Managing with Markov Baseball fan—and analyst—Carl Morris shows a statistical path to more runs scored. t has attracted less attention, perhaps, than searches for Carl N. Morris, professor of statistics and of health care pol- Big Foot or a cure for the common cold, but the quest for the op- icy, might be better known for his work in hospital-quality eval- timal baseball statistic continues to confound even the brightest uation, but he has spent countless hours assessing the squeeze minds. The Nielsen ratings that determine the exchange of bil- play and sacrifice bunt with pages of numbers that would leave lions of advertising dollars may be based on a small fraction of most fans downright vertiginous. It’s hard to imagine Morris IAmerican homes, presidential vote-counts have been unmasked as getting more worked up over universal healthcare than he does hopelessly murky—yet to approximate that Derek Jeter had 500 when his beloved Red Sox squelch a rally with a misguided at- times at bat instead of 502 is heresy of the highest order because tempt to steal second base. numbers in baseball, from batting averages to earned-run averages His research and equations render simple batting averages to brain-bending formulae longer even than this sentence, are and runs batted in—not to mention the “homers-hit-by-a- counted and scrutinized more precisely than any survey or census. shortstop-under-a-full-moon” stat epidemic of modern base- That pursuit continues all the way to the ball—hopelessly simplistic and anti- Harvard statistics department. by ALAN SCHWARZ quated. Employing the concept of Mar- 34 May - June 2002 Portrait and collage by Jim Harrison Reprinted from Harvard Magazine. For copyright and reprint information, contact Harvard Magazine, Inc. at www.harvardmagazine.com kov processes, Morris looks beyond conventional categories like credit for the run that scored plus the expected .231 he added. doubles and walks to place those events in the context of how • The Yankees’ Jason Giambi bats with men on second and third they a≠ect the events around them—and, therefore, a team’s and none out. He pops up. When Giambi came up, his team ex- chances of scoring. “A lot of the physical world is Markovian, pected to score 1.957 runs, but he left with an expected potential and baseball is, too,” says Morris. “Looking at the game that way of 1.353, so he gets credit for negative .604 runs. can give you a much better idea of the value of a player or strat- • Alex Rodriguez of the Texas Rangers strides to the plate with egy than the conventional methods can.” a man on first and two out, a situation that has the Rangers ex- Markov theory concerns events that are conditional upon pected to score .239 runs. If he hits a home run, his NERV is the those that precede them and a≠ect those that come after. (The two runs that scored minus .239, because the next batter no longer stock market and weather patterns are Markov processes; coin has a man on first base and the added scoring potential that al- flips and poker hands are not.) Baseball might not seem the most lows. If Rodriguez strikes out, his NERV is minus .239, since he has fertile ground for truly sophisticated statistical analysis: anyone ended the inning and there’s no hope to score any more runs. who has heard an 0-for-10 ballplayer say he’s “due for a hit” can Such analyses can’t reliably determine the relative skills of be forgiven some skepticism, while most baseball general man- Babe Ruth and Ted Williams—for one thing, baseball has only agers would think a Poisson distribution concerns the breakup recently begun to keep situation-specific data. But Morris’s ap- of the 1997 Florida Marlins. But Markov theory applies perfectly proach neatly unveils the benefits and costs of certain in-game to baseball, because a hitter who rips a double hasn’t necessarily strategies. For example, is the sacrifice bunt (say, making the helped his team score; his play succeeds only if a batter before first out intentionally to move a runner from first to second) ever him has reached base or if a hitter after him drives him home. a good idea? Almost never. The matrix shows why: the state be- Morris’s method can measure the true contribution of every fore has a NERV of .907, the state after just .720, meaning that the result a batter can produce—from triples and home runs to sac- only time you’d want to sacrifice is if you need a single run late in rifices and double plays—by examining the true e≠ects of each the game. Yet some traditionalist big-league managers also try event. Batters always hit in one of 24 situations: with zero, one, this ploy in early innings. “You really could manage a team better or two men out, and with one of eight configurations of men on by looking at that matrix,” Morris asserts. base (none, first, first and third, and so on). A hopelessly compli- NERV clarifies a concept that major-league teams are only cated and time-consuming process determines the average num- now beginning to grasp: the preciousness of outs. Outs are base- ber of runs that teams score in each scenario—for instance, a ball’s clock; you get only 27 of them, and squandering them can team with one out and a man on second scores on average .720 be deceptively catastrophic. Wonder why there are so few stolen runs in that inning. By examining what statisticians call the bases in modern baseball? You need a 71 percent success rate—a “change in state” between one batter and the next, the actual number easily determined through NERV—to break even. contribution of each hitter can be precisely determined. Morris (When informed a few years ago that his Oakland Athletics calls these Net Expected Run Values (NERV) and o≠ers the fol- were last in the league in stolen bases, team general manager lowing hypothetical ex- Billy Beane instinctively amples, using aggregate replied, “Good.”) statistical data from last Major-league baseball year’s American League was stuck in the statisti- season. cal dark ages when Morris • Nomar Garciaparra of was growing up in San the Red Sox comes up Diego in the 1950s. He with a man on first and loved the Red Sox for their none out. If he drives the high Fenway Park-aided man home with a double, batting averages and he has created more than longed to be their man- the one run his RBI ager, but chose a safer ca- would reflect. Since the reer route by earning an matrix (see the chart on aeronautical engineering page 85) shows that the degree at Cal Tech. “I state he batted in usually couldn’t make a paper results in .907 runs and glider that would fly, the state he left the next though,” he says, “so I batter (with a man on went into mathematics.” second rather than first) After 10 years at the pres- results in 1.138, he gets tigious Rand Corporation, Morris accepted a statis- At left, statistician Carl tics and mathematics pro- Morris; at right, Boston fessorship at the Univer- Red Sox shortstop Nomar Garciaparra connecting for sity of Texas. During the a double at Fenway Park. (please turn to page 85) ASSOCIATED PRESS/VICTORIA AROCHO Harvard Magazine 35 Reprinted from Harvard Magazine. For copyright and reprint information, contact Harvard Magazine, Inc. at www.harvardmagazine.com MANAGING WITH MARKOV Morris says. “A profes- (continued from page 35) Net Expected Run Values (NERV) sional statistician can, out MEN ON BASE of love for the game, im- 1970s, as a diversion, he dabbled 0 1 2 3 1,2 1,3 2,3 1,2,3 prove the way baseball is in sports analysis, principally 0 0.537 0.907 1.138 1.349 1.515 1.762 1.957 2.399 played.” tennis. Until then, Morris will “I don’t go out of my way to 1 0.294 0.544 0.720 0.920 0.968 1.140 1.353 1.617 continue to refine his advertise my baseball work, for OUTS analysis of baseball’s criti- 2 0.114 0.239 0.347 0.391 0.486 0.522 0.630 0.830 fear people will have nothing cal moves: when to send to do with me as an academic,” The matrix shows the expected number of runs scored, on a runner around third, jokes Morris, who came to average, in each of 24 possible game situations. A batter when to play the infield Harvard in 1990. Analyzing comes up with 0,1,or 2 outs (rows) and one of eight possi- in, when the numbers call ble scenarios of men on base (columns). Men on first and American League 2001) baseball has become simply his third, for example, appears in the table as “1,3.” for a squeeze play. He can (Data: hobby—an enthralling hobby STEVE ANDERSON still remember how the that is potentially valuable to 1964 San Francisco Giants major-league teams. With today’s tre- Would Morris consider bringing his all but ruined their pennant hopes by mendous computing power (not to men- approach to a major-league organization? laying down foolish sacrifice bunts. “It tion the financial cost of signing a multi- He’s quick to reveal that he developed the was killing me,” he groans. If Morris can million-dollar free agent who fails) many Markovian approach, but didn’t invent it.