What we think about when we can't sleep
So once again I can't sleep. And I'm sitting here, in the dark, with the fans blowing, and I can't sleep, and so I try doing some math in my head to put myself to sleep.
Tonight I tried to calculate why managers don't call for 1st-3rd double-steals more often with runners on the corners. Clearly the mathematics are in the favor of a catcher-shortstop combination being able to get the ball back to home plate before a runner on third can make it there. Here's the math I did in my head, using estimates all the way for numbers I don't know exactly. One of the major problems was that I couldn't concentrate on the math very well; math I used to be able to do instantly in my head now takes forever, even in the dark, with silence, and my eyes closed.
First I had to calculate the distance between home plate and 2nd base. I could have simply doubled the distance of the pitching rubber to home, a number I know (60.5 feet) but that's slightly off, since the rubber is a bit closer to home plate than it is to second base. I also didn't think of this until it was too late.
Instead, I used Pythagoras to square 90 (to 8100) and add it together (to 16200) and then take the square root (which I estimated to be roughly 125; it's actually 127.irrational). Step one over.
Then I had to calculate how long it takes a ball thrown by the catcher to make it to second base (and the return throw to make it home). I probably underestimated how fast a catcher can throw the ball to second; I supposed the average speed was 80mph. A ball thrown at 80mph takes 1/80 hours to go one mile, and 60/80 is 6/8 which is 3/4 of 1/60 (i.e. a minute) so 45 seconds.
125 feet is how much of a mile? 5280 feet divided by 125 feet... I guessed it was around 42. so 45 seconds divided by 42... basically one second. So it takes one second for a catcher to throw from home to second. Add a half second (complete conjecture) to reverse the throw, and assuming another 80mph average throw back home, and it takes 2.5 seconds to complete a round trip. Step two over.
I was already suspicious, because I knew that 2.5 seconds wasn't even close to enough time for a runner to make it to home plate, and yet the 1st-3rd double steal does happen occasionally. So I probably underestimated the turnaround time (since the shortstop has to tag the runner from first). Maybe it's one second. Total time: three seconds.
Yet how fast *can* a runner on third make it home, assuming he has to wait until the catcher releases the ball to take off? Again, I went to numbers I knew, and used math to get the rest of the way.
I assumed a fast runner like Carl Crawford could run about a 4.4 40-yard dash. That may be generous, or it may be slighting him. I don't really know. A 4.4 40 is a very fast time, but Crawford is a very fast player.
Either way, 4.4 is a fairly convenient number for me to pick, as it's easily divisible by four; since the 40-yard dash is a run of 120 feet, and the distance between bases is 90 feet, all i have to do is take 3/4 of the 40 time to get the time between bases. (Yes, the runner has an assumed lead off third, but we'll ignore that.)
So someone who runs a 4.4 40 gets from 3rd to home in 3.3 seconds. The transfer between catcher to shortstop to catcher takes three seconds. Even someone super-fast like Carl Crawford would have to rely on a slow-throwing catcher, a slow-throwing shortstop, or a botched exchange at second base in order to securely reach home. And that's why you don't see the 1st-3rd double steal much.
(Again, these numbers are completely made up and way off from how it works in reality. This post is just me explaining how I do math in my head to try and fall asleep, and how this time it failed miserably.)
