Moskowitz&Wertheim2011battingaverages

s N . 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 gaso- line, the price even extends to nine-tenths of a cent, say, $2.99° for a gallon of unleaded. This entire concept, of course, is silly. Pur- chase one gallon of $2.99° 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 end- ing 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 con- sumers 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 pro- e R e SRy Y ~ye———rre T PP = N/ i y 5 ROUNDING FIRST m 9 fessors, 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 performarice 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 admis- sion. 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. Base- ball, 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 notori- ous "Mendoza Line" of a .200 batting average. But no benchmark

4 = SCORECASTING is more sacred than hitting .300 in a season. It's the line of demar- cation between all-stars and also-rans. It's often the first statistic cited in making a case for or against a position player in arbitra- tion. Not surprisingly, it has huge financial value. By our calcula- tions, 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 par- amount 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 ~®=Last at-bat 0.16 0.14 b 2 2 012 [<4 & ol o x = = 008 w o & 006 1 2 z & 0041 @ w o | 002 | 04 , ; 0.298 0.299 0.3 0.301 BATTING AVERAGE ROUNDING FIRST m 3 We looked at the same numbers, and here's what we found. Play- ers hitting .300 walked 14.5 percent of the time and players hit- ting .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 bas ever drawn a base on balls in bis 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 *+® Before last game ™% =Before last at-bat ==L ast at-bat 0.1 PERCENTAGE OF WALKS PER AT-BAT 0.08 '.' ......... "°'° *os oo 'fi"* h L / e 006 -~ 0.04 0.02 0 — 0208 0.299 03 0.301 BATTING AVERAGE

96 @ SCORECASTING What's more surprising is that when these .299 hitters swing away, they are remarkably successful. According to Pope and Si- mohnson, in that final at-bat of the season, .299 hitters have hit al- most .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 hit- ters? 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 aver- age 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 dispropor- tionately 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. At first we wondered whether pitchers might be complicit, serv- ing up fat pitches to help their colleagues on the last day of the season, when games seldom mean much. It brings to mind the ROUNDING FIRST W 97 DISTRIBUTION OF MLB PLAYERS' BATTING AVERAGE BEFORE, DURING, AND AFTER LAST AT-BAT OF SEASON **® Start of last game ==& =Before last at-bat = After last at-bat 160 1 140 4 n 120 - o Y 3 g 100 ™ o o g 80 1 fiooau..tl'git P00 sPDo e s o ugmi, = L " b p ] =z 60 4 40 20 g 0.298 0.299 03 0.301 BATTING AVERAGE 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 base- man 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.