You know how people say “What are the odds?”, meaning that something probably did not happen by random chance alone? I got to thinking about that saying regarding the current situation with the Mueller investigation. I read that:
None of the 16 lawyers known to work for special counsel Robert Mueller are registered Republicans
There are 13 registered Democrats on the investigation and three lawyers with no party affiliation
Campaign finance records reveal that 11 lawyers are Democratic donors
OK … what are the odds that this just happened by random chance? I mean, it could be just an unfortunate or fortunate happenstance, depending on your political leanings.
Now, to calculate the odds, we have to look at the underlying populations in the places where these folks come from. Most of them seem to be from New York, so let’s look at New York voters. By registration, 49.4% of the New York voters are Democrats, 23.9% are Republicans, and the rest are either independents or decline to state.
So … if we pull sixteen people from that pool, what are the odds that thirteen of them will be Democrats? You can do this in Excel, using the following formula:
=BINOM.DIST(successes, trials, probability, cumulative)
The name of the Excel function,”BINOM.DIST”, indicates we’re calculating what is called a “binomial” (two-sided) distribution. In this case, the two sides are Democrats vs. non-Democrats. The “cumulative” in this formula means it will return the odds of getting thirteen or fewer Democrats out of sixteen Mueller lawyers … so we set that to “FALSE” meaning we just want the odds of exactly 13 Democratic lawyers.
“Successes” means the number of Democratic lawyers, thirteen. “Trials” means the total number of Mueller’s lawyers, sixteen. And “Probability” is the chance that a random person from New York is a Democrat, which is 49.4%. So our final Excel formula is:
=BINOM.DIST(13, 16, .493, FALSE)
That returns the value of 0.007 … meaning that the odds are one thousand to seven AGAINST it being a random occurrence …
However, to be fair, we probably ought to include the odds of there being thirteen or more Democratic lawyers in the bunch … and when we do that we find that the odds jump up to one thousand to nine AGAINST there being thirteen or more Democratic lawyers on Mueller’s team.
Also, to be fair we should do a “sensitivity analysis” to allow for the fact that in New York, Democratic lawyers may be more than about half of the population of all New York lawyers. So let’s see what happens if we assume that they are say sixty percent of the population.
In that case, the odds go up to a whopping one hundred to six AGAINST the idea that it’s just by chance that Mueller’s team would have thirteen or more Democratic lawyers out of sixteen … not a bet I’d care to take.
So I fear that as a mathematician of very little brain, I’d have to say that Mueller has most definitely stacked the deck.
Glorious sunshine here today, the ocean is visible in the far distance, the world is good … and as always, the homestead requires work, so I’m headed outdoors to grab a pick and a shovel and continue digging back the hillside where it’s slumping into the house. Hey, I figure, why should illegal immigrants have all the fun?
Best of this life to you all,
“When you are a Bear of Very Little Brain, and you Think of Things, you find sometimes that a Thing which seemed very Thingish inside you is quite different when it gets out into the open and has other people looking at it.”
A. A. Milne, “Winnie-The-Pooh”