# On-base plus slugging

On-base plus slugging

On-base plus slugging (OPS) is a sabermetric baseball statistic calculated as the sum of a player's on-base percentage and slugging percentage.[1] The ability of a player to both get on base and to hit for power, two important hitting skills, are represented. An OPS of .900 or higher in Major League Baseball puts the player in the upper echelon of hitters. Typically, the league leader in OPS will score near, and sometimes above, the 1.000 mark.

## Formula

The basic formula is

$OPS = OBP + SLG \,$

where OBP is on-base percentage and SLG is slugging average. These averages are defined

$SLG = \frac{TB} {AB}$

and

$OBP = \frac{H+BB+HBP} {AB+BB+SF+HBP}$

where:

Although OBP and SLG have different denominators, it is possible to rewrite the expression for OPS using a common denominator. This expression is mathematically identical to the simple sum of OBP and SLG:

$OPS = \frac{AB*(H+BB+HBP)+TB*(AB+BB+SF+HBP)}{AB*(AB+BB+SF+HBP)}$

## Interpretation of OPS

Unlike many other statistics, a player's OPS does not have a simple intrinsic meaning, despite its usefulness as a comparative statistic.

One fault of OPS is that it weighs on-base average and slugging percentage equally, although on-base average correlates better with scoring runs.[2] Statistics such as wOBA build on this distinction using linear weights, avoiding OPS' flaws. Magnifying this fault is that the numerical parts of OPS are not themselves typically equal (league-average slugging percentages are usually 75-100 points higher than league-average on-base percentages). As a point of reference, the OPS for all of Major League Baseball in 2008 was .749.[3]

## An OPS Scale

Bill James, in his essay titled "The 96 Families of Hitters"[4] uses seven different categories for classification by OPS:

Category Classification OPS Range
A Great .9000 and Higher
B Moderate .8333 to .8999
C Above Average .7667 to .8333
D Average .7000 to .7666
E Below Average .6334 to .6999
F Terrible .5667 to .6333
G Atrocious .5666 and Lower

This effectively transforms OPS into a 7 point Likert Scale. Substituting typical Likert scale quality values such as Excellent (A), Very Good (B), Good (C), Average (D), Fair (E), Poor (F) and Very Poor (G) for the A-G categories creates a subjective reference for OPS values.

## History

On-base plus slugging was first popularized in 1984 by John Thorn and Pete Palmer's book, The Hidden Game of Baseball.[5] The New York Times then began carrying the leaders in this statistic in its weekly "By the Numbers" box, a feature that continued for four years. Baseball journalist Peter Gammons used and evangelized the statistics, and other writers and broadcasters picked it up. The popularity of OPS gradually spread, and by 2004 it began appearing on Topps baseball cards.[6]

The Top 10 Major League Baseball players in lifetime OPS, with at least 3,000 plate appearances through 2011 are (active players in bold):

1. Babe Ruth, 1.1638
2. Ted Williams, 1.1155
3. Lou Gehrig, 1.0798
4. Barry Bonds, 1.0512
5. Jimmie Foxx, 1.0376
6. Albert Pujols, 1.0372
7. Hank Greenberg, 1.0169
8. Rogers Hornsby, 1.0103
9. Manny Ramírez, 0.9970
10. Mark McGwire, 0.9823

The top ten is divided evenly between left-handed and right-handed batters, but the top four were all lefties. Jimmie Foxx has the highest career OPS for a right-handed batter.

The Top 10 single-season performances in MLB are (all left-handed hitters):

1. Barry Bonds, 1.4217 (2004)
2. Babe Ruth, 1.3818 (1920)
3. Barry Bonds, 1.3807 (2002)
4. Barry Bonds, 1.3785 (2001)
5. Babe Ruth, 1.3586 (1921)
6. Babe Ruth, 1.3089 (1923)
7. Ted Williams, 1.2875 (1941)
8. Barry Bonds, 1.2778 (2003)
9. Babe Ruth, 1.2582 (1927)
10. Ted Williams, 1.2566 (1957)

The highest single-season mark for a right-handed hitter was 1.2449 by Rogers Hornsby in (1925), (13th on the all-time list). Since 1925, the highest single-season OPS for a right-hander is 1.2224 by Mark McGwire in (1998), which is good for 16th all-time.

OPS+, Adjusted OPS, is a closely related statistic. OPS+ is OPS adjusted for the park and the league in which the player played, but not for fielding position. An OPS+ of 100 is defined to be the league average. An OPS+ of 150 or more is excellent and 125 very good, while an OPS+ of 75 or below is poor.

The basic formula for OPS+ is

$OPS+ = 100 * (\frac{OBP} {*lgOBP} + \frac{SLG} {*lgSLG} - 1)$

where *lgOBP is the park adjusted OBP of the league (not counting pitchers hitting) and *lgSLG is the park adjusted SLG of the league.

A common misconception is that OPS+ closely matches the ratio of a player's OPS to that of the league. In fact, due to the additive nature of the two components in OPS+, a player with an OBP and SLG both 50% better than league average in those metrics will have an OPS+ of 200 (twice the league average OPS+) while still having an OPS that is only 50% better than the average OPS of the league.

Through 2011, the career leaders in OPS+ (minimum 3,000 plate appearances, active players in bold) were

1. Babe Ruth, 206
2. Ted Williams, 190
3. Barry Bonds, 181
4. Lou Gehrig, 178
5. Rogers Hornsby, 175
6. Mickey Mantle, 172
7. Dan Brouthers, 170
7. Albert Pujols, 170
9. Joe Jackson, 169
10. Ty Cobb, 168
11. Jimmie Foxx, 163

Source: Baseball-Reference.com - Career Leaders & Records for Adjusted OPS+, as of September 28, 2011.

The only purely right-handed batters to appear on this list are Hornsby, Pujols, and Foxx. Mantle is the only switch-hitter in the group.

The highest single-season performances were:

1. Barry Bonds, 268 (2002)
2. Barry Bonds, 263 (2004)
3. Barry Bonds, 259 (2001)
4. Fred Dunlap, 258 (1884) *
5. Babe Ruth, 256 (1920)
6. Babe Ruth, 239 (1921)
7. Babe Ruth, 239 (1923)
8. Ted Williams, 235 (1941)
9. Ted Williams, 233 (1957)
10. Ross Barnes, 231 (1876) **
11. Barry Bonds, 231 (2003)

* - Fred Dunlap's historic 1884 season came in the Union Association, which some baseball experts consider not to be a true major league

** - Ross Barnes may have been aided by a rule that made a bunt fair if it first rolled in fair territory. He did not play nearly so well when this rule was removed, although injuries may have been mostly to blame, as his fielding statistics similarly declined.

If Dunlap's and Barnes' seasons were to be eliminated from the list, two other Ruth seasons (1926 and 1927) would be on the list. This would also eliminate the only right-handed batter in the list, Barnes.

## Notes

1. ^ See www.baseballprospectus.com or rec.sport.baseball.
2. ^ Lewis, Michael. Moneyball: The Art of Winning an Unfair Game, 2003.
3. ^ http://www.baseball-reference.com/leagues/MLB/2008-standard-batting.shtml
4. ^ James, Bill. The 96 Families of Hitters. The Bill James Gold Mine, 2009, p.24.
5. ^ John Thorn and Pete Palmer, The Hidden Game of Baseball, pp. 69-70.
6. ^ Alan Schwarz, The Numbers Game, pp. 165, 233.

## References

• Thorn, John; Pete Palmer (1984). The Hidden Game of Baseball. Doubleday & Company. ISBN 0-385-18283-X.
• Schwarz, Alan (2004). The Numbers Game. Thomas Dunne Books. ISBN 0-312-32222-4.

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