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

by L. Jon Wertheim

  “How can we get in?” Huizinga asked his colleague. “I’m sure it’s closed to the public.”

  “Easy,” the professor explained. One of his MBA students, Erik Zhang, was a family friend of Yao’s, tasked with running the workout. Zhang had wanted to reschedule his midterm so that he could help Yao impress the scouts. The professor told Zhang he could postpone the exam. As a gesture of thanks, Zhang agreed to sneak the professor and a friend into the workout.

  After walking into a dingy gym in downtown Chicago, alongside Pat Riley, Huizinga watched as Yao displayed his dazzling skills before a small audience of NBA scouts, executives, and coaches. “It was a cool afternoon,” says Huizinga. “I thought that was that.” But then Zhang invited Huizinga along for dinner. Huizinga didn’t know Chinese, but he knew basketball, and he knew all about negotiating. Zhang also realized that the Chinese authorities might be more receptive to dealing with a college professor than with a slick, in-your-face NBA agent. By the end of the meal, the group had suggested that Huizinga be Yao’s representative.

  So it was that John Huizinga, a University of Chicago professor by day, spent the better part of the last decade moonlighting as the agent for the Houston Rockets center, arguably the most popular basketball player on the planet. Huizinga traveled the world, negotiated more than $100 million in salary for his client, and haggled over the fine print on sneaker contracts. Says Huizinga: “It’s also meant that I’ve watched more NBA basketball than you might think humanly possible.”

  In so doing, he began noticing something curious about blocked shots in basketball. Some of them, he believed, had much more value than others. A block of a breakaway layup? That’s pretty valuable, since the opposing team is almost surely going to score. If the blocked shot is recovered by a teammate, who then starts his own fast break—a “Russell,” to borrow the coinage of popular columnist Bill Simmons—well, that’s even more valuable. After all, it not only prevents the opponent from scoring but leads to two points on the other end. Contrast this with a block of an awkward, off-balance leaner as the shot clock expires, or of a three-point attempt—that is, a shot much less likely to be successful. Or consider a shot swatted with bravado into the stands, enabling the opposing team to keep possession. Those blocks aren’t nearly so valuable.

  Huizinga calculated that if context were taken into account, fans and coaches might think differently about the NBA’s top shot blockers. He teamed with Sandy Weil, a sports statistician, to examine the last seven seasons of NBA play-by-play data, focusing on the types of shots blocked (e.g., jumpers versus layups) as well as the outcomes from those blocks (e.g., tipping to a teammate versus swatting out of bounds). They estimated the block of an attempted layup or a “non jump shot” to be worth about 1.5 points to the team. Without the block, opponents score or draw fouls most of the time, resulting in 1.5 points on average. For jump shots, which go into the hoop with less frequency, the value of a block is only one point. And so on.

  Huizinga and Weil also assigned a value to the outcome of each block. Blocking the shot back to the opponent was assigned one value. Blocking the ball out of bounds so that the opponent retained possession but had to inbound the ball was worth slightly more. Blocking the ball to a teammate was worth the most. Finally, they examined goaltending, the least valuable block for a team, as it not only guarantees two points to the opponent but occasionally results in a foul, leading to a three-point play.

  Sure enough, Huizinga and Weil found that if you rank players on the value of their shot blocks, taking into account the types of blocks and the outcomes, it differs significantly from the NBA’s list of the top shot blockers, which is simply numerical. As one glaring example, in 2008–2009, Orlando’s abundantly talented, abundantly muscled center, Dwight Howard, blocked 232 shots, which factored heavily in his winning the NBA’s defensive MVP award. Yet his accumulation of blocked shots was actually worth less, Huizinga and Weil calculated, than the 149 shots blocked by San Antonio’s Tim Duncan. How? It turned out that Howard often blocked shots into the stands, whereas Duncan often tipped the ball to a teammate. More important, Howard also committed goaltending violations more often than Duncan did. (In fact, Duncan, despite being a prolific shot blocker, hasn’t goaltended in over three seasons.) Howard may have blocked 83 more shots than Duncan did, but they amounted to a value of only 0.53 points per block for the Magic. Duncan’s average block was worth 1.12 points for the Spurs.

  When the top shot blockers were reranked by the value of their blocks rather than by the sheer number, Duncan’s status as a truly elite center was affirmed. Though he’s never led the NBA in blocked shots, four times over the last decade he’s posted the highest value-per-block totals. By comparison, Dwight Howard’s best showing on a value basis is fifteenth. Milwaukee center Andrew Bogut, not known as a particularly fearsome shot blocker, delivers value. Mavericks big man Erick Dampier does not. And Huizinga’s client, Yao Ming, falls squarely in the middle.

  The following table shows the ten most valuable shot-blocking performances over the last eight NBA seasons and the ten least valuable performances on a value-per-block basis. Tim Duncan owns four of the ten most valuable performances; Dwight Howard owns three of the least valuable.

  Of course, the total value of one’s shot-blocking is the number of blocked shots times the value of the blocks. If all your blocks are Russells, the most valuable type of block, but you produce only a handful of them a year, your score will not be very high. Similarly, if you block a ton of shots but most of the blocks aren’t that valuable, that isn’t so useful to the team, either.

  Although the study tried to account for as many factors as possible, it’s not perfect, as Huizinga and Weil readily admit. There’s no accounting, for instance, for the increased fouls a shot blocker can accumulate with overly aggressive play or the potential increases in offensive rebounds—when the team shooting recovers the ball—that occur when the shot blocker leaves his man to attempt a swat. The study also can’t account for any intimidation factor: how many shots a player may deter with his mere presence, how many times he causes the shooter to change his trajectory and angle. Still, the research highlights that not all blocks are created equal. It’s the value of an act, not the act itself, that ultimately matters.

  TEN MOST VALUABLE SHOT BLOCK PERFORMANCES FROM 2002 TO 2009

  TEN LEAST VALUABLE SHOT BLOCK PERFORMANCES FROM 2002 TO 2009

  That triggers a question: Why do we—and the NBA—count blocks rather than value blocks? The short answer: Counting is easy; measuring value is hard. We see this all the time in many facets of life and business. People count quantities (easy) rather than measure importance (hard) and as a result sometimes make faulty decisions. We award certificates for perfect attendance but seldom ask whether the winners learned more while in school. The associates promoted to partner in a law firm often are those who bill clients the most hours, but did they do the best work? We often care too much about how many stocks we own and not enough about the more relevant issue: the value of those stocks.

  Sports, too, are filled with rankings based on simple numbers that don’t always correspond to value. The interception of the nothing-to-lose Hail Mary pass on the play before halftime is worth far less than, say, Tracy Porter’s game-sealing pick of Peyton Manning in the fourth quarter of Super Bowl XLIV. But the stats don’t distinguish it as such. The value of an empty-net goal in hockey—when a losing team removes its goalie to have an extra skater on offense—isn’t nearly as important as a decisive overtime goal. Yet the stat sheet doesn’t make a distinction between them. Savvy general managers can recognize (and exploit) this kind of information, acquiring and unloading talent accordingly, much the way investment managers look for undervalued securities to buy and overvalued ones to sell.

  After the 2009–2010 NBA season, Dwight Howard was named the league’s best defensive player for the second year in a row. The vote was a landslide: Howard received 110 out of 122 first place votes. Howard le
d the league in both rebounds (13.2) and blocked shots (2.78) per game, the first player to lead in both categories for two consecutive years since the NBA started tracking blocked shots in the 1973–1974 season. But the voting surely would have been closer if his blocks had been valued and not simply tallied. Howard’s coach, Stan Van Gundy, observed: “I think people see the blocked shots and they see the rebounding, but I don’t think unless you’re a really astute observer that they see the other things he does for us defensively.”

  Other astute observers, though—basing their judgment on value, not raw quantity—might reach a less flattering conclusion.

  ROUNDING FIRST

  Why .299 hitters are so much more rare (and maybe more valuable) than .300 hitters

  Whether we’re buying batteries at Walmart, a fast-food value meal, or even a house, odds are good that the price ends in a nine. We’re numb to seeing $1.99 bottles of Coke, $24,999 cars, and even $999,999 McMansions on cul-de-sacs. In the case of gasoline, the price even extends to nine-tenths of a cent, say, $2.999 for a gallon of unleaded. This entire concept, of course, is silly. Purchase one gallon of $2.999 gas and it will cost you $3.00. It takes ten gallons before you realize any savings—and it’s a mere penny at that—over gas priced at an even three bucks.

  The difference between a price ending in a nine and one ending in a whole number is virtually meaningless, accounting for a negligible fraction of the purchase price, but test after consumer test reveals that there is great psychological value in setting a price point just below a round number. Even among sophisticated consumers who recognize the absurdity of it all, paying $9.99 is still somehow more palatable than paying $10.00. (Factor in sales tax and you’re paying over $10 in both cases, which makes it more absurd.) Round numbers are powerful motivators—whether it’s to hit them or avoid them—in all sorts of contexts.

  Devin Pope and Uri Simonsohn, then a pair of Wharton professors, examined the prices of millions of used cars and found something that was at once peculiar and predictable: When the mileage on the vehicles eclipsed 100,000, the value dropped drastically. A car with 99,500 miles might have sold for $5,000, but once the odometer of that car—identical year, model, and condition—rolled over 500 more times and posted 100,000 miles, the value fell off a cliff. Why? Because customers for a used car set a benchmark of 100,000 miles, and woe unto the seller whose jalopy eclipsed that number.

  When the two economists looked at the market for jewelry, they saw that pieces are sold as full karats and half karats but almost never as 0.9 karats. Why? Because shoppers have set a goal of a round number—“I want to buy her at least a two-karat ring”—and don’t want to come up a little bit short. To do so would make them feel they had shortchanged the intended recipient.

  In looking at human behavior, Pope and Simonsohn found that we’re slaves to round numbers. Every year more than a million high school students take the SAT, aiming for a round-numbered score as a performance goal. How do we know this? Until 2005, the SATs were scored between 400 and 1600 in intervals of 10. When students posted a score ending in a 90 (1090, 1190, 1290, etc.), they were 20 percent more likely to retake the test compared with students whose score ended in a round number (1100, 1200, 1300). The difference in the scores might be as small as a single question, and according to Pope and Simonsohn, those ten points do not disproportionately change an applicant’s chance of admission. Still, it meant everything to many teenagers (perhaps because they figured schools would have round score cutoffs). The most noticeable difference in students who decided to retake the test? It was between those scoring 990 and those scoring 1000.

  Some of the most arresting results came when the researchers considered the behavior of Major League Baseball players. Baseball, of course, is flush with “round number targets.” Pitchers strive for 20-win seasons. Ambitious managers challenge their teams to win 100 games. Hitters try like hell to avoid the notorious “Mendoza Line” of a .200 batting average. But no benchmark is more sacred than hitting .300 in a season. It’s the line of demarcation between all-stars and also-rans. It’s often the first statistic cited in making a case for or against a position player in arbitration. Not surprisingly, it has huge financial value. By our calculations, the difference between two otherwise comparable players, one hitting .299 and the other .300, can be as high as 2 percent of salary, or, given the average Major League salary, $130,000. (Note that though the average MLB salary is $3.4 million, it’s closer to $6.5 million for players batting in the .300 range.) All for .001 of a batter’s average, one extra hit in 1,000 at-bats.

  Given the stakes, hitting .300 is, not surprisingly, a goal of paramount importance among players. How do we know this? Pope and Simonsohn looked at hitters batting .299 on the final day of each season from 1975 to 2009. One hit and the players could vault above the .300 mark. With a walk, however, they wouldn’t be credited with an at-bat or a hit, so their averages wouldn’t budge. What did these .299 hitters do? They swung away—wildly.

  FREQUENCY OF WALKS DURING LAST AT-BAT OF SEASON

  We looked at the same numbers, and here’s what we found. Players hitting .300 walked 14.5 percent of the time and players hitting .298 walked 5.8 percent of the time, but in their final plate appearance of the season, players hitting .299 have never walked. In the last quarter century, no player hitting .299 has ever drawn a base on balls in his final plate appearance of the season.

  The following chart highlights these numbers. Note that it spikes like the EKG of a patient in cardiac arrest.

  If we look at the likelihood of a walk for hitters just below .300 versus just above .300 before the last game of the season—or even during the last game but before the last at-bat—we don’t see any stark differences. But for that last at-bat, when they’re desperate to reach that .300 mark, they refuse to take a base on balls, swinging away to get that final hit that will put them over the line. The following chart highlights this, even indicating that before the last game, .299 hitters actually walk slightly more than .301 hitters.

  FREQUENCY OF WALKS DURING LAST GAME OF SEASON

  What’s more surprising is that when these .299 hitters swing away, they are remarkably successful. According to Pope and Simohnson, in that final at-bat of the season, .299 hitters have hit almost .430. In comparison, in their final at-bat, players hitting .300 have hit only .230. (Why, you might ask, don’t all batters employ the same strategy of swinging wildly, given the success of .299 hitters? Does this not indict their approach the rest of the season? We think not. For one thing, these batters never walk, so their on-base percentages are markedly lower than those of more conservative hitters. Also, if every batter swung away liberally throughout the season, pitchers probably would adjust accordingly and change their strategy to throw nothing but unhittable junk.)

  Another way to achieve a season-ending average of .300 is to hit the goal and then preserve it. Sure enough, players hitting .300 on the season’s last day are much more likely to take the day off than are players hitting .299. Even when .300 hitters do play, in their final at-bat they are substituted for by a pinch hitter more than 34 percent of the time. In other words, more than a third of the time, a player hitting .300—an earmark of greatness—will relinquish his last at-bat to a pinch hitter. (Hey, at least his average can’t go down.) By contrast, a .299 hitter almost never gets replaced on his last at-bat.

  With the .299 players swinging with devil-may-care abandon and the .300 hitters reluctant to play, you probably guessed the impact: After the final game of the season, there are disproportionately more .300 hitters than .299 hitters. On the second-to-last day of the season, the percentage of .299 and .300 hitters is almost identical—about 0.80 percent of players are hitting .299, and 0.79 percent of players are hitting .300. However, after the last day of the season, the proportion of .299 hitters drops by more than half to less than .40 percent and the proportion of .300 hitters rises to 1.40 percent, more than a twofold increase. The chart below shows these statistics graph
ically.

  DISTRIBUTION OF MLB PLAYERS’ BATTING AVERAGE BEFORE, DURING, AND AFTER LAST AT-BAT OF SEASON

  At first we wondered whether pitchers might be complicit, serving up fat pitches to help their colleagues on the last day of the season, when games seldom mean much. It brings to mind the batting race of 1910, one of the great controversies in baseball history. That year, the Chalmers Auto Company promised a car to the player who won the batting crown. Ty Cobb was leading by nine points heading into the final game of the season, and much as some players still do today, Cobb took the day off to protect his lead. Cobb was a contemptible figure, a virulent racist disliked by most of his fellow players, including his own teammates. Cleveland infielder Nap Lajoie was second in the batting race and far more popular than Cobb. On the season’s final day, playing against the St. Louis Browns, Lajoie went eight for eight in a doubleheader, including seven bunt hits that “dropped” in front of a third baseman who had been positioned by his manager to play in short left field. When Lajoie reached safely on one bunt that was ruled a sacrifice, the Browns brass offered the official scorer inducements to reconsider. (He declined, and the executives who tried to bribe him were effectively kicked out of baseball for life.) Despite the generosity/complicity of the opponents on the season’s final day, Lajoie lost out to Cobb, .385 to .384.

  We found no evidence of similar collusion today between pitchers and .299 batters on the final day of the season. Even if the pitchers are aware that the hitter they’re facing is just below the .300 threshold, there’s no indication they’re tossing meatballs destined to be hit. Looking at the Pitch f/x data, which tracks not only the location but the speed, movement, and type of every pitch thrown, we found that neither the location, type of pitch, speed, movement, or any measureable attribute of pitches was reliably different when a pitcher faces a batter with a batting average just below the .300 mark at the end of the season. Pitchers either are unaware that batters are just shy of .300 or don’t care—they pitch the same way to a .299 hitter as they do to a .300 batter in the last game of the season.