## Monday, August 31, 2020

### What are the odds?

The Shekel poses the rhetorical question: What are the odds that all three men who attacked Kyle Rittenhouse were convicted felons?

Knowing a little bit about functional statistics, I want to make a stab at answering that.

Aaron, the author of the blog shares that approximately one Wisconsin resident in fifty is a convicted felon. I see no need to dig into that.

The difficulty

The difficulty is that the question is posed AFTER the data is known.

Statistics generally works by making a hypothesis and then accessing or creating data. The fact that the data was known leads the reader to a conclusion that seems obvious.

Consider the monkey throwing three darts at a newspaper listing all of the stocks on the New York Stock Exchange.

Depending on which stocks the darts hit, one might reach the conclusion that the monkey was programmed to hit high-dividend stocks or are Technology or Financial stocks or all have the letter "A" as the second letter in their ticker symbol.

One way to deal with the problem of no a priori hypothesis is to change the hypothesis. Instead of asking "What are the chances of all three attackers being randomly drawn from the general population of Wisconsin being convicted felons" we might ask "What are the chances of the next two attackers being drawn from the general population of Wisconsin and having the same criminal status as the first attacker."

The second hypothesis is still weak but it makes a passing nod to the problems of making a posteriori hypothesis.

In the case of the first hypothesis, one would draw the conclusion that the odds were 1-in-125,000

In the case of the second hypothesis, one would draw the conclusion that there is a 1-in-2500 chance that the second two attackers would be felons just like the first attacker.

That suggests that there is a 2499-in-2500 chance that the Leftist demonstrators on the streets of Kenosha that night were a distinct population compared to the general population of Wisconsin. One could even go out on a limb and make the case that riots somehow attract convicted felons.