Whiff Rate and Four Seam Fastballs

I was over at Brooks Baseball looking at their Pitch F/X cards, which are beginning to make my talents redundant and obsolete (that is a good thing, less work for me).  I decided to compare the velocity numbers from yesterday to swing and miss rates for four seam fastballs to determine if the two were related.  They were not in the least.  So, I decided to run a regression on several Pitch F/X derived measures and using the Orioles pitchers as a population base.  This is a pretty simple exercise and should not be taken as anything profound.

Population: Orioles currently on the 40 man roster who appeared in a 2011 MLB game.  Said pitchers need to have a four seam fastball and a change up.  I limited it to change ups because I wanted to see the interplay between the two pitches and thought it could make things more difficult if I grouped them in with cutters and splitters.  This resulted in the following pitchers being included:

Brian Matusz, Jason Berken, Chris Tillman, Troy Patton, Zach Britton, Zachary Phillips, Brad Bergesen, Matt Lindstrom, Luis Ayala, Jason Hammel, Jake Arrieta, and Jim Johnson

I chose to include the following metrics and a brief reasoning:

% Four Seamer: prevalence may mean batters can assume a four seamer
4S Horizontal Movement: unlikely to affect things as it stays in the bat plane
4S Vertical Movement: movement out of plane may affect whiff rate
4S Velocity: movement past swing area may affect whiff rate
4S vs Changeup Slot Release: any difference in release point
4S vs CH Horizontal Movement: can the batter perceive a horizontal difference?
4S vs CH Vertical Movement: can the batter perceive a vertical difference?
4S vs CH Velocity: does differences in velocity play into a 4S whiff rate?

Result
Only the % Four Seamer (p = 0.10) and 4S vs CH Velocity (p = 0.08) were relatively close to being significant factors in determining whiff rate.  For MLB quality pitchers going against MLB quality batters, the other variables do not appear to approach anything close to significance (all other p values greater than 0.40).

To elaborate, % Four Seamer approached significance in that the fewer four seam fastballs thrown in relation to other pitches, the most often a batter swung and missed a pitch.  This appears to be a situation where the batter is not able to sit and assume a fastball is coming.  By increasing the element of surprise, a batter cannot simply guess on a pitch and has to quickly recognize what is coming out of the pitcher's hand.  This probably elicits a "Well, yeah, of course."

The reason why a 4S vs CH Velocity is important is also something that is probably well understood.  The shorter the time the ball passes through the swing plane, the less likely the bat will be able to hit it.  To provide some context to this, let's create a scenario.  Troy Patton throws a 90 mph fastball.  That fastball takes 0.45 seconds to reach home plate and an additional 0.015 seconds to pass by it.  An MLB batter with decent bat speed can generate a velocity of 100 mph with his bat, which takes about 0.014 seconds to pass through home plate.  If the batter expects a fastball and swings without change in bat speed, we get the following:

A line drive swing should overlap with the ball for about two feet.  By expecting a 90 mph fastball, the batter can maintain contact from about a 1.5 mph in either direction.  In Robert Adair's Physics of Baseball book, he estimates that a batter must decide to swing or not before the ball is 0.22 seconds from the plate in order to make contact.  Conventional wisdom suggests that a change up needs to be at least 5 mph different than the 4S to be usable in the Majors, which is a difference of 0.02 seconds in reaching the plate in comparison to the 4S.  The best change ups tend to be 8-10 mph slower than the 4S.

It may well be that MLB quality batters correctly read or are able to adapt quickly enough when the arrival time between a 4S and a change differ by 0.02 seconds or less.  It may also be quite difficult to make up the difference if the difference is twice that.  Of course, there is likely a survivorship issue here with speed and arm slot.  There may be certain requirements in place for this population to be established before this relationship occurs.