For some reason I put this together as a nice $\LaTeX$ PDF. Not entirely sure why, but that is how it exists now. Perhaps because it got a bit lengthy and involved.

Speaking of lengthy and involved, here’s the TLDR of 3 main points I think are interesting:

  1. How confident should you be that your challenge will succeed to pull the trigger? You need to be about 50% sure.
  2. Shown in Figure 2, human umpire accuracy isn’t all that it’s cracked up to be. Sure, they may get 90% of all calls correct, but on the close calls, they are hardly better flipping a coin.
  3. Having rules where you never challenge is a bad policy. It may seem like a good way to avoid burning a challenge in a low-leverage situation, but in reality you need to be able to capitalize on a bad call whenever it happens.

If you’re still wanting 12 more pages of insight, continue on ahead.