Yeah, nobody likes the old THAC0 system, but that's all I know. I was just reading off the tables in the old Dungeon Master's Screen, Fighter THAC0 = 20 at level 1, hoping that the basic probabilities would be similar in 5E. But even 55% is nowhere near 95%. I think it is still safe to say that 1st level characters should not hit very often, so if I ever see a 95% chance on my screen feedback in Chapter 1, I would not be inclined to believe it. Once again, the Mists of Leira shroud us with unknowing.
It just depends on what you're fighting, I guess. Fighting some bandits, or goblins that are at a CR of what you're level is, it's not going to be the same as trying to hit an Ancient Red Dragon or something. That said, seeing the actual die rolls might make people slow down on the "but they're just trying to pad their hours played" or what have you. Probably not, because they still won't understand probability any better, but who knows, it could help.
