Re: Why we need computers calling balls and strikes
Thinking about the technical feasibility of real-time automatic tracking of pitches, I think it is definitely possible depending on the requirements (I know, that's such a cop-out). But for an initial goal-post, I'll go with 1 cm in a single direction (up/down, left/right, etc.). Cheap? No. Possible? Very.
My solution requires five infrared cameras placed at various useful angles. Optical sensors afford very good angular resolutions of a few miliradians. In other words, a single camera should be able to place the location of a baseball in a spacial area plus or minus the size of half a baseball. With just one sensor, we're on the right track but don't achieve all the accuracy we need. That's okay, the other cameras and processing will buy us some more. The cameras don't have to be super-duper high speed either, a frame rate of 100-150 Hz should be good enough.
I would then arrange the cameras as follows: two will be located above the backstop, one will be located in the batter's eye, in line with the pitcher. That last part is important, because while we can adjust for any angular offset, it will have some detrimental effects. The second camera will be above the backstop, high above home plate. The next two will face head-on with the batter with one on each side to allow for left- and right-handed hitters. The last camera will go somewhere else. It doesn't really matter where, but the farther separated from the other cameras the better. The last camera only exists to help time sync the other three (we can ignore the camera staring at the batter's backside). The first camera will give us the up/down and left/right position of the ball. The second camera will give the left/right and let us know when the ball crosses the plate. The third and fourth camera will also let us know when the ball crosses the plate and how high the pitch is.
One of the fundamental problems with tracking objects, whether it's a baseball or a supersonic jet is contrast with the background. For this reason, I think IR is the way to go (specifically, long-wave IR). If our eye was the camera and we could only stare directly onward to a hitter, I doubt any of us would be able to see the ball at all. The ball is mostly white and often the home team is wearing a white jersey. Similarly, looking directly down on the plate gives us the same problem: the plate is also white. IR provides us with the contrast to know what is the ball and what is a player or dirt or the plate. And since it's optical, we still have our angular resolution. It also helps that our background is cooperative. That is, we know it and it won't be changing rapidly. The location of the plate doesn't change (a good thing), the amount of IR it radiates might as afternoon turns into evening and such. But taken over the length of time for one pitch, it will be constant. Contrast can be further improved with a simple treatment to the ball or the thread in a player's uniform. It's completely invisible to the players without any eye safety concerns.
After applying some real-time image processing and estimation techniques (both of which are widely used in many applications), we will have a volume of space that is elliptical but hopefully close to spherical in shape and ~3.5" to each side. This is our uncertainty volume at the time the ball or strike decision must occur. Place the ball in the center of that volume. Repeat this for the height of the strike zone for each batter for each pitch. There's your answer.
I REALLY like thinking about this problem.
What if this wasn't a rhetorical question?
All models are wrong. Some of them are useful.