examined how the pitcher threw the next pitch. We found that when pitchers face a 3–2 count that started off 0–2, they throw far fewer fastballs and more changeups and curveballs than do pitchers facing the same full count but who started off 3–0. In a full count, a pitcher who starts off 0–2 is 51.5 percent likely to throw a fastball, 21.0 percent likely to throw a curve, and 8.2 percent likely to use a changeup. The same pitcher facing the same 3–2 count who starts off 3–0 throws a fastball 55.4 percent, a curve 17.7 percent, and a changeup 7.3 percent of the time.

  This is consistent with the principles of loss aversion. Changeups and curveballs are more risky and aggressive pitches. Pitchers will tell you that fastballs are more reliable and conservative. So a pitcher facing the possibility of a loss, because he used to be ahead in the count, will throw more aggressive pitches to avoid that loss. “I gotta get this guy out now!” The same pitcher in the same situation who was once behind in the count will throw more conservatively. He feels less urgency, and his best effort is not being summoned as a result. Like the golfer attempting a conservative putt for birdie, his choice suggests the attitude “I didn’t expect to be here anyway, so no great loss if this doesn’t work out.”

  Even more interesting: Pitchers facing a mental loss because they were once ahead in the count 0–2 not only pitch more aggressively but achieve more favorable outcomes. They’re more likely to strike out the batter—from swinging and missing as well as from called strikes. In addition, batters in these situations are less likely to make contact with the ball. They foul off fewer pitches and put the ball in play less often—and when they do put it in play, it’s more likely to result in an out.

  The batting average of Major League hitters facing a pitcher with a 3–2 count who was once ahead 0–2 is only .220 compared with a batting average of .231 when facing the same 3–2 count against the same pitcher
who once was behind in the count 3–0. That’s an 11-point difference for the same count against the same pitcher. Slugging percentages are nearly 20 points lower (0.364 versus 0.382), and virtually all other hitting statistics are lower in these situations as well. As with the higher success rate for identical par versus birdie putts in professional golf, pitchers who adopt less conservative strategies because of loss aversion fare better.

  We can also look at this from the batter’s perspective. A loss to a pitcher is a gain to a batter. Thus, a batter facing a 3–2 count who was initially in an 0–2 hole views this as a mental gain: “I thought I was going to strike out, but now I could easily walk or get a hit.” And a batter who was initially up 3–0 views the full count as a potential loss. “I thought I was going to reach base, and now I might not.” Loss aversion predicts that the batter will behave more aggressively in full counts when the count was previously 3–0 and more conservatively when the count was previously 0–2—the opposite behavior of pitchers. And that’s true. Batters are more conservative on 3–2 counts if they started out 0–2, swinging at fewer pitches, even those down the center of the strike zone. And when they swing, the outcomes are worse: more strikeouts, fewer balls put in play, and when they are put in play, more outs.

  Thus, it’s no surprise that their hitting numbers are lower—batters become too conservative at precisely the time when pitchers are becoming more aggressive. Similarly, a batter who was previously ahead 3–0 in the count will be much more aggressive on a 3–2 pitch, just when the pitcher becomes more conservative. Considering this behavior, the difference in hitting statistics makes a lot more sense.

  In football we can conduct a similar field experiment (literally). Ask yourself, when are teams in identical situations more likely to go for it on fourth down based on where they started the series? Let’s imagine that two teams each have the ball fourth and goal at the one-yard line. In the first example, the team started the series on the one-yard line and in three unsuccessful plays did not move the ball. In the second example, the team started at the ten and gained nine yards in three plays.

  In the first example, you’ve seen that either the other team’s goal-line defense is really good or the first team is having a hell of a time moving the ball 36 inches. Why tempt fate? Kick the field goal, right? In the second example, they’ve moved the ball nine yards in three downs. Odds are good that they can pick up one more yard on fourth down, so they’d be more inclined to go for it, right?

  Wrong. The results among NFL teams run completely counter to this. Teams in the first example are far more likely to go for it than are those in the second example. Why? Loss aversion. The team that started the drive first and goal at the one-yard line is thinking touchdown. They’ve already mentally accounted for the seven points. If, a few plays later, it’s still fourth and goal, they don’t want to lose the touchdown they thought was “in the bank.” In the second situation, the prospect of a touchdown is more of a “gain,” and the team is more likely to play conservatively, the same way a golfer guides a birdie putt or a pitcher throws a fastball on a 3–2 count when he started off 3–0.

  Facing fourth and goal from the one-yard line, NFL teams go for it 67 percent of the time if they started with first and goal from the one-yard line but only 59 percent of the time if they started first and goal from the ten-yard line. More generally, if teams that are facing fourth and goal from the one started inside the three-yard line, they go for it 66 percent of the time. But if the same teams started from the eight-yard line or farther out, they go for it only 61.5 percent of the time. This is exactly the opposite of what many would expect.

  Loss aversion is a powerful tool for predicting when teams will go for it on fourth and goal. When a team starts out first and goal at the one-yard line and is then pushed back to fourth and goal at the two- or three-yard line, the likelihood that they’ll go for it is 35 percent. And if it’s fourth and goal from the two- or three-yard line and they didn’t start out at the one? They go for it only 22 percent of the time. In other words, even when pushed back a couple of yards—implying that the defense is making a strong goal-line stand or that the offense has been ineffective—teams are still much more willing to go for it than if they had been moving the ball forward and found themselves in the same position. Exactly the opposite of what most of us might expect, but consistent with loss aversion.

  Here’s another way to evaluate the power of loss-averse behavior in the NFL. An extreme case of shortsighted loss occurs when a team scores a touchdown that is then nullified by a penalty. Imagine a kickoff for a touchdown. The returner makes a sharp cut, sees an empty field before him: 50, 40, 30, 20, 10.… He crosses the goal line, spikes the ball in the end zone, and is mobbed by teammates while the coach high-fives his assistants. But wait, there’s a flag on the play: an illegal block. So the team starts the drive back on its own 20-yard line.

  How do teams respond, having gone from the ecstasy of gain to the agony of loss so quickly in such situations? On drives in which a touchdown was called back because of a penalty, teams are 29 percent more likely to go for it on fourth down than they would have been otherwise (controlling for the number of yards to go, the position on the field, and the score in the game). Loss aversion dictates that the team will fight like crazy to get that touchdown back. And teams attempt to do so on that drive, as opposed to later in the game. Of course, whether a team scores on any particular drive is largely irrelevant. All that matters is the final score.

  Loss aversion affects the NBA in a similar way. Team A is winning by a healthy margin and probably is thinking, “We’ve got this game in the bag.” Mentally, they’ve already chalked one up in the win column. Then Team B makes a comeback, as NBA teams so often do. Suddenly the win Team A thought it had is in doubt. Worse, if Team B actually takes the lead heading into the fourth quarter, Team A is facing a potential loss. Conventional wisdom suggests that Team A will play passively. Countless times, we’ve heard a losing coach in this situation complain, “We stopped being aggressive.” Yet the principles of loss aversion suggest that in the face of this kind of loss, the team will play more aggressively. It is in the face of a gain that they will play more conservatively. Who’s right?

  Examining nearly 5,000 NBA games, we studied situations in which two teams headed into the fourth quarter within 5 points of each other but one team had led by at least 15 points in the third quarter. In other words, we looked at the final 12 minutes of close games in which one of the teams came from behind by a significant margin. We then subdivided our sample into two scenarios: In the first, the team that was ahead by 15 or more is still ahead, but by fewer than 5 points. This team is still facing a gain, but the prospect of a win is no longer as certain as it once was. In the second situation, the team that was ahead is now down by fewer than five points heading into the final period. Here, that team is facing a gut-wrenching loss. Its lead has evaporated, and now it’s behind, going from what was a sure win to the real possibility of a loss.

  It turns out that teams that had once been ahead by a lot but are now trailing by a few points in the fourth quarter start to play very aggressively: They shoot more three-pointers and shoot more frequently, taking shots four to five seconds faster than they normally do. This is exactly what loss aversion predicts. Facing a potential loss in a game they were sure they would win, like golfers facing par putts, they ramp up the aggression. By contrast, the team that previously had a large lead and is now up only a few points at the beginning of the fourth quarter starts to play very conservatively: Its players shoot fewer three-pointers and shoot less frequently, taking more time than normal between shots (i.e., holding the ball longer).

  Time and again, we hear coaches implore players, “Forget about what just happened,” “You can’t change the past,” or “Put it behind you.” The message: It doesn’t matter how you arrived at this point, just play as you normally do. In theory, they’re right. But it’s like asking the home owner to forget about her
purchase price when she considers a lower offer on her property. For professional athletes, the past is relevant and it’s hard to block out how they got into their current predicament.

  Research by Antonio Damasio of USC and George Loewenstein of Carnegie Mellon laid bare the power of loss aversion with a curious experiment. They revisited classic loss aversion experiments but tested subjects with brain damage in the area that is thought to control emotion. Compared with normal subjects, the emotion-impaired patients did not exhibit the same penchant for loss avoidance. As a result, in an investment game the researchers had designed, the brain-damaged, emotionally impaired subjects significantly outperformed the other, normal subjects. Why? Because they treated losses no differently from gains. The lesson? Short of a lobotomy, we all fall victim to loss aversion.

  Loss aversion influences everything from everyday decisions to athletic performance to individual investments. It also affects our behavior as sports fans. Thanks to loss aversion, we tend to place a higher value on objects we own than on objects we don’t even if it’s the same object. In theory, our willingness to pay for something should be the same as our willingness to be deprived of it. If you value LeBron James at $40 in your fantasy league, presumably you would pay $40 to own him or accept $40 to sell him. But it seldom plays out this way.

  This phenomenon, related to loss aversion, has a name—the endowment effect—coined by Richard Thaler, a behavioral economist at the University of Chicago. Thaler found that people feel the loss of something they own much more deeply than they feel the loss of something they don’t own. If we give you $100 and then take it away, that’s much more painful than telling you that we were going to give you $100 but decided not to.