Scorecasting (16 page)

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.

Data, however, tell us what isn’t the same: Batters hitting .299 swing more liberally, taking fewer called strikes and balls but having more swings and misses, even when facing three balls in the count. In their last at-bat they did everything possible
not
to draw a walk. As a result, they got more hits. In comparison, .300 batters drew many walks and did not swing on three-ball counts.

Of course, the .300 mark isn’t the only round number players strive to attain. The century mark for runs batted in (RBIs) is another coveted goal, and we see the same pattern, with many players ending the season with 100 RBIs and few ending with 99. Again, the differences are generated mostly from the last game and even the last at-bat of the season. First, players stay in the game long enough to hit their hundredth RBI, skewing the numbers. Remove that last at-bat and the prevalence of players with 99 RBIs is equal to that of those with 100.

The same pattern emerges for players with 19 or 29 (or 39 or 49) home runs. Players do everything possible to move up to the next round number, and so on their last at-bat, they “swing for the fences.” We see a disproportionate number of players hitting 20 or 30 (or 40 or 50) home runs compared with 19 or 29 (or 39 or 49) home runs, often thanks to that last at-bat.

We see the same thing with pitchers trying to reach 20 wins for the season. Managers will even use their starting pitchers in relief toward the end of the season to boost their win totals. As with .300 versus .299 hitters, year to year we see more 20-game winners than 19-game winners.

Like achieving a .300 batting average, the difference between having 99 versus 100 RBIs, or 29 versus 30 home runs, or 19 versus 20 wins as a pitcher is worth real money in terms of future salary. Teams, owners, and general managers (GMs) clearly value the higher round numbers. In this respect, players may be acting economically rationally, responding to the incentives provided by teams to do everything they can on their last at-bat to reach those numbers.

We also noticed something else. The numbers above and those from the study looked back only to 1975, a period during which free agency was in force.
^*
We took a look at the data going way back before free agency (prior to the early 1970s). We found that the number of players hitting round numbers exactly, relative to those just missing them, diminished significantly before the free agent era, another clue that players are responding to the
financial lure of round numbers.

The puzzle is
why
the Republic of Sports values round numbers so much. One might even contend they should value round numbers
less
because they are being gamed by the players. Is the extra salary paid for a .300 hitter really justified when it is determined largely by a single at-bat on the last play in what was probably a meaningless game at the end of the season or when it was attained by sitting out the last game to ensure that the player’s average didn’t go down? The difference between a .300 and a .299 hitter is negligible—one misdirected ground ball, one blooper into short center field, one random bounce, one generous judgment by an official scorer over the course of a season. We would argue that .300 and .301 hitters
are overvalued and .298 and .299 hitters are undervalued. A hedge fund manager would spot this as an “arbitrage” opportunity and unload the overvalued asset and buy the undervalued one. A savvy GM might consider doing the same thing: trading the .300 hitter for a player who hit just under .300, saving many thousands without affecting the hitting performance of his lineup.

Want an example of a player who has benefited greatly from round numbers? In 2003, remarkably,
Bobby Abreu, then of the lowly Phillies, entered the last game of the season hitting .299 with 20 home runs and 99 RBIs, just shy of two prized benchmarks. The Phillies, long since eliminated from the playoffs, faced the Atlanta Braves, a team that had clinched the NL East title several weeks before. In the first inning, Abreu hit a groundout to first base that scored a runner on third, giving him 100 RBIs for the season. However, the groundout lowered his average to .2986 (172 hits in 576 at-bats). Coming up to bat again in the bottom of the third inning, he singled to center, driving in another run, giving him a .300 average for the season. He was taken out of the game before he could bat again.

A year later, in 2004, Abreu again entered the last game of the season hitting .299, and once again the Phillies were out of playoff contention. In his first at-bat he doubled, giving him a .300 average (172/573) for the season. However, he also had 29 home runs, so he continued playing to try to hit his thirtieth. After his hit in the first inning, he had a cushion—he could make an out and still keep his average above .300. (If he failed to get a hit, his average would drop to .2997—172 hits in 574 at-bats—and still round up to .300.) In the bottom of the third inning, Abreu went deep on an eight-pitch at-bat, hitting his thirtieth home run
and
getting a .301 average for the season. And what did he do? You guessed it. He left the game before he could bat again.

In his dozen full Major League seasons, Bobby Abreu has had
five
seasons finishing with exactly 20 or 30 home runs,
seven
seasons finishing with 100 to 105 RBIs, and
no
seasons with 95 to 99
RBIs. Put it this way: Surely, breaking these thresholds didn’t hurt his contract negotiations. In 2002, he was awarded a five-year, $64 million contract with a $3 million signing bonus. With the previous contract he was making $14.2 million over three years.

Athletes and fans also care deeply about the milestones of career statistics. No elite baseball player wants to end his career with 999 RBIs or 299 pitching victories. (Not for nothing is the Bernie Mac movie called
Mr. 3000
, not
Mr. 2999.
) And no career stat seems to get more attention than home runs. Whenever a player nears a benchmark in home run totals, the milestone becomes a millstone. In the summer of 2010,
Alex Rodriguez, the Yankees’ controversial slugger, hit his 599th home run in his 8,641st at-bat, a clip of one dinger every 14.4 plate appearances. However, it took him 47 at-bats—including 17 straight hitless ones—to finally reach his 600th home run on August 4, 2010. (It also took him 29 at-bats to go from 499 to 500.) Yet after hitting his 600th home run, A-Rod went on a five-game hitting streak; within the next ten days, he’d hit home runs 601, 602, 603, and 604. Why was going from 599 to 600 more important than going from 598 to 599 or 600 to 601?

As you might have guessed, it’s not just baseball that reveres round numbers. In the NFL, rushing for 1,000 yards is a benchmark every running back strives to achieve. A 1,000-yard rusher is perceived to be worth more than his 990-yard counterpart, and so running backs entering the last game just under 1,000 yards naturally get the ball more often than normal (18.3 versus 14.7 carries on average) and rush for more yards than normal (78 versus 62.5). Players with just over 1,000 yards run the ball in their last game about the same as they always do—67.2 yards on 15.5 carries—which is less than the numbers for their counterparts who started the day on the short side of 1,000 yards.

Of course, part of what we see in professional sports is driven by incentives. Although most sports and teams frown on bonus clauses—in which players are rewarded for hitting statistical benchmarks that
might put individual interests before team interests—players do stand to gain in future contracts if they break certain thresholds. The question is, what’s so special about those benchmarks? Is achieving 1,000 yards rushing really that much more valuable than getting 999? The lure of round numbers creates artificial barriers and causes us to overemphasize and overvalue them and, more to the point for general managers, undervalue those who barely miss the mark.

The same is true, of course, of areas outside sports. In the financial markets, we see perhaps the most extreme example of targeting numbers. Every fiscal quarter corporations announce their earnings numbers, which are compared to target earnings set by analysts’ consensus forecasts on Wall Street. Beat your earnings forecast by a penny or two a share and your stock price will rise. Miss it and see that price plummet. But of course the target is just an estimate, with plenty of chance for error. Beating it or missing it by a little is likely to be the result of good or bad luck—in other words, randomness. Surely, failing to hit a quarterly target by a few pennies shouldn’t matter in the long run, should it?