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?
Tell that to corporate executives. Among the tens of thousands of earnings announcements and earnings estimates each quarter, very few firms miss by a penny. Just like aspiring .300 hitters, a huge number of firms each year meet their targets exactly or exceed them by a penny. How do they do this? Well, accounting rules offer some discretion for the way corporations deduct expenses, report income, depreciate assets, and so on, and all these things can be used to alter the bottom line slightly. If its earnings are going to fall a bit short, a corporation may take a tax deduction this quarter rather than next or defer the expense on new equipment until next year to bump up earnings this year. The following graph, from an academic paper by Richard Frankel and Yan Sun from Washington University in St. Louis and William Mayew of Duke University, highlights this phenomenon. Plotting the frequency of corporate earnings “surprises”—the difference between the actual earnings numbers and the consensus forecast set by analysts—shows that a disproportionate number of firms exactly meet their target, having zero earnings surprises. Another huge percentage of firms beat their targets by exactly one penny. In contrast, very few firms miss by a penny. From a statistical standpoint this is extraordinary. Randomness suggests that as many firms would miss by one cent as would meet or beat the target by one cent.
FREQUENCY OF FIRM QUARTERLY EARNINGS SURPRISES
If the graph looks eerily familiar, it should—it resembles the number of .300 hitters plotted against the paucity of those hitting .299. Corporations, like professional athletes, continually work to “manage” (or game) their performance numbers. Athletes do this each year before the season ends, corporations each quarter before they’re evaluated by investors and analysts.
Early on, investors in the financial market, just like sports GMs, seemed to play along. Miss your target by a cent and your stock price plummets. Beat your target by a penny and your stock price rises. However, investors have caught on. Today, just meeting an earnings target isn’t enough. The stock price will drop. Why? Because investors have figured out that just meeting the target probably means the firm did everything it could to make its earnings look good. Translation: The news is not quite as rosy as the earnings numbers indicate, just as many of the players who squeak by with .300 probably have averages that inflate their actual performance. Come salary time and after-season trades, GMs and owners take note.
* Free agency allows players to negotiate and sign with other teams once their contracts expire. Previously, teams could invoke “reserve clauses” that allowed them to repeatedly renew a player’s contract for one or more years and did not allow the player to terminate it.
THANKS, MR. ROONEY
Why black NFL coaches are doing worse than ever—and why this is a good thing
Even without the benefit of hindsight, Tony Dungy seemed to be the perfect representation of what NFL teams look for in a head coach. He carried himself with a quiet but towering dignity, at once firm and flexible, stern and compassionate, fully committed to his job, his family, and his faith. His players revered him. His assistants aspired to be him. Even the doctrinaire members of the media spoke of him in glowing terms. Mel Blount, the Pittsburgh Steelers’ Hall of Fame cornerback, played with Dungy in the late 1970s. “Even then you knew it,” says Blount. “Tony was born to be a head coach in the NFL.”
After a long stint—too long, many thought—as an NFL assistant, Dungy, an African American, finally got his chance. The Tampa Bay Buccaneers hired him as head coach in 1996. Although Dungy acquitted himself well, he couldn’t alchemize his passion and professionalism into victories—at least not enough of them. In six seasons, Dungy’s teams won more than half their games and he took the Bucs to the playoffs four times, but the teams struggled once they got there. Two days after a 31–9 defeat to the Philadelphia Eagles in the 2001 postseason, Dungy was relieved of his coaching duties—a decision that seemed validated when his successor, Jon Gruden, coached the team to a Super Bowl win the next season.
At the time, Dungy’s firing left the NFL with just two African-American head coaches, roughly 6 percent. On its face, it was a dismal record, especially when you considered that African Americans made up nearly three-quarters of the league’s players. And this wasn’t an “off year.” In 1990 and 1991 there was just one African-American head coach in the NFL. From 1992 to 1995 there were two. There were three between 1996 and 1999, and there were two in 2002. This struck many as wrong, but statistics alone weren’t enough to show bias. One could just as easily claim that the disproportionately small pool of white players was, statistically anyway, more anomalous. It wasn’t unlike the English Premier League in soccer, where 75 percent of the coaches are British but the majority of the players come from outside England.
Yet Johnnie Cochran Jr.—the controversial lawyer remembered best for his glove-doesn’t-fit defense of O. J. Simpson—joined forces with another activist attorney, Cyrus Mehri, and decided to challenge the NFL’s hiring practices. At the time, Cochran and Mehri had been working on a case targeting what they saw as biased employment practices at Coca-Cola. In the course of the Coke case, they had crossed paths with Janice Madden, a sociologist at the University of Pennsylvania specializing in labor economics. Madden was in Atlanta, working on the same case, using a statistical model to demonstrate that women were not, as the company alleged, inferior salespeople. A thought occurred to Cochran and Mehri: Maybe Madden could initiate a similar study with respect to NFL coaches.
Although Madden shares a surname with former NFL coach, popular NFL announcer, and video game impresario John Madden, the football similarities ended there. She was not much of a fan. Her husband was a Philadelphia Eagles season ticket holder, but she preferred to spend her Sundays at home. Still, she made Cochran and Mehri an offer: “If you can put the data together for me, I’ll do this pro bono.” They did, and she did.
Madden found that between 1990 and 2002, the African-American coaches in the NFL were statistically far more successful than the white coaches, averaging nine-plus wins a season versus eight for their white counterparts. Sixty-nine percent of the time, the black coaches took their teams to the playoffs, versus only 39 percent for the others. In their first season on the job, black coaches took their teams to the postseason 71 percent of the time; rookie white coaches did so just 23 percent of the time. Clearly, black coaches had to be exceptional to win a job in the first place.
Perhaps, one could argue, black coaches ended up being offered jobs by the better teams: the franchises that could afford to pursue talent more aggressively. Madden reran her study, controlling for team quality. African-American coaches still clearly outperformed their colleagues. If this wasn’t a smoking gun, to Madden’s thinking, it surely carried the strong whiff of bias. If African-American football coaches were being hired fairly, shouldn’t they be performing comparably to white coaches? The fact that the win-loss records of African-American coaches were substantially better suggested that the bar was being set much higher for them.
When Madden went public with her findings, she was blindsided by the criticism. The NFL made the argument that Madden’s sample size—in many seasons there were just two African-American coaches—was too small to be statistically significant. Whose fault was that? Madden wondered. At the national conference for sports lawyers, an NFL executive dismissed Madden’s work, suggesting that she could have run the numbers for “coaches named Mike” and for “coaches not named Mike” and come up with similar results. (Curious, Madden ran the numbers and found that this wasn’t the case.)
Still, due in no small part to the work of a female sociologist whose football knowledge was admittedly modest, the NFL changed its ways. In 2003, the league implemented the so-called Rooney Rule, named for Dan Rooney, the progressive Steelers owner who chaired the committee looking into the issue. The rule decreed that teams interview at least one minority applicant to fill head-coaching vacancies. Otherwise, the franchise would face a stiff fine.
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nbsp; In 2003, the NFL levied a $200,000 fine against the Detroit Lions when the team hired Steve Mariucci without interviewing any other candidates, black or white. (Mariucci went 15–28 and was fired in his third season.) The league achieved its aim. By 2005, there were six African-American coaches in the NFL, including Dungy, who had been hired by the Indianapolis Colts.
And how has this new brigade of black coaches done? Worse than their predecessors. Much worse, in fact. From 2003 to the present, African-American coaches have averaged the same number of wins each season—eight—as white coaches. They are now slightly less likely to lead their teams to the playoffs. Their rookie seasons are particularly shaky: They lose slightly more games than white coaches do in the first season. In 2008, for instance, Marvin Lewis coached the Cincinnati Bengals to a 4–11–1 record, which was only slightly better than the job Romeo Crennel did a few hours’ drive away in Cleveland, where the Browns stumbled through a 4–12 season. Lewis and Crennel still fared better than yet another African-American coach in the Midwest, Herman Edwards, who oversaw a misbegotten Kansas City Chiefs team that went 2–14.
Scorecasting: The Hidden Influences Behind How Sports Are Played and Games Are Won Page 11
