Baseball Trigonometry

Amidst all the baseball stats that we here at GOI throw out ad nauseum, it is easy to forget just how geometric the game of baseball really is. A round ball being hit by a round bat. 90 feet between each base. 60' 6'' from the mound to the plate with a 10'' elevation. The list goes on and on. But as Hawk Harrelson has been known to do, he has invented a new trigonometric property that has gone overlooked for nearly 130 years. After a close play at the plate that resulted in the force out of Chris Getz, Hawk and Stoney reviewed the play several times on replay to see if indeed the runner was out on the bang bang play. Stone commented that from his vantage point, Getz was barely out on the play. Hawk put in his two cents by stating that he has a different angle to the plate than his broadcast partner and thought the throw just beat the runner.

Although Hawk's claim that he has a different view of the plate is valid, it may not have any relevance when it comes to deciphering a play at the plate. Hence, I decided to do a little trigonometry and see what Hawk actually meant by "a different angle".

I'm going to make several assumptions, seeing as how I dont have access to the blueprints of Miller Park. I'll make a rough estimate that the announcing box is about 200 feet away from home plate. Seeing as how this is Hawk and Stone's first year together, I'll assume they're still trying to get that intimacy, so I will give them a 7 foot cushion between their eyes. We'll also disregard any curvature to the upper deck or anything like that since the effect is miniscule. All that's left is the math.



From my calculations, it appears that the angle separating Hawk and Stone's view of home plate is 2 degrees. Surely baseball is a game of inches, but how big a difference is 2 degrees from 200 feet away in the eyes of a 67 year old man? Maybe he should also claim that the light from home plate arrived to his eyes about 12 nanoseconds before it did to Steve's eyes.

If umpires cant get calls right from 5 feet away there is really no point of trying to do so from 200. Prime example today when the home plate ump mistook a foul tip by Ryan Braun for getting hit in the head. I get those confused too.