It’s two pitches into Game 3 of the National League Championship Series between the San Francisco Giants and St. Louis Cardinals, but Professor of Statistics Carl N. Morris has already stopped watching. Tucked onto his neon orange clipboard is a receipt-sized table packed with an arcane set of numbers the announcers have probably never seen: the average number of runs per inning major league baseball teams scored in 2001 in each of 24 possible situations, ranging from bases empty and 0 out to bases loaded and 2 out.
“I’m hoping to see second and third with one out,” Morris says as Cardinals leadoff hitter Fernando Viña grounds out to shortstop, “because something comes out in Markovian theory that’s very interesting. When the third-base runner sees the ball hit on the ground to second base, he has to make an instinctive calculation whether try for home. The question is, what is the probability he will score that would justify going? If it’s greater than 7 percent”—he pauses to emphasize the surprisingly low figure—“you go.”
A walk and a double briefly shift Morris’ attention back to the television from the hypothetical situations where the mind of a statistics professor is wont to dwell. But as a J.D. Drew fly ball to centerfield leaves the runners stranded and the Cardinals scoreless in the first, Morris returns to his chart. Taking out a mechanical blue pencil and scientific calculator, Morris lays out the formula for the new all-in-one offensive statistic he has developed, Runs Per Game (RPG).
While Harvard sports aficionados typically think of the Crimson’s star wide receiver when seeing the name Carl Morris in the sports pages, it is the former chair of the statistics department who was recently featured in a column on ESPN.com. A slightly frail-looking white-haired 62-year-old whose athletic career peaked on his high school tennis team, Morris would seem an unlikely subject for a feature on the sports website. But Morris’s efforts to promote RPG, a statistical formula that predicts how many runs a lineup of nine of the same player would score in a game, earned him a column focusing on the statistic and its new record-holder, Barry Bonds (who happens to be fourth up in the bottom of the first). The formula has won him acclaim from academic colleagues—Morris gave a talk to the American Statistical Association on Sept. 25 to discuss the formula—as well as sabermetricians, people who dedicate their lives to the analysis and improvement of baseball statistics.
Unlike the statistics that appear on the back of a baseball card, which are either counting (total home runs or wins) or percentage (batting average or slugging percentage), Morris’s formula was derived from a technique in academic statistics known as Markovian modeling, which he says makes it qualitatively different from any statistic a casual fan would be familiar with. RPG, Morris says, takes much of the interpretation out of statistics (different fans may value on-base percentage or RBI differently, and sabermetricians frequently assign debatable weights to statistics such as stolen bases) and says with statistical certainty how many runs per game nine of a given player would produce on average. Adjusting for annual fluctuations, RPG predicts how many runs teams actually score to a very high degree.
“I want to anchor things back to runs,” he says. “I always want to get away from statistics and be more of a solid measure of things...If I have nine players of equal ability, this is exactly what would happen. You can prove it’s right using math a good high school student would know. If you played baseball on the moon and averaged 300 runs a game, the formula would still be legitimate.”
The idea behind RPG is not new. In 1977, Morris’ friend Thomas Cover, now Li Professor of Electrical Engineering and Statistics at Stanford, published an article in the Journal of Operations Research that introduced the precursor to RPG, Offensive Earned Run Average (OERA). “We wanted a simple statistic that would summarize the offensive power of a player,” Cover says. “We imagined putting the batter in all nine positions and seeing how many runs he would generate.” Using an elaborate process called matrix inversion and the 24-square expected runs table reprinted on Morris’s clipboard, Cover’s paper explained how advanced statistical techniques could predict how many runs a lineup consisting of nine of any given player would score.
However, a garden-variety Statistics 100 course doesn’t come close to teaching you how to figure out an OERA. Morris’ contribution was to derive a simple formula, RPG, that calculated OERA without advanced techniques. “This [OERA] paper lay dormant [until] Morris found a simple formula for it,” Cover says. “He has made it a worthwhile statistic. I’m involved in the past history of it, but Morris is the one who’s made this work.”
Morris’ RPG formula can be approximated by just three components. First is the on-base odds, or the ratio of times a player reaches base to the number of times he makes an out. Second is a statistic Morris calls batting texture, which is the average contribution relative to a single a player makes when he reaches base. Walks are worth three-quarters of a single, doubles 1.5 times as much, triples twice as much and home runs three times as much, so a player whose plate appearances resulted only in doubles and outs would have a batting texture of 1.5. The final elements are simple calculator tricks: multiplying by a constant and raising the value to a power derived from major league aggregate scoring data, that converts this number to runs per game. Morris has posted an RPG calculator online at http://rpgcalc.butchwax.com.
Morris says he developed the simple RPG formula over 20 years ago, but only began calling sportswriters to let them know about the statistic when he calculated that a team of nine 2002 Bondses would score an astronomical 22.4 runs per game—smashing the record held by Babe Ruth of 18.5 runs per nine innings in 1923. “What’s bugging me,” he says, “is that this incredible thing is happening and nobody notices. I wanted to make sure people knew it. Imagine if when Bonds had 73 home runs nobody counted!”
In the bottom of the second, the Giants threaten a big inning. Singles by J.T. Snow and David Bell put men on first and second, and pitcher Russ Ortiz is safe at first after bunting the runners over. It’s bases loaded, none out, and impossible to tear one’s eyes away from the television—unless you’re Carl Morris, who is tracking the inning’s evolution on his expected-runs table. Only after announcing that the Giants should score 2.4 runs in this inning does Morris pick up his head to watch leadoff man Kenny Lofton battle Cardinals starter Chuck Finley.
Lofton grounds into a fielder’s choice, and Snow is thrown out at the plate. Any baseball fan knows this was bad for the Giants, but only Morris can say just how bad. “That guy cost them 0.8 runs,” he says. “And he lowered the probability of their scoring at least one run from .89 to two-thirds.” As Rich Aurilia comes up, Bonds lurks in the hole. Aurilia flies to center, driving in Bell, and second baseman Jeff Kent follows up the sacrifice with a single, loading the bases with two out for the man who put RPG on the map. With the bases loaded, it doesn’t take a degree in statistics to know the Cardinals have to pitch to Bonds.
On the first pitch, Bonds flies out to shallow right, ending the inning. For once, Morris is just another fan. “Maybe he does choke,” he says of Bonds, who had a career batting average below .200 in the postseason before 2002.
Statistics and baseball have been intertwined for Morris ever since he first pored over box scores as a teenager in the 1950s in San Diego. Watching the then-minor league San Diego Padres, Morris says he developed an “early love for quantitative systems and theories” and actually wanted to be a statistician when he was very young. “I thought it would be such fun to figure things out like batting averages as a young teen,” he says, “but I dismissed it [as a career], like being a movie star. Then I found out there was a real field called statistics.”
When he got to Caltech as an undergraduate and saw that academic statistics was a viable career, he says, baseball remained at the forefront of his budding statistical mind. “Baseball helped me understand statistics and relate it to a system I knew well,” he says. As a professor now, Morris still uses baseball examples in lectures to illustrate ideas.
After getting his Ph.D. from Stanford, Morris worked for 11 years at the Rand Corporation as a national researcher, applying his knowledge of statistics in the real world so he “could do more than teach the same courses I’d taken.” But even working as a statistician outside the ivory tower, baseball was never far away. “Hospitals are like baseball players,” he says. “They have batting averages for certain types of surgeries.”
Besides baseball and hospitals, perhaps the most obvious application of statistics is to gambling. In the 1960s, Morris and Cover frequently capitalized on their knowledge of statistics at the blackjack table. “We’d get kicked out of casinos for counting cards,” Morris recalls. “[Cover] is a great gambler. Back then, they’d deal one deck down to the last card, so sometimes you knew exactly what to do.”
His knowledge of gambling theory also helped him get married. Two years into his job at Rand, Morris went to Reno with his girlfriend, Anne, whom he wanted to marry but feared would decline his proposal. He won a dollar following a straightforward technique at the roulette table: Bet a dollar on red, if you lose bet two dollars on red, if you lose again bet four dollars on red, and so on and so on. When the board finally comes up red, you win a dollar. He gave the dollar to his girlfriend in 20 nickels, who lost 19 of them at the slots before winning the jackpot of $8 on the very last nickel. Eight dollars was, coincidentally, exactly the price of a marriage license in Nevada—and the couple were married the next day. “My life could have been very different if she hadn’t hit the jackpot,” he says.
After he left Rand in 1978, Morris went to the University of Texas-Austin, where he raised three children before getting divorced in 1990. Soon after he became single, Morris received an offer from Harvard and relocated to Cambridge, where he now lives not far from campus.
Surprisingly, Morris doesn’t watch much baseball in his down time. Sabermetricians are generally regarded as a new wave of baseball analysts whose highly quantitative approach to the game is contested by purists, but Morris manages to be both at once. The Cardinals-Giants playoff game is the first game he has watched from start to finish all year.
Wouldn’t watching more baseball lead to better statistical insight? Maybe, but while most sabermetricians laud modern teams who make decisions based on better statistical information, Morris waxes nostalgic for the days when batting average was still taken seriously. Contemporary baseball makes him, like many other fans, mad. “It’s gotten out of hand,” he gripes. “Salaries have gone up by 100 times and teams are still only winning one-half their games. The really big money and big seats go to corporations, and you get away from what it’s really all about.”
It seems strange how much time Morris spends with his tables while watching a game, but, he says, it’s the ability to do so that makes baseball unique—its built-in pauses enable fans to “sit for two or three hours in the sunshine and talk about players and strategies. It’s a great way to relax.” He offers some animated moments—when the Giants threatened in the bottom of the ninth before losing 5-4, he chides Giants second baseman Jeff Kent, “You friggin’ turkey! Don’t swing at bad pitches!” But Morris has a very different relationship to today’s “corporate game” than he did to the Class AAA San Diego Padres 50 years ago.
What’s a fan to do? “One thing to do is sit back and calculate formulas,” Morris says. “That’s fun.”
