Sunday, August 1, 2010

Do knuckleballers induce slumps?

The knuckleball is a very unusual pitch. It's thrown significantly slower than every other pitch, and it's been said to mess with a hitter's timing. Hitters seem to do fine against the knuckleball (KB), but I've heard people say that they'll go into a slump after facing the knuckler. Today I thought I'd investigate. Retrosheet's game logs provide the starting pitcher for every game as well as the basic offensive statistics needed to compute on-base percentage (OBP) and slugging percentage (SLG), so getting data was easy.

I picked out six knuckleballers, either famous or contemporary: Tom Candiotti, Charlie Hough, Steve Sparks, Tim Wakefield, Phil Niekro, and Hoyt Wilhelm. There are some other famous ones, like Joe Niekro, but they didn't throw it for their whole career. I searched through the data to find any games that one of these pitchers started, and then looked at their opponent's OBP and SLG in their kth game after the knuckler game (k=1,...,3 is all that was needed), and paired that with the team's average OBP and SLG over the whole season, with the intention of studying the paired differences to look for a post-KB game effect. I assumed that the differences were independent - which is at least approximately true.

To calculate the team's overall strength I had to use the unweighted average OBP and SLG, i.e. I averaged the OBP and SLG from all 162 games rather than adding all the count data together to find the weighted average. This was necessary because the weighted average tends to be higher than the value for a single game.

The differences between the season average and the kth game average have a beautiful bell-shaped curve (for both OBP and SLG), so I used two paired t-tests to see if the differences were significantly greater than zero. Since each difference is actually based on the difference of two averages, both of which might have a slightly different sample size each time (at-bat totals won't be exactly the same every game), I could probably be more efficient by assigning some weights to the differences, but I highly doubt this would make a non-negligible difference in the p-values.

The third column in the following two tables shows the average for the kth game after the knuckleball game, k=1,...,3, with the average season total for the teams in the sample in the second column. The p-values are testing OBP>post-KB OBP and SLG>post-KB SLG respectively, and they are based on a paired t-test.

game OBP post-KB OBP p-value

game SLG
post-KB SLG p-value

The knuckleball actually does seem to sap the team's power the day after they face it. Actually most of the next day woes are due to Candiotti's and Wakefield's effects, in particular Wakefield's. His tables are below:

game OBP post-KB OBP p-value

game SLG
post-KB SLG p-value

The overall effects are higher in Wakefield's tables because he's pitched in an offensive era. Hitters really do seem significantly worse than normal the day after they face him - even with the Bonferroni correction, the SLG decrease is significant, and the OBP decrease is marginally significant. The unweighted averages of OBP and SLG are .316 and .398 in games Wakefield pitches - actually quite close to the averages of the opposing team on the following day, and both lower than the overall average. Hough, Niekro, and Wilhelm are the superior pitchers, but maybe they didn't throw the knuckler as often as Wakefield does, and hence don't screw up the hitters' next day timing as much? Or maybe it has something to do with contemporary hitters not seeing the knuckler as often as guys in the past may have? Steve Sparks doesn't cause this next day drop-off though.

Thanks to Ben Shaby for suggesting this idea. The information used here was obtained free of charge from and is copyrighted by Retrosheet. Interested parties may contact Retrosheet at "".