*UPDATE (9-25-10): In a linear regression study of 580 teams from the last 20 seasons—in which I took both OBP and slugging into account– OBP had a multiplying coefficient of 18.9, nearly twice as much as Slugging’s coefficient of 9.7. The formula looked like this: Runs/Game = (18.9 x OBP) + (9.7 x SLG) — 5.6 . The regression suggests that small changes in OBP are worth twice as much as small changes in Slugging. However, since an increase in OBP implies an increase in Slugging–unless the OBP comes only from walks–there is a small adjustment that needs to be made. If OBP changes 100 points, we can estimate that Slugging will change about 130 points because the two are correlated themselves. *

*As an example, take two teams, one with a .300/.400 OBP/Slugging split and one with a .350/.465 split. The first team should score about 4 runs per game, and the second team about 5.5. Of that 1.5-run increase, the regression estimates that 0.9 runs come from the OBP surge, but just 0.6 from the Slugging, even though the team’s slugging percentage actually increased by more than its OBP!*

*As another example, take one team with a .300/.500 split, and one with a .400/.400 split. Though both teams have an OPS of .800, the first team is expected to score 4.9 runs per game while the second should score about 5.8. This suggests that, in many situations, trading slugging for OBP could be a good idea.*

*It should be noted that there are even better, more specific ways to measure offensive ability. This regression had an R^2 value of 0.91. In the regression that I used for Run Values, the R^2 value was above 0.95, indicating an even better correlation and more potential for accurate team/player evaluations. OBP and Slugging are convenient stats for measuring offensive ability, but there are equally available stats that are better. I suggest wOBA, which can be found on Fangraphs, among other sites. *

**The Original Article:**

When Michael Lewis’ book, *Moneyball*, about the Oakland Athletics came out earlier this decade, the world found out about the “secret.” Get guys on base and reduce outs. That’s how you score runs. But is OBP really what general managers should be targeting? What about rabid fans who can’t wait to get rid of ______________ (appropriate names for the blank include Carl Everett or Milton Bradley) and just want something to indicate they are correct?

In an attempt to quantify the run-scoring correlation of certain offensive stats, I calculated a simple linear correlation coefficient between batting average, on-base percentage (OBP), slugging percentage, on-base plus slugging (OPS), and a new OPS stat (OPS*), versus runs scored. This new OPS stat weights doubles, triples and home runs less than the traditional slugging percentage does according to a linear weights formula derived years ago by one Ferdinand Lane and reproduced by Pete Palmer [1] (weights are 1, 1.72, 2.52 and 3.39 for single, double, triple and home run, respectively).

A coefficient closer to 1.00 indicates that the offensive stat is *more* linearly correlated to runs scored, or in our case, a better indicator of runs scored. Using each team’s offensive figures from 2004 through June 8, 2009, I calculated the following coefficients:

Average: 0.697

OBP: 0.827

Slugging: 0.863

OPS: 0.927

OPS*: 0.932

This tells us that our OPS* stat, utilizing a weighted version of slugging percentage, is the most linearly correlated stat to runs scored, though not any more significantly that the conventional OPS. OPS is a good statistic because it are easy to find and/or calculate, and its representation of run scoring is excellent. OPS is probably the more important statistic to the common fan trying to figure out if his team should be scoring more or less runs, or whether a certain player on his favorite team is helping the offense out at all.

Answering the question, “what’ more important?” from Billy Beane’s perspective is a more difficult task. Gauging how many more runs are produced from OBP points versus slugging points depends on where those points are coming from: walks or homers, or something in between? Using the trend lines from above, I can estimate run scoring potential from these increases in OBP and slugging.

A team that raises its OBP from .300 to .400 is expected to increase it’s runs scoring from 3.7 runs/game to 6.7. The equivalent increase in slugging would be about 131 points, on average. An increase in slugging from .358 to .489 predicts a scoring increase from 3.7 to 5.8 runs/game, an obvious downgrade from the OBP surge. However, if a team increases its OBP purely by walking more, then the 100 point increase in OBP will likely only increase run scoring from 3.7 to less than 5 runs/game. What a GM can take from this is that, while increases in OBP seem to lead to more run scoring than equivalent increases in slugging percentage, this is only the case when these increases come with a mix of walks and hits.

Bill James argued that any linear method used to quantify run scoring could not be accurate because run scoring is not linear. To this criticism, Pete Palmer replied, “Actually he is right. Baseball is not linear. The linear weight values do vary slightly with the overall level of batting. A single is worth slightly more in a good hitting year and an out is more costly. However, within the range that is actually found in major league play, these variations are small. You could develop a model with a different set of weights for each season, but it wouldn’t change the results much” [2].

[1]Schwarz, Alan. *The Numbers Game. *Published by St. Martin’s Press, New York: 2004. Page 36.

[2] <http://www.hardballtimes.com/main/article/pete-palmer-interview>

Did Beane talk about OPS much? I completely forget. Seems people like to claim moneyball doesn’t work, when in fact Theo Epstein of the red sox is Beane’s prodigy.

Moneyball didn’t mention OPS much, though if you read my addition above, perhaps OBP is the more important component of OPS than slugging…also check out this guy’s post: http://midwestbias.wordpress.com/2009/03/30/ops-correlates-with-something/

the weighted ops seems negligible considering it’s minuscule difference in comparison to the normal ops. interesting that principal stats of baseball are generally BA for hitters and wins for pitchers considering their inutlility.

It takes enough work to create that OPS* stat that it’s probably not worth going into unless you happen to have a lot of time on your hands (like me!).

I’m a bit out of my depth here, but Tae Nae’s post makes me wonder: at what point would the (apparently slight) disparity between the OPS and OPS* coefficients make an analytical difference? In other words, how many games would have to be in your sample before OPS* became a significantly better indicator of run scoring than OPS?

WillB:I re-ran the correlation to include data back to 2000, or approximately 300 teams, in the hopes of seeing a more significant difference. With the increase in sample size, the OPS and OPS* are now .939 and .944, respectively. While this is almost the exact same difference as before, with more data we can be a little more sure in the belief that OPS* is a slightly better indicator. However, if the difference in correlations remained the same, it would take about 2,300 samples (data back to the 1920s) to assert that OPS* was the better indicator at the 5% level, 1,500 samples at the 10% level, and 950 samples at the 20% level.Basically they’re both good indicators.

[…] Base Percentage vs. Slugging Percentage A while back, I wrote a post about the importance of On Base Percentage (OBP) and Slugging Percentage (Slugging) to scoring […]

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