Why Raul Ibanez's Breakout Is Not Caused by Steroids

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.

Steroids? Nope.

You're currently logged into Facebook

Do you want to share your Bleacher Report activity on Facebook?