Much has been made about Jerod Morris’ blog post regarding Raul Ibanez’s unexpected performance thus far. The post attempts to bust any steroids claims using statistical evidence—not to accuse him of taking performance-enhancing drugs, as the media is making it out to be.
In his final three years as a Seattle Mariner, Ibanez hit a respectable .291/.354/.492, with an average of 26 home runs and 113 RBI per year. This year, his first in the National League in his 14-year career, the 37-year-old is hitting .325/.380/.671 with 20 home runs and 55 RBI.
Ibanez has just three fewer home runs this year than the 23 he hit in 2008, in 452 fewer plate appearances.
Only once in his career has Ibanez hit over .300, and never has he had an OPS above .900. He’s on pace to smash his career highs at age 37, something seen in recent memory only by Barry Bonds.
There are two main factors that could be the cause of his offensive explosion. First, his switch from the AL to the NL and from Safeco Field to more hitter-friendly Citizens Bank Park; and second, random fluctuations resulting from lack of significant sample size.
Let’s deal with the former first. Based on players who moved from the AL to the NL since 2000, and Safeco Field’s and Citizens Bank Park’s four-year park factors from 2005 to 2008, Ibanez would have expected his batting average to increase by 5.8 percent, his on-base percentage by 6.2 percent, his slugging percentage by 10.1 percent, and his home run rate by 20 percent—just by his moving to Philadelphia.
(Those are multiplicative, not additive, by the way. Batting average is multiplied by 1.058, for example, and not increased from, say, .300 to .3058.)
If we adjust his 2006-08 stats from Seattle accordingly, his previously good batting line is now great: .308/.376/.541, with 31 home runs and 116 RBI per year.
His current OBP of .380 is in line with his adjusted OBP, but the slugging percentage is where the major difference lies—an actual .671 versus the adjusted .539.
Why is the disparity so large?
Ibanez has hit 20 home runs in just 80 fly balls, a HR/FB ratio of 25 percent. The league average falls around 10 or 11 percent; Ibanez’s was 10.7 and 10.9 percent each of the past two years, respectively.
From 2006 to 2008, Ibanez’s HR/FB percentage was 12.7 percent. Our estimate for his HR/FB percentage this year is about 14.6, which includes a 20 percent increase and a slight regression to the mean (15 percent, to be exact).
This means that we would expect 11 or 12 home runs in 80 fly balls for Ibanez. (By the way, if we prorate 12 home runs in his 255 plate appearances to an average of 681 in his last three years in Seattle, we’d get an average of 32 homers per year. We previously estimated 31 home runs in Philadelphia for Ibanez.)
If we then take away eight of his 20 homers—and add four doubles, assuming half of those eight are outs and half are doubles—his slugging percentage falls to .566 and his OPS to .946. And if those eight non-homers turned out to be all outs, his actual performance this year would actually be worse than what his adjusted stats estimated.
The second hypothesis as to why Ibanez’s stats are so high is random fluctuation. In THE BOOK: Playing the Percentages in Baseball, the authors show that random fluctuation (known as standard deviation, or SD) in a binomial (such as on-base percentage, in which there are only two options—in this case, reach base or get out; slugging percentage, however, is not a binomial) is calculated as
where OBP is the player’s true talent OBP (or any other binomial) and N is the number of plate appearances, currently 255 for Ibanez. My preseason projection for Ibanez was a .359 OBP in the NL and in Philadelphia, but that is equal to an OBP of .348 in a neutral league and park, which is our estimate of his true skill.
Thus, the random fluctuation in Ibanez’s OBP is .03. There’s a 68 percent chance that Ibanez’s current OBP is within one SD of his true talent and a 95 percent chance that it’s within two SDs. (We’ll use his projection instead of his true talent, however, because we want both his projection and actual stats to be in the same environment—Philadelphia.)
In other words, if Ibanez repeated this season 100 times with the same true talent, surrounding cast, and other variables, his OBP would be anywhere from .329 to .389 (within one fluctuation of his true talent) 68 times, and between .299 and .419 all but five times, all due to random variation.
That means that Ibanez, with his .380 OBP, is currently within the range of our projection; his actual OBP is just 0.021 better than his projection, less than one SD.
Applying this to batting average, we see Ibanez is hitting 37 points better than his preseason projection of .288. The fluctuation for his average is 0.028, which means Ibanez is well within two SDs of his projected average.
The outlier is, of course, home runs. We calculate that the fluctuation of Ibanez’s home run percentage (home runs per plate appearance, not per at-bats) is 0.011, but his current percentage of 7.8 percent is over three-and-a-half SDs above his preseason projection of 3.8 percent.
(The probability that he’d finish above three SDs from his projection is just 0.3 percent, which shows that his home run percentage is due for a major regression.)
But remember that eight of his home runs were due to his inflated HR/FB rate? The 12 homers he should have based on his prior HR/FB rate results in a 4.7 home run percentage, less than one fluctuation, which suggests that Ibanez’s 12 “true” home runs actually somewhat represents his true skill level.
The stats show that aside from his insanely high HR/FB rate (20 home runs in 80 fly balls), Ibanez’s current stats are not too far off from his true talent level. Both his on-base percentage and home run percentage are within one fluctuation of his projection, something we’d see 68 percent of the time, and his batting average is within 1.3 SDs of his projection.