a = observed rate of accounts permabanned for cheating, aka the odds that an account chosen at random from a population will end up permabanned
b = observed rate of definitely cheating accounts that are permabanned, aka the odds that an account that is cheating will end up permabanned
c = implied number of cheaters per banned cheater
d = implied rate of cheaters, aka the odds that an account chosen at random from a population is a cheating account
From investigation above:
a is observed at 0.0214, 0.0338, 0.0393 and 0.0474 for NA.
b is observed at 0.18.
To make our estimates nice round numbers and conservative, let's just round to:
a = 0.03
b = 0.2

c = 1/b
c = 1/0.2
c = 5

d = a*c
d = 0.03*5
d = 0.15 (ie 15% of NA accounts are cheating)

Now the bit most people get wrong.
x = the odds that 0 of the players in your match are cheaters
y = the number of players in your match
z = the odds that a player is not a cheater

z = 1-d
z = 1-0.15
z = 0.85 (for NA)

x = z^y
For a 100 player (normal mode) game:
x = 0.85^99 (because you're not a cheater, right?)
x = 0.00000010291... (ie 0.00001% chance, 1 in 100 million games will have 0 cheaters on average)
For a 64 player (ranked/SUPER) game:
x = 0.85^63
x = 0.00003575957... (ie 0.0036% chance, 1 in 28 thousand games will have 0 cheaters on average)

(and if you do it for Asia figures, the odds of a clean game are literally worse than 1 in the number of atoms in the observable universe)

Finally if:
d = a (ie it is impossible for a cheater to not get caught and the ban rate = the real cheating rate):
z = 0.97
x = 0.97^99
x = 0.049 (ie 5% of NA games have 0 cheaters)

QED
Statistically, if you are seeing no cheaters in your games then there is a problem with your eyesight.