User:Gnevins/WOBA

In baseball, wOBA (/'woʊbə/, 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.

Background Information
Baseball statistics are used to quantify the value of a player. Conventional statistics, like batting average, RBI, stolen bases, and strikeouts, can be evaluated to get a general sense of a player’s value. However, sabermetric statistics collect more advanced data and often value a player’s performance more effectively than conventional statistics. While many sabermetrics are difficult to understand to the general sport fan, wOBA is an easy statistic to grasp to the general baseball fan. wOBA is on the same scale as OBP, so if a baseball fan understands what a good OBP is, then he/she will understand how to interpret wOBA.

The ability to win baseball games is directly correlated to the number of runs scored. As a result, wOBA was created to determine how effective a player is at creating runs. wOBA is a statistic that weights on base percentage and slugging percentage. The ability to get on base and/or hit for power are important to scoring runs. Michael Lewis, creator of Moneyball, portrayed the importance of avoiding outs to winning baseball games. Baseball is not like other sports that have clocks; the most valuable asset that baseball teams have are outs, since there are only 27 of them per game. Since outs are so valuable, wOBA typically has more value going to the on base component than the slugging percentage component, although hitting for power is important to scoring runs as well. A major difference between wOBA and other statistics is that wOBA weights how a player got on base. A home run is not four times as valuable as a single, and a double is not twice as valuable as a single. The coefficients in the wOBA formula are used to quantify the difference in value between different instances of getting on base.

In a study conducted by Philip Beneventano of Ernst and Young, he analyzed the effects of wOBA, OBP, and Slugging Percentage on a baseball team’s runs scored. It was concluded that wOBA was the most effective statistic in this set at forecasting runs scored. wOBA had the highest coefficient of determination in the study, so it was most effective at explaining the changes of runs scored between different teams. SLG accounts for a hitter’s power, but it weights singles, doubles, triples, and home runs as 1, 2, 3, and 4 respectively, even though sabermetric studies prove that these coefficients aren’t entirely accurate. OBP is the frequency that a hitter gets on base. Since a walk and a home run are counted the same in OBP, this statistic isn’t the most effective at predicting runs scored. A healthy mix of OBP and SLG, wOBA is a more effective statistic at predicting runs scored, especially since it includes specific weights for each instance of getting on base.

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, RC, 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 not just whether the runner reached base but how. 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 to an out. The coefficients change each season based upon how often each event occurs.

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 an estimate of how many runs a player is worth to his team. Similarly, a 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.

2019 Formula
Per Fangraphs, the formula for wOBA in the 2019 season was:

$$wOBA=\frac{(0.69*NIBB) + (0.719*HBP) + (0.87*\mathit{1}B) + (1.217*\mathit{2}B) + (1.529*\mathit{3}B) + (1.94*HR)}{AB + BB - IBB + SF + HBP} $$

where:


 * NIBB =  Non-intentional bases on balls
 * HBP = Hit by pitch
 * 1B = Single
 * 2B = Double
 * 3B = Triple
 * HR = Home run

—————


 * AB = at bat
 * BB = Base on balls
 * IBB =  Intentional base on balls
 * SF = sacrifice flies
 * HBP = Hit by pitch

Evolution of the wOBA Formula
The wOBA formula has evolved since its inception in 1871. The linear weights in the wOBA formula often change from year to year based on league-wide offensive trends. These weights measure the effects that certain offensive statistics have on their run values. As average run values per game change per season, each linear weight in the wOBA formula changes as well. The original formula, created in 1871, used different weights for each element from the 2019 formula. There is an inverse relationship between runs per game (or runs per plate appearance) and the linear weights of many (but not all) offensive events in the wOBA formula.

In 1871, the average runs per plate appearance was 0.237. The corresponding linear weight for singles and home runs was 0.938 and 1.584, respectively. In comparison, as previously stated, the linear weights in 2019 for singles and home runs were 0.870 and 1.940, respectively, with an average runs per plate appearance of 0.126. There were more runs being scored in the 19th century compared to today, so the value of a home run contributed less to every run scored. Most, but not all, linear weights in the formula show this pattern. As shown, the linear weight for singles was higher in 1871 compared to 2019, and the average runs were higher in 1871 than in 2019.

The linear weights for walks and singles are weighted less with fewer runs scored, but the values of doubles, triples, and home runs become more valuable when less runs are scoring. There is almost half as many runs being scored in today’s game compared to 1871, so the linear weights adjusted accordingly in the modern formula. In 2014, the number of runs scored per game were minimal. Runs per plate appearance was 0.107. When runs were scored, they were valued at a premium because of the scarcity of total runs being scored. Accordingly, the linear weights for the 2014 wOBA changed to account for the increased value in power hitters.

Ranges for elite, very good, etc.
The following table serves as an aggregate summary of various wOBA scales available online.

Best and Worst wOBA in 2019
The table below shows the top 10 and bottom 10 players in terms of wOBA for the 2019 season, according to Fangraphs. As shown, there is a wide discrepancy between the top and bottom performers in the MLB.

Opposing Pitcher wOBA Allowed
While wOBA is often used to evaluate hitters, this statistic can also measure the effectiveness of pitchers. A pitcher’s wOBA allowed is measured by averaging the wOBA of all opposing hitters that a pitcher faces. It is similar to the concept of Batting Average Allowed except the linear weights of wOBA are used in the traditional wOBA formula. There is a clear correlation between a hitter’s wOBA and his opposing pitcher’s wOBA allowed. Hitters tend to perform better when the opposing pitchers they face have higher wOBA allowed values.

Expected wOBA
wOBA can be translated to Expected Weighted On Base Average (xwOBA). Expected baseball statistics take advantage of Statcast data since 2015 to predict the expected value of a statistic based on launch angle, exit velocity, and sprint speed. Expected statistics essentially take the defense out of the equation. Since a hitter has control of his exit velocity and launch angle, but has less control of where the ball is hit and no control of the defense in the field, xwOBA shows the true value of a player. If a player has a high xwOBA but a significantly lower wOBA, the hitter got unlucky because fielders were making good plays or he was hitting the ball at fielders. This is also used to evaluate pitchers’ performance. xwOBA allowed is used to determine how effective a pitcher’s pitches are at getting hitters out. If a pitcher has a high xwOBA allowed but a lower wOBA allowed, then he is getting lucky since hitters are making good contact but the fielders are making good plays on the ball.

wOBA by Position
wOBA can be used to measure the effect of a player’s value on his team’s chance of making the playoffs. MLB data from 2010 to 2014 was used in a study by Heath Detweiler to determine how well wOBA at each position correlated with their team making the playoffs. The following data is from this study. wOBA is used to measure a player’s offensive value. When comparing wOBA at each position, offensive value at catcher, first base, second base, and left field have the highest offensive values. The defensive ability for center fielders and shortstops is important, so offensive value is not as valuable for those positions.