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Get Four
|  | NOVEMBER 5, 2003
What's a Ball Player Worth? Two game-theory experts have developed a model they claim can tell the champs from the chumps. And they're getting a chance to prove it Can B-schoolers teach Major Leaguers? They're going to try. Benjamin Polak, a game-theory expert at Yale School of Management, and Brian Lonergan, Polak's former PhD student, have developed a novel way to evaluate baseball players, based on probability theory. Bouyed by the success of other quantitative methods used by such American League playoff teams as the Oakland A's and Boston Red Sox, as well as by the surprising Toronto Blue Jays (who finished five games over .500), Lonergan will begin consulting with a National League ballclub this winter. Using reams of historical data, Lonergan and Polak can measure the probability of a team's chance of winning a game, given any set of circumstances. With each at-bat, a player can help or hurt his team's chances. Here's how their method works: Let's say the home team is down by two runs in the bottom of the fifth inning, with no outs and a runner on second base. At that moment, the home team has a 39% chance (or 0.39 probability) that it will win. If the batter grounds out, and the runner at second fails to advance, the team's chance of winning falls to 33%. The difference between the two, -0.06, is assigned to the batter who just grounded out. DIFFERENT ANGLE. Polak and Lonergan add up all of a player's outcomes for the season. Doing so yields the exact number of wins -- or losses -- a player contributed to his team, relative to an average player. For example, New York Yankees slugger Jason Giambi contributed 4.9 wins (unadjusted for special circumstances -- see footnote in table below, which shows who would win 2003's MVP and Cy Young awards, according to this method). On the other end of the spectrum, maligned Yankees pitcher Jeff Weaver contributed -2.5 wins (also unadjusted). If all of the players' net win contributions are added up, the result equals the number of games over .500 the team finished in the regular season (the 2003 Yankees finished 101-61, 20 games above .500). The method has some distinct differences from other quantitative analyses, such as the "sabermetrics" (named after SABR, the Society for American Baseball Research) method popularized by baseball historian Bill James and others. Sabermetrics also seeks to assign portions of wins to different players, but it relies on selective weighting of certain baseball statistics, such as a hitter's on-base percentage or a pitcher's earned-run average, and uses regression analysis to examine those stats' effect on wins or runs scored. Lonergan and Polak claim that their method, which doesn't rely on traditional statistics, eliminates a step -- going directly to the measurement of game outcomes. UNFAIRLY PENALIZED? Another advantage is that their game-theory approach automatically rewards "clutch" hitters and pitchers. That's because a home run in the eighth inning of a close game raises a team's chances of winning considerably more than a home run late in a blowout game. Thus, a batter with a knack for the big hits will have more net win contributions than a slugger who built up gaudy numbers in relatively meaningless situations. The effect is similar with pitchers. By Lonergan and Polak's count, Los Angeles Dodgers closer Eric Gagne contributed 8.8 net wins in 2003. With a marginal closer, who contributes no net wins, L.A. would have been a sub-.500 ballclub. But won't that unfairly penalize great players on teams with poor pitching? Not necessarily, says Lonergan. He points out that the Detroit Tigers, one of the worst teams in baseball history, the Anaheim Angels, who finished close to .500, and the Red Sox, who totaled 95 wins, played in 36, 37, and 42 one-run games, respectively. They also played in 17, 16, and 16 extra-inning games. FINDING BARGAINS. Thus, the argument that Tigers players had less opportunity to be "clutch" falls apart. The Angels and Red Sox had an equal opportunity to stink. "There are differences across teams, but in practice they are small," Lonergan says. "In general, a hitter's opportunity to make an impact is proportional to his number of plate appearances." Baseball general managers could use Lonergan and Polak's approach to see which free agents are bargains and which are overpriced. The PhDs say net wins on the free-agent market cost about $2 million each, based on recent signings and the players' eventual real-life performance. With that knowledge, Lonergan could peg the players who are most likely to add net wins to a particular team for the least amount of money. He has spoken with a few Major League Baseball teams, but only one National League team -- which asked not to be identified -- has agreed to work with him thus far. SLIPPERY THINGS. Lonergan, whose day job is valuing power plants as a consultant with Charles River Associates, says he stumbled onto the method while getting a PhD in economics at Yale, working on a short paper about why baseball players are paid so much. "I needed some way to value wins," he says. So, with Polak, he developed the game-theory model. Polak, a British ex-pat who grew up on cricket and soccer, says he's a devoted, though not-quite-so-long-suffering, Chicago Cubs fan after getting his masters' degree at Northwestern University. Lonergan's and Polak's algorithm has its limitations. For one, no statistical model can compute slippery things such as clubhouse atmosphere, a winning tradition, or team chemistry (or in the Yankees' case, the "Stadium Ghosts" that always seem to haunt the Boston Red Sox). The model also falls short in terms of measuring defensive prowess. "The data just aren't very good," Lonergan says. Other baseball quant jocks have run into the same problem. Baseball tracks fielding percentage, but that measure doesn't factor in a player's range or speed. Thus, a team like the World Series champion Florida Marlins, who beat the vaunted Yankees in part due to speed and defense, confounds statisticians of all persuasions. "WE'LL USE ANYTHING." Agent Jeff Borris of Beverly Hills Sports Council points out that this model might be held back because it doesn't rely on traditional baseball stats, which may make some uncomfortable. "Generally speaking, the clubs stick with the meat-and-potatoes statistics," Borris says. "People know about on-base percentage." Lonergan and Polak know their probability-based approach faces an uphill climb to mass acceptance, especially given the experience level of most baseball people with game theory. Of course, in negotiations, most agents will welcome any positive information about their clients -- wonkish or not. "We'll use anything we can get our hands on," says Jeff Moorad of Moorad Sports Management, whose clients include Red Sox star Manny Ramirez and Minnesota Twins outfielder Shannon Stewart. If Lonergan's first baseball consulting job goes smoothly -- and produces wins -- other agents may take notice, too. Well, at least half of them, anyway. Passing Out the Hardware
Who were baseball's most valuable players in 2003? Here's how they score according to who contributed the most net wins to their teams during the regular season*:
Most Valuable Player
* Win contributions are adjusted for ballpark differences, strength of opposition, and comparisions to marginal players
Data: Brian Lonergan and Benjamin Polak  By Brian Hindo in New York
BW MALL
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