Posted by polarsi on 6/20/2016 12:01:00 PM (view original):
"For instance, if offense is 50/50 run/pass in a scenario. If I pick 100% run, I'll be right 50% of the time. But if I pick 50/50 (correctly matching their balance), I'll be right 25% and wrong 75%."
I'm no statistician, but if you use 50/50 you will be right on average 50% not 25% of the time; you'll get half wrong and half right on his pass calls and the same again on the run. The potential variance (good or bad) is greater though.
It's good question and one I've thought too long about and results steadily getting worse because of it. Let's hope someone can put us straight
It is essentially guessing a coin flip. There are two possible outcomes and two possible guesses. Let's say you are against an offense that (in that particular down and distance) is 50/50 run/pass just like a coin flip. So let's break this down as if it was a coin flip.
If you are guessing 50% of the time heads and 50% of the time tails, here is what happens.
There are 100 coin flips. Of those, 50 are heads and 50 are tails. There are 100 guesses -- also 50 heads and 50 tails. For each flip there are four possible scenarios -- two of which you guess correctly and two you guess incorrectly.
Each flip you have a 50% chance of being right and a 50% chance of being wrong. When you mix your guesses 50/50, variance enters into it. It easily becomes possible to end up being right 75% of the flips or only 25% of the flips. If you you keep the guess the same every time, you lower the variance and you ensure you are right 50% of the time instead of probably being right about 50% of the time.