The Physics of Calling Pitches from Your Sofa

Why does the team I root for remind me of an old Michael Jackson video? They also wear a glove on just one hand for no apparent reason. So, in a moment of frustration and disgust I decided to change the channel and watch the ESPN game instead.

Now, I enjoy the technology in baseball broadcasts probably even more than the next guy, but does ESPN really need to show the PITCHf/x strike box in real time? It makes it harder to follow the trajectory of the pitch, the framing efforts of the catcher, and the reaction of the batter. It is simply a major distraction.

By the time I gave up and went back to watch my guys blow another game, our ace had been perfect through six. A righty was leading off the seventh as I sat on the edge of my couch, locked in on every pitch. I was so focused that I noticed the big guy had nearly pinpoint control, but the ump seemed to be a bit off. He was calling pitches on the outside corner balls and giving strikes for pitches that were clearly inside.

The strange thing is, when they showed the PITCHf/x trajectory – between pitches as they should – the ump seemed to be getting them right. What gives?

Looking carefully, I noticed the image on the screen from the center field camera is not directly in line with home plate. On a recent Sunday, I surveyed 14 broadcasts. I was quite surprised to discover there were only three distinct camera positions in center field.

In five of the games, the right edge of the rubber was aligned with the far corner of the left batter’s box on the TV screen. In six broadcasts, the left edge of the pitcher’s rubber was aligned with the far corner of the batter’s box. Three games had the center of the rubber aligned with the center of the plate, but the camera angle was much higher than the other two orientations.

Figure 1 illustrates the situation in which the right edge of the rubber is aligned with the corner of the left batter’s box. The slanted blue line is the line of sight of the center field camera. For those of you with a love/hate relationship with math – and by that I mean mostly hate – you might want to ignore the next three paragraphs where I work out the geometry of the situation.

The base of the blue triangle is the width of the batter’s box (48 inches) plus the space between the box and the plate (six inches) plus half the width of the plate (8.5 inches) plus half the width of the rubber (12 inches). You need only half the plate to align with the center of the rubber. The total is 74.5 inches.

It is 726 inches (60 feet, six inches) from the front of the rubber to the back of home plate. We need to add the width of the rubber (six inches) and subtract the 8.5 inches of the point of home plate and subtract the 36 inches of half the batter’s box to get 687.5 inches for the height of the blue triangle. The spot where the edge of home plate bends toward the point is at the center of the six-foot batter’s box.

The tangent of the angle is related to the ratio of the base to the height. The result is a camera angle of 6.2 inches. This works out to the camera being about 50 feet toward left field from straightaway center.  Here are my estimates for the other two camera positions.

Camera Position Estimates

Orientation	Angle	Camera Position
right rubber at batter’s box	6.2˚ left	50’ toward left
left rubber at batter’s box	4.2˚ left	30’ toward left
center alignment	5.9˚ high	47’ above ground

When we look at the image from center field, we generally take our queue for the location of the strike zone from the position of the catcher’s target. Figure 2 shows the top view of a right-handed batter getting an outside pitch (left image) and an inside pitch (right image). The vertical line is the trajectory of the ball, while the line slanted at 6.2 degrees is the line-of-sight of the camera; in other words, what you see on the screen.

An outside pitch that looks to the camera like a strike on the outside edge is clearly outside at the catcher’s mitt. A pitch on the inside black of the plate looks like it was never close to home plate.

The second camera location in the table would produce the same errors, only a bit smaller in size. What about the high-angle view from center field looking over the pitcher’s head? Do you expect me to just give you the answer?  Get out some paper and start making some sketches. Okay, okay, here’s what I got. The pitch at the top of the strike zone looks like a ball while the one well below the knees looks like a strike. My answer here assumes a horizontal trajectory of the ball, which is not quite the case.

What you see as far as balls and strikes really depends upon the direction you’re looking. Have you noticed that the benches most often complain about high and low pitches? They rarely howl at inside or outside calls. From the dugout they are in the ideal spot to see the height of the pitch, especially since their eyes are nearer ground level than the ump’s.

When you start to think about this issue, you might suspect the home plate ump is in about the worst position for calling balls and strikes. In fact, in the 1800s umps often did call pitches from behind the pitcher. This location has the advantage of a clear view of the top, bottom, inside and outside of the strike zone.

However, the zone is a three-dimensional space. Therefore, umpires also need a top view. They are trained to place their eyes at the inside top corner of the zone. That leaves a bit of judgment in calling pitches low and away. The ones that make it to the bigs are over 95 percent accurate, although they seem to have idiosyncrasies that are measurable.

If you examine games shown at different angles, you’ll also note a variation in the way balls and strikes appear, depending upon the pitcher. A righty releases the ball a foot or more to the right of the line between the center of the rubber and the middle of the plate. From one of the side-angle views, the release point appears to be directly in front of home plate due to the camera angle. So, it looks as though every pitch is going to be a strike until the ball veers away just as it nears the plate.

Conversely, for a southpaw, every pitch looks wide (to a right-handed batter) until it appears to sweep across the plate at the last second.

Well, this explanation has gone on long enough. I need to get back to this pitching masterpiece – nine more outs to go. I just hope my guys have figured out why they wear their gloves.