Fastballs and Changeups, Oh My!

With Johan Santana pitching last night and Cole Hamels tonight, there’s been a lot of talk about the pitchers’ differential between the speed of their fastball and their change-up helping a pitcher strike out more batters. Seems like common sense, but I decided to see how much of a relationship there actually was, so off to FanGraphs I went. This is your warning to exit now if you don’t like math.

I sorted the starting pitchers first by innings pitched over the past three calendar years. I got their K/9 rates, fastball and change-up usage rates, and fastball and change-up average speeds. In another column, I subtracted the average change-up speed from the average fastball speed, giving us the differential. Then, I eliminated all starters who used their change-up less than 10% of the time. It’s an arbitrary cut-off point, but we don’t want to study pitchers who never use a change-up like Tim Wakefield.

We’re left with 30 pitchers, which adequately satisfies our sample size requirement.

Next, I plugged the differentials and the K/9 rates into a scatter plot, added a trend line with a y=mx+b equation and an R-square. I don’t actually use the equation for anything but I put it up in case anyone wants to toy with it. In case you’re unfamiliar, the R-square tells us how much of the change in X can be explained by the change in Y.

(Click the image for a larger version. I have no idea why the images are blurry — anyone have any ideas as to why this is? The pictures look fine when viewed on my computer so I think it’s ImageShack‘s fault.)

We have an R-square of 0.22, which means that about 22% of the change in a pitcher’s strikeout rate can be explained by the difference in speed between his fastball and change-up. The relationship is positive, meaning that the wider the gap between the FB and CH speeds, the more strikeouts he’ll achieve.

It will start to get real math-heavy here, so brace yourselves.

Next, we want to run a test to see if the correlation coefficient (.47) is reliable using the null hypothesis that there is no correlation between FB/CH differential and K/9. In a two-tailed test using a 95% level of confidence with 28 degrees of freedom (30 players minus 2), we find that our test statistic must lie between negative 2.048 and positive 2.048 to conclude that there is no significant correlation.

A t-test for a correlation coefficient gives us a test statistic of 2.83 which falls in our region of rejection. Thus, we conclude that there is, in fact, a statistically significant correlation between FB/CH differential and strikeout rate based on the group I’ve selected. Not a surprising conclusion, but interesting nonetheless!

I’m sure that if I lowered the threshold below 10% CH usage, or if I used pitchers over two calendar years instead of three (or pitchers over a three-year period other than present minus three years), we’d see less of a correlation. Unfortunately, I don’t have the database skills to extract that.

This is a rough and incomplete look at the relationship, but it’s something I threw into a spreadsheet on a whim. Much better than watching the Mets BABIP-luck their way into a win against Cole Hamels (as I was writing this article, BABIP started to swing back in the Phillies’ favor in the top of the seventh — hey, Paul Bako sighting!).

Feel free to add your thoughts, questions, and criticisms. I especially want criticism, so have at it. I’m not aware of any other studies that have been done on this relationship, but if you know of any, please let me know.

Addendum: What this “study” ignores, among other factors, is pitch sequencing, which obviously would have a large effect on k-rates. If you have two pitchers who are 75% FB, 25% change-ups, the pitcher who goes FB, FB, CH, FB, CH, FB, FB, FB will most likely be more successful than the pitcher who goes FB, FB, FB, FB, FB, FB, CH, CH. The pitcher vs. batter match-ups exemplify the Nash equilibrium, but that makes my head explode.

On That Raul vs. Blogger Ordeal…

If you haven’t heard about Angry Raul, click here to get caught up. Here’s the tl;dr version:

  • Blogger says it’s possible that Raul Ibanez could be using steroids, despite the lack of any positive drug tests.
  • Mainstream media picks up on blogger’s article, publicize and rip it.
  • Raul Ibanez hears about blogger’s article, gets angry at accusations.

Unfortunately, just about everyone is responding in an emotional manner and not really taking the whole scenario into account. Nothing the blogger said was accusatory. Had he flat-out stated, “Raul is on steroids” or something like that, it’s a different story. But he said it’s a possibility, like saying there’s a possibility it might rain tonight. You’re sticking your head in the sand if you don’t think there’s even a remote possibility any athlete is on performance-enhancing drugs.

Throughout my response here, I’ll try to refrain from pushing my own agenda with regard to the steroid issue.

First, as I mentioned, the blogger didn’t say anything accusatory. Check the article out yourself, but I’ll quote some snippets as examples:

  • In fact, the 37-year old Ibanez has been so good that it has led to the inevitable speculation that his improvement may be attributable to factors other than his new lineup, playing in a better ballpark for hitters, or additional maturation as a hitter. In this day and age of suspicion at any significant jump in numbers, even over small sample sizes, it is what it is – and such speculation is to be expected.

Not accusatory in the least. You hear this — “the speculation is inevitable in this era” — almost ad nauseam on ESPN when they have their pseudo-intellectual debates between such noted scholars as Skip Bayless, Jemele Hill, Woody Paige, and Jay Mariotti. It’s okay when the MSM does it, but not a friggin’ blogger. No, not those nerds who live with mom and don’t wear pants and have level 80 World of Warcraft characters and wore a Jedi suit to prom.

Shortly after the above quote, the blogger in question quotes a member of his fantasy baseball league who thinks Ibanez is on something. If quoting someone’s opinion is being accusatory then he’s guilty as charged. However, look at it this way: during the O.J. Simpson trial, how many of us said out loud in public that we thought he was guilty without question? Did we deserve punishment for having such opinions? Did the MSM deserve punishment when they did their “this is what the populace thinks” pieces? If not, then why does this blogger?

Next snippet:

  • [...] any aging hitter who puts up numbers this much better than his career averages is going to immediately generate suspicion that the numbers are not natural, that perhaps he is under the influence of some sort of performance enhancer. And since I was not able to draw any absolute parallels between his prodigously improved HR rate and his new ballpark’s hitter-friendliness, it would be foolish to dismiss the possibility that “other” performance enhancers could be part of the equation.

In science, you never eliminate any possible explanations unless you can prove them wrong repeatedly. What the blogger is practicing here is good science. He stated his hypothesis, did his research, and came to a conclusion that he had no conclusion and that the many possible explanations are all still valid as far as he can see. There is nothing wrong with that.

He did not say, “Raul is on the ‘roids.” He essentially said, “Based on the evidence at hand, I cannot rule out the possibility that he is not on ‘roids.”

  • Sorry Raul Ibanez and Major League Baseball, that’s just the era that we are in — testing or no testing.

Again, not accusatory; just matter-of-factly-speaking. How many players have drawn suspicion of steroid use just this year alone?

  • Personally, I am withholding judgment until we see a full seasons’ worth of stats.

I think the MSM and Ibanez missed this quote when they were tearing the blogger to pieces. In fact, throughout the article, he makes clear what he really thinks about Ibanez: small sample size, he’ll decline as the season progresses, etc. So accusing the blogger of something he did not do is exactly what the MSM is berating him for doing. That’s known as hypocrisy.

  • And maybe that training included…Well, you know where that one was going, but I’d prefer to leave it as unstated speculation. However, if Ibanez ends up hitting 45-50 homers this year, you can bet that I won’t be the only one raising the question.

Asking questions is never a bad thing. It’s what intelligent people do. The even more intelligent people ask questions and then attempt to answer them.

John Gonzalez of the Philadelphia Inquirer set up a nice strawman in his article about the issue:

  • Then JRod dismissed all the evidence of opportunism, pivoted like a second baseman turning a double play, and fired his conclusion into the mitts of conspiracy theorists and amateur drug testers everywhere [...]

Where did this happen? I saw no signs of any pivoting.

If Woody Paige said this on ESPN’s Around the Horn, nobody would have batted an eyebrow. Somehow, a blogger does it, and he’s betraying law and ethics; he’s liable to be sued; he represents everything that’s wrong with blogging, etc.

What this is, really, is the MSM seeing a door slightly ajar and busting it wide open — one of few opportunities they have ever had to really criticize bloggers for what they do (and oftentimes do better than their paid counterparts). This is the mainstream media fighting over territory it’s already lost and will continue to lose. It is not about wrongfully accusing Ibanez of any wrongdoing.

The blogger has written a response to the fury that has come about as a result of his article, check it out if you have a minute. He apologized and accepted partial blame, something I commend him for doing even though I feel he did absolutely nothing wrong.