wOBA

In baseball, wOBA (/wʌ-bɑː/, or weighted on-base average) is a statistic, based on linear weights, designed to measure a player's overall offensive contributions per plate appearance. It is formed from taking the observed run values of various offensive events, dividing by a player's plate appearances, and scaling the result to be on the same scale as on-base percentage. Unlike statistics like OPS, wOBA attempts to assign the proper value for each type of hitting event. It was created by Tom Tango and his coauthors for The Book: Playing the Percentages in Baseball.

Usage

In 2008, sabermetrics website FanGraphs began listing the current and historical wOBA for all players in Major League Baseball. It forms the basis of the offensive component of their Wins above replacement (WAR) metric. Sites such as The Hardball Times have studied wOBA and found it to perform comparably to or better than other similar tools (OPS, Runs created, etc.) used in sabermetrics to estimate runs. The Book uses wOBA in numerous studies to test the validity of many aspects of baseball conventional wisdom.

The benefit of wOBA compared to other offensive value statistics is that it values how the runner reached base, not just if they reached base. Events like Home Runs, walks, singles, etc. are given their own weight (or coefficient) within the linear formula. The weighting is based on the increase in expected runs for the event type as compared with an out. The coefficients change each year, and are based on how often the each event occurs in Major League Baseball over the course of a season.

Because the coefficients are derived from expected run value, we can use wOBA to estimate a few more things about a player's production and baseball as a whole. When using the formula (shown below), the numerator side on its own will give us a estimate of how many runs a player is worth to his team. Similarly, at team's wOBA is a good estimator of team runs scored and deviations from predicted runs scored indicate a combination of situational hitting and base running.

Current Formula

Per Fangraphs, the formula for wOBA in the 2018 season was:

$wOBA={\frac {(0.69*NIBB)+(0.72*HBP)+(0.88*{\mathit {1}}B)+(1.247*{\mathit {2}}B)+(1.578*{\mathit {3}}B)+(2.031*HR)}{AB+BB-IBB+SF+HBP}}$

where:

• AB = at bat
• BB = Base on balls
• IBB = Intentional base on balls
• NIBB = Non-intentional bases on balls
• SF = sacrifice flies
• HBP = Hit by pitch
• 1B = Single
• 2B = Double
• 3B = Triple
• HR = Home run
• PA = Plate appearance

Standard Formula

A basic and speed version was also introduced, with fixed constants that does not change year to year:

Basic Version
numerator:

• 0.7: UBB+HB
• 0.9: 1B+ROE
• 1.3: 2B+3B
• 2.0: HR

denominator: ​PA - IBB - SH
Speed Version
numerator:

• 0.7: UBB+HB
• 0.9: 1B+ROE
• 1.25: 2B
• 1.60: 3B
• 2.0: HR
• 0.25: SB
• -0.5: CS

denominator: ​PA - IBB - SH

Scale

There is no widely agreed upon scale for wOBA. This table serves as an aggregate summary of other wOBA scales available online.

wOBA Scale

Classification	Range
Elite	.400 and Above
Very Good	.371 to .399
Good	.321 to .370
Average	.320
Bad	.291 to .320
Very Bad	.290 and below

Original Formula

The formula, as it originally appeared in The Book, is

$wOBA={\frac {(0.72*NIBB)+(0.75*HBP)+(0.90*{\mathit {1}}B)+(0.92*RBOE)+(1.24*{\mathit {2}}B)+(1.56*{\mathit {3}}B)+(1.95*HR)}{PA}}$

where:

• NIBB = Non-intentional bases on balls
• HBP = Hit by pitch
• 1B = Single
• RBOE = Reached base on error
• 2B = Double
• 3B = Triple
• HR = Home run
• PA = Plate appearance

References

• Tom Tango, Mitchel Lichtman, and Andrew Dolphin. The Book: Playing the Percentages in Baseball. Washington, D.C.: Potomac Books, 2007. ISBN 1-59797-129-4.