Scorecasting (15 page)

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 led 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
 

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, $2.99
⁹
for a gallon of unleaded. This entire concept, of course, is silly. Purchase one gallon of $2.99
⁹
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.

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.

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 graphically.