We are expected to believe the following set of facts regarding the recent gubernatorial race in AZ:
So across Arizona, 51.2% of voters favored Katie Hobbs.
That came from reading 1,328,695 ballots that went straight through the machines, and another 214,371 ballots that had to be adjudicated (because of whatever causes adjudications: imperfect ovals, stray marks, and so on and so forth).
Let us treat this like a coin-flipping contest with two rules:
- Every time we flip the coin and it comes up Heads, we give Katie Hobbs a vote. But we are using a specially-weighted coin that comes up “Heads” 51.2% of the time (not just 50%). This reflects the extra edge Katie has in Arizona (per official results).
- We are going to flip the coin 214,371 times.
We should expect Katie to win 51.2% X 214,371 = 109,758 times.
Imagine Katie is so lucky she wins many more times than expected: 133,850.
How far a departure from the expected outcome is that?
133,850 actual wins – 109,758 expected wins = 24,092 variance from expected outcome
So Katie won an extra 24,092 times. Precisely how lucky is Katie?
To know that, we must calculate the Standard Deviation, which is the probability of a Heads X the probability of a Tails X the number of flips, and then that quantity square-rooted.
51.2% X 48.8% X 214,371 = 53,562
And the square root of 53,562 is roughly 231.
So a Standard Deviation = 231
How vast is Katie’s luck?
24,092 (Katie’s variance from expected) divided by 231 (the size of a Standard Deviation) = 104
For Katie to win 24,092 times more than expected in this coin-flipping contest is an event of 104 Standard Deviations (also known as “a 104-sigma event”).
Expressing the odds of such an event is not easy.
Here are the odds for/against events of lower Standard Deviations:
Here is how to read that (remembering that “Sigma” means “Standard Deviation”):
The odds of a 1 – Sigma event are 33.5%.
So the odds of it happening are about 1 in 3.
The odds of a 2 – Sigma event are 4.7%.
So the odds of it happening are 1 in 21.
The odds of a 3 – Sigma event are .277%.
So the odds of it happening are 1 in 361.
The odds of an 8 – Sigma event are .00000000000000125%.
So the odds of it happening are 1 in 800 trillion.
The odds of a 10 Sigma event are 1 in 65 million trillion.
And so on and so forth, until we get all the way to Katie Hobbs’ luck:
The odds of an event of 104 Standard Deviations can be written 1 in:
In sum, if we are to believe the official narrative:
Katie Hobbs has the support of 51.2% of Arizonians. Half-filled in ovals and stray marks caused 214,371 ballots to need to be adjudicated. Katie won not 51.2% of those, but 62.4%. The odds of that kind of luck are 1 in 4 trillion trillion trillion trillion trillion trillion trillion trillion trillion trillion trillion trillion trillion trillion trillion trillion.
So your saying there’s a chance?