How Sabermetrics Works

­Like a player's RBI record, batting average -- the number of hits divided by the number of at-bats and the most common measure of hitting ability -- can be misleading. If you only look at batting average, then you're ignoring how the player­ contributes to a team's offense in other ways, like earning a walk or hitting for power.

Stats like the number of hits aren't that straightforward either. If a player has 2,300 hits in his career, that's generally considered quite good. But what if the player simply managed to play a long time and his career batting average was .260 with few extra-base hits (doubles, triples, home runs)? He still had a great career, but was probably less valuable than a player who played for less time and accumulated the same number of hits with a higher average and more extra-base hits. Then again, what if the former player was among the top defensive players?

If judging a player in the context of history, consider also that some periods in baseball have been known as more favorable to hitters or pitchers, just as some parks now, by virtue of their dimensions, altitude, wind and other factors, produce higher or lower run totals than the league average. The period from about 1900 to 1919 was called the Dead Ball Era because of, among other things, the type of baseball that was used, which was soft, and hitters used heavier bats. Also, the popular hitting style of the day -- placing one's hands high on the handle of the bat -- tended to produce fewer extra-base hits. Sabermetricians have produced formulas in an attempt to produce more objective judgments of players' abilities throughout the various eras of baseball.

For example, to judge batting ability, Bill James proposed a mathematical formula to determine how many runs a hitter creates because, in the end, runs are what count [source: Albert]. James devised the runs created statistic, which goes:

Runs Created = [(Hits + Walks)*(Total Bases)]

     (At-bats + Walks)

Another problem with traditional statistics is that not all outs are equal. The way in which a batter makes an out can affect the outcome of an inning. Say there's a runner on second with one out. If the batter at home plate strikes out, nothing happens (unless the runner decides to steal a base). But if the batter hits a slow roller to first base and the runner manages to get to third while the batter is being tagged out, then the batter made a more useful out.

With pitching, wins are highly dependent on amount of runs a team scores for their pitcher. A good pitcher might have an ERA (earned run average) of 3.50, meaning that he allows, on average, 3.5 runs per game. But if his team's offense only averages 3 runs during his starts, then that pitcher will have a very poor win-loss record that doesn't accurately reflect his performance. Conversely, good run support can make a bad pitcher look better than he is.

­ERA can be inflated by poor defense. Although runs caused by errors don't count against a pitcher's ERA, some pitchers have the disadvantage of playing in front of defenses that, while not necessarily committing a lot of errors, don't have the range and effectiveness of other teams' defenses. For example, a player may get to a ball but have a weak arm and not throw the ball quickly enough to get a runner out. This situation could cause runs to score, and the pitcher would be credited with giving up the runs since technically no errors were committed.

­In 1998, Juan Gonzalez won the American League MVP award, but in many categories, including James' runs created stat, he trailed Albert Belle. However, Gonzalez's Texas Rangers finished first in their division, ahead of Belle's Chicago White Sox. So did Belle, who finished eighth in the voting, deserve the MVP award? Was he more valuable than Gonzalez? Maybe, but defense also counts, and the writers who vote on the award generally prefer players who perform well for teams that make the playoffs versus those that excel on poorer teams. And despite being a great player, Belle's fiery personality often worked against him in the eyes of the press.

The same year, pitcher Rick Helling, a teammate of Gonzalez, tied for the league lead with 20 wins, despite having a mediocre 4.41 ERA. (His overall record was 20-7). Roger Clemens finished the year at 20-6 -- just one less loss -- yet he won the Cy Young Award as the American League's best pitcher. But that's because he led the league with a 2.65 ERA and had a league-best 271 strikeouts (compared to Helling's 164).

Both of these examples highlight some of the problems with traditional statistics that we just mentioned. Often in who-deserves-the-award debates, people casually throw around statistics that may not best indicate a player's skill or value. Sabermetric measurements aim to fill in these knowledge gaps. Some are rather basic, like WHIP -- walks and hits per inning pitched -- which measures how many base runners a pitcher allows.

WHIP = (Walks + Hits)

(Innings Pitched) 

A good WHIP is generally around 1.30 or below, with anything close to 1 or below it being considered spectacular

­On the next page, we'll look at some of the more complex sabermetric stats, but first we'll consider how sabermetrics is useful in answering seemingly subjective or unanswerable questions.

For 15 years, Leo Mazzone was pitching coach for the Atlanta Braves. Mazzone was considered one of the best pitching coaches around as his pitchers were usually among the top in the league [source: Schwarz]. His ability to resuscitate the careers of struggling pitchers or those recovering from injuries was particularly admired. But was Mazzone good or just lucky, the beneficiary of having talented pitchers signed to play for the team?

­J.C. Bradbury, an economics professor, analyzed the ERAs of pitchers playing for Leo Mazzone and when they weren't with Mazzone. He accounted for factors like age (since pitchers are generally better at certain points in their careers) and ballpark (some ballparks are bigger and easier to pitch in than others). He found that pitchers under Mazzone had an ERA that was lower by 0.62, a dramatic and valuable difference [source: Schwarz]. Others analyzing Mel Stottlemyre, who has been a coach for the Yankees, Astros and Mets, found that his pitchers had ERAs 0.30 lower under him [source: Schwarz]. In the studies, the authors acknowledged that some other factors, like good personnel decisions by the general managers, may contribute to these coaches' successes. But some of Mazzone's coaching practices may also help, like having his starting pitchers throw twice between starts instead of once, which is common practice.

­Bill James has created dozens of sabermetric statistics, and others have contributed their own metrics. Many of these statistics have several different versions, with various organizations tweaking components of the formulas. So sabermetricians may rely on different formulas, but their style of analysis, their search for objective truth, their reliance on hard data vi­ewed in context -- all of these are part of sabermetrics.

Each sabermetric tool has its uses and drawbacks, but some are more commonly used than others. For example, EqA, or equivalent average, measures a player's hitting ability, accounting for factors like league averages, park effects and pitcher quality. A simplified version of EqA is calculated as:

EqA = [Hits + Total Bases + 1.5*(Walks + Hit by Pitch) + Stolen Bases][At-bats + Walks + Hit by Pitch + Caught Stealing + (Stolen Bases)/3] 

Win shares is both the title of a Bill James book and the name of a sabermetric statistic that's been criticized by some sabermetricians and tweaked by others. Like its peers, it uses an immensely complicated formula, but it produces a single number that purportedly measures how much a player contributes to his team's wins. A player's win shares is actually how many wins he generated for his team multiplied by three. Multiplying by three creates larger numbers that emphasize the differences among players [source: Studeman].

Win shares are divided into three groups: hitting, pitching and fielding. Players who play more demanding defensive positions get more credit for win shares, as do high-strikeout pitchers because they don't require as much defensive help as a pitcher who gets a lot of groundball or flyball outs [source: Studeman]. Since win shares are based on a player's statistics for only one year, they're not good for predicting future performance but are useful for measuring a player's contribution to a team's success.

Another popular sabermetric stat is VORP -- value over replacement player. Developed by Keith Woolner of the Cleveland Indians, VORP uses an "average" baseball player as a reference point to determine value. For VORP, a replacement-level player is one who's below average. Often these replacement-level players spend a lot of ­time on the bench or shuttle between the highest level of minor league baseball and the majors

VORP doesn't take into account defense, but there is a modified version of VORP -- VORPD -- that does. The equation also considers position because some positions (like shortstop and catcher) are more demanding defensively, and players at those positions are usually not as talented offensively as first basemen or right fielders. The actual equati­on is very complicated, and there are several versions. But it does produce a single number -- say, 85.4 for Albert Pujols in 2006 -- that allows you to easily measure a player's value and compare him to others [source: Baseball Prospectus]. It also allows for comparing values of hitters and pitchers.

Sabermetrics is also useful for making more accurate predictions. The Pythagorean expectation looks at a team's runs allowed and runs scored to determine its expected winning percentage.

Winning Percentage = [Runs Scored Squared]/[Runs Scored Squared + Runs Allowed Squared] 

James later modified his original formula, using 1.82 as the exponent instead of 2, so the formula isn't perfect. But it allows someone to consider what role random chance plays, how many games a team was "expected" to win, or if, say, a team's record was skewed by an eight-game period during which its generally moribund offense caught fire and averaged an uncharacteristic 10 runs per game.

­For predicting individual player performance, Baseball Prospectus, a think tank devoted to baseball statistical analysis, uses a set of formulas known as PECOTA to predict future performance. PECOTA is a favorite of both fantasy baseball lovers and baseball professionals.

­Many sports besides baseball require several players to succeed for a play to go well, making it difficult to apply sabermetrics to these other sports. The beauty of baseball is that its statistics generally capture the performance of one player. And that player's success is often determined by his own actions, although some factors, like defense, can involve more than one person.

In football, a quarterback who completes a pass may be seen as having made a successful play, yet other players were involved in that success, such as the offensive line protecting the quarterback from being sacked. And what if it was only a 4-yard pass, and the play occurred on the third down with 5 yards to go? Now the team must punt, and so the failure may rest with the quarterback -- who didn't pass to someone farther downfield -- or with the receiver, who wasn't able to gain additional yardage after catching the ball. As always, context is important.

There are attempts being made to bring sabermetrics-style thinking into other sports. John Hollinger, who works for ESPN.com, is well-known for his basketball writing and creative use of statistics. Football coaches are turning to the kind of statistical analysis that has already become popular in baseball. Patriots' Coach Bill Belichick and his staff have been to known to turn to statisticians for advice on punting situations and the efficacy of two-point conversions. A Web site called FootballOutsiders.com has created statistics like DVOA -- defense-adjusted value over average. Billy Beane has been involved with trying to apply sabermetric techniques to soccer, acting as an advisor to the San Jose Earthquakes MLS team.

People have contemplated applying general sabermetric techniques not only to sports but to other aspects of life and business. Sabermetrics is often admired for its reliance on hard data, its rigorous process of analysis, its willingness to question previously held assumptions and its search for hidden advantages, all of which are potentially useful in business. Billy Beane's success as an imaginative, statistically minded GM has earned him positions on company boards. In 2006, Time Magazine named Bill James one of the world's 100 most influential people.

In an October 2008 New York Times op-ed, Beane, along with Newt Gingrich and Sen. John Kerry, wrote about using sabermetric-style techniques for improving health care by focusing on data mining, statistical analysis, reducing medical errors and cutting costs. If sabermetrics could get those two politicians to agree on something, then it must have some value.

To learn more about baseball and for links to a range of sabermetric-related Web sites, click on over to the next page.