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Sunday, April 06, 2014

Why outfielders should throw to the cutoff man

A Cardinal Sin of outfielding is to throw home directly, rather than bypassing the cutoff man.  I've always wondered, however, if there are times when that really is the optimal decision for an outfielder.  Allowing the infielder to catch, grab, and then throw the ball must take time, and that's all time that the ball could be advancing toward home plate.  I figured air resistance might be negating some of that gain, but I wasn't sure that it would be enough to matter.

Therefore, I really liked David Kagan's article at Hardball Times last week on the physics of hitting the cutoff man.  David's piece shows that, in fact, one of the major advantages of hitting the cutoff man is that it is a straighter path to get to home plate.  When you throw directly home, you have to use a high launch angle because you have to overcome gravity every step along the way.  Throwing to the cutoff man is a more direct route, and the infielder then has a nice, short throw, again with very little need to elevated launch angle. His diagram shows this best:
Once one also includes factors like air resistance that leads to decreasing velocity during flight (blue line), the total flight time of a ball thrown directly home from 270 feet was 2.75 seconds, compared to just 2.39 seconds.

Now, when hitting the cutoff man, the infielder still needs to catch, transfer, and throw the ball, which must take another half-second to a second (this would be a fun thing to measure...I'll be watching for that in future ballgames).  Therefore, if the infielder is major league baseball-level efficient, we're looking at nearly equal travel times.

Consequently, the benefits of hitting the cutoff man seem to be as follows:

  1. Nearly equal time to plate, because the gains of bypassing the infielder are mostly offset by higher launch angle, and thus distance traveled, that are required to get the ball to home plate from the outfield.
  2. Improved accuracy by infielder on throw, because slight errors in trajectory angle make less of a difference when you're closer.  I'm guessing this is a really big deal.
  3. Ability to prevent the batter from advancing to second base.

Postcript: I'd like to formally apologize to my infielders in 8th grade little league when I bypassed the cutoff man and tried to throw out a batter running to third base.  I didn't succeed, but we might have if I'd thrown to the cutoff man!