propability of 5 bans??

We currently have 134 champions in the game. Hypothetically speaking, each champion has an equal ban rate (I don't think there is a good way to calculate it otherwise): You have a 1 in 67 chance of having 9 bans. You have a 1 in 4442 chance of having 8 bans. You have a 1 in 287430 chance of having 7 bans.

And keeps going on like that using a factorial system. Granted this is rough math based off educated guesses that I don't want to take the time to go super in depth to verify.

Realistically, there are probably about 30 champions that will see regular banning. Assuming those all have equal ban rates: 1 in 15 of having 9 bans. 1 in 210 of having 8 bans. 1 in 2730 of having 7 bans.

Now if you trim it down even more to the REALLY hated champions and assume they get banned almost every game, I come up with... and I'll throw in +2 mystery champs that I may have missed. That makes 12 champs. 1 in 6 of 9 bans. 1 in 30 of 8 bans. 1 in 120 of 7 bans. 1 in 360 of 6 bans. 1 in 720 of 5 bans.

These numbers are by no means accurate, because different champs always have different levels of hate, but I came up with these numbers by dividing the number of champions in the pool and using a backwards factorial.

If I had to go off my raw gut instinct though knowing how bans work in actuality, I would say It would look like a bell curve with 8 being the majority, 7 and 9 being close behind it, 6 and 10 having a decent drop off of about half of 7 and 9, and 5 rarely happening.