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Perfect Pitch: is it possible?

We're going to explore how good someone's perfect pitch could be. How well can a human discern the frequency of a sound? Then we'll show how this pertains to the ability to throw and hit the perfect pitch.

How accurately can you hear pitch?

The measurements that show how many frequencies a person can distinguish show that humans can discern about 1500 different pitches.  How do they do this?  It's done by a vibrations picked up at the ear drum then transmitted to the cochlea via three tiny bones (that server to amplify the vibrations due to leverage.) The cochlea is a small tube that's about one inch long (rolled up) and gets smaller the further away from the entrance point the smaller the tube gets.  This causes sounds of different frequencies to have peak intensities at different points along the cochlea.  The intensity causes the hairs that line the tube to fire in proportion - hence which hairs fire tells you the frequency (pitch) and how many fire (and their rate) tell you the loudness.  

Now the cochlea is only about 3.2 cm long.  So 1500 pitches imply you can differentiate a peak of sound intensity every 20 microns (a micron is a millionth of a meter or about a thousandth of an inch, commonly called a mil.)  Since there are only about 16,000 to 20,000 of these hairs, your brain can figure out the peak of the intensity distribution to about 10 hairs.  Pretty amazing signal processing going on!

How does this help with pitching the perfect pitch?

The perfect pitch is one that the batter can't predict where it is going. Mariano Rivera was the expert at this. Here's what you have to understand to make the perfect pitch.  First spinning a ball can cause the ball to move due to the Magnus force.  (You can read all about the details in my old physics professor Adair: The physics of baseball and some more detailed work is here.)  But all you need to really know is that all the spin of the baseball around the direction of travel makes no difference to the path of the ball.  You can imagine this as a ball coming toward you and spinning either clockwise or counter-clockwise; this spin makes no difference in the path the baseball takes.  However, if it's spinning in any other direction, it tends to move in that direction. What this means is that you have two directions of spin you can put on a ball. One of them causes the ball to move in the direction of the spin, the other doesn't do anything to the direction the ball moves.

 How does this help us throw the perfect pitch?  Baseball players pick up the spin of a pitch by the color of the baseball.  This is shown below in a graphic from a reddit discussion.

What's the trick that some pitchers have figured out?  The trick is that in addition to the spin that makes the ball move, you can rotate the ball clockwise or counter-clockwise and not effect it's movement.  Thus you can take any of the pitches shown above and add additional spin that blurs the characteristics of what the ball looks like.  If you can spin the ball in the right direction you can make all pitches look just like a four-seam fastball.  

This was Mariano's big secret.  This is also the secret of the 'no-dot' slider.  You add additional spin to the ball to move the 'dot' either above or below the line of sight.  Now the batter can't tell what you are throwing, so they have to guess, because there's not enough time to figure it out by looking at the trajectory of the ball.  If you try to do that it won't work as you have to wait too long to start your swing, you'll miss the ball.  Typically a hitter has to decide where the ball is going to end up at the plate when it's only traveled about 20% of the way to the plate.  The only way to do this is to look at the color of the ball.  And maybe the arm action of the pitcher.  Mariano's arm action varied by less than 2% between the two pitches he used (a cutter and a fastball) so there was no help there.  Once a pitcher learns how to remove the color cue, they become the perfect pitcher.

Can you pitch the perfect pitch?

You can't completely hide the spin, but you can obfuscate it. Can you obscure it enough so that the perfect batter can't differentiate your pitches?  Let's see how many sensing signals a batter gets to use to determine the spin/color of a baseball.  The batter has to figure this out when the baseball is 50 feet away.  A baseball is approximately 3 inches in diameter.  At 50 feet this subtends about 3 (inches) / (2 * pi * 50 (feet) *12 (inches/feet) ) (=% of circumference) * (360 degrees/circumference) or about 0.3 degrees of the batters field of view.  Since One degree of visual angle is equal to 288 ┬Ám on the retina (Drasdo and Fowler (1974) this image is about 10 microns (or millionths of a meter) in size.  Sound familiar?  That's about how accurately the hairs in your middle ear could determine an intensity peak. It ended up being about 10 hairs.  

How does this compare to the retina?  

There's approximately 17,500 cones in 1 degree in the most sensitive part of the eye. A cone makes a signal depending on the intensity of light hitting it. The image of the baseball covers (0.3 * 0.3 = 9 %) of this area (called the fovea.)  This means that the image is seen by about 1,500 cones.  There are three types of cones that respond to different colors.  To figure out what color the baseball is there are three measurements of 500 different signals.  The ratios of these signals map to our perception of the color.  A cone can distinguish about 100 different colors, so technically you can see around a million different colors (100 * 100 * 100.) However, since a baseball is essentially red and white, the batter isn't really seeing different colors, but different intensities or hues of the same color.  It turns out that the batter can also discern about 100 different hues. 

How many different hues can a pitcher give a baseball?  Let's assume, that like for hearing, it takes about 10 sensors to make a measurement.  This means that the eye gets about 50 separate spatial measurements of the hue of a baseball when it's 50 feet away.  That's why the batter can see 'tracks' or 'dots', they can measure the relative intensity of the color red in about 50 spots on the baseball.  By spinning the ball clockwise or counter-clockwise, in addition to the spin that makes the ball move, the pitcher can make the color of the ball the same regardless of the pitch they are throwing.  Thus, it doesn't even matter that the batter can see all these different hues!

What's the best batting average against the perfect pitch?

First we have to figure out how close the batter has to get to guessing where the ball is going to cross the plate so that they can hit it.  In other words, when someone is swinging at a ball, how much can they adjust the swing of the bat so that they can still hit the ball on the sweet spot? According to this paper, the last 150 to 200 ms of ball travel are totally unusable by the batter.  Also, according to Ted Williams, you've identified what type of pitch it is in the first 100 ms.  You do that by the spin.  Now you can't do that anymore.  So you have to guess what kind of pitch it is.  If the pitcher only has two pitches, like Mariano, you get it wrong half the time. The batting average of batters facing Mariano over his career was .209.  The average batting average during this time was about .265.  So not knowing which pitch was going to come dropped the average by 20 %.  If the batter guessed wrong and couldn't adjust the drop should be 50%.  Thus the batter can adjust 60% of the time.

Let's see how much better a pitcher could be if they had three different indistinguishable pitches.  The batter has to distinguish three trajectories.  I'm guessing that the batter is just guessing when they realize they are wrong.  In this case it would drop the batting average by another 20%!  Look for some pitcher to have a batting average against of 40% below the average, and you'll know why.

Thanks for reading.
 -Dr. Mike


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