This isn't as important as #12, so it is a separate issue, but I wanted to make a note of it so I do it later.
[x] The PlayerPickers don't change based on the floor, so the JavaScript won't prevent you from inputting a player that isn't on your floor. Django will take care of it, but that's not as slick as doing it in real time.
[x] If the player box is empty, the typeahead still shows stuff. That shouldn't happen.
This isn't as important as #12, so it is a separate issue, but I wanted to make a note of it so I do it later.