Weighing in on Our National Pastime

Where have you gone, Joe DiMaggio?

While we Americans constantly spend a crazy amount of time reveling in thoughts of our great national hobby, we only get to actually engage with it once every four years.

Of course I’m talking about Presidential elections.

This is such a year, yay.

But who will emerge from the semifinals to meet up in the championship game?

Let’s make some predictions!

But first, here is what has me thinking about this. The talk this week has been about additional evidence that Biden is perhaps unfit for office. The special counsel appointed to investigate Biden’s improper possession of classified documents supported his case that charges should not be brought in part by citing memory failings and other “fuzzy” thoughts. Biden then doubled down on the problem by making a gaffe when attempting to defend himself.

I have been ruminating with a theory that Gavin Newsome will be the eventual Democratic nominee. But there are other contenders. Perhaps this is all just wishful thinking. Alas, there doesn’t seem to be a lot of hope we get fresh blood.

As likely as it seems that we will get Biden vs. Trump II, there are many reasons why we might not. These guys are very old and quite unliked.

Further, Biden told us he wouldn’t be running if Trump were not running. The other side of this coin is I think if Trump so how drops out, the Democratic Party will beg, borrow, steal a way to replace Biden as the nominee.

With that background, allow me to get to my predictions as of this Super Bowl Sunday.

• Probability Biden is the Democratic nominee¹ on election day:

  • p(Biden) = 85%

• Probability Trump is the Republican nominee on election day:

  • p(Trump) = 90%

• Therefore, the implied probability Biden and Trump are the D & R contenders come election day:

  • p(Biden & Trump) = .85 * .90 = 76.5%²

• Which means the implied probability Biden and Trump are not the contenders:

  • p(~Biden & ~Trump) = .15 * .10 = 1.5%

• And the implied probability that Biden or Trump (which in logic means one or both) is out of the race by election day:

  • p((~Trump & Biden) or (Trump & ~Biden) or (~Trump & ~Biden)) =
    (.15 + .10) - (.15 * .10) = [1 - .765] = 23.5%

• Summarizing all of this in a 2 x 2 matrix yields:

I kind of like those odds given the dismal landscape otherwise. Which gets me thinking about some conditionals.

• Probability Biden is in/out of the race by election day assuming Trump is out:

  • p(Biden | ~Trump) = 20% :: p(~Biden | ~Trump) = 80%

• Probability Trump is in/out of the race by election day assuming Biden is out:

  • p(Trump | ~Biden) = 75% :: p(~Trump | ~Biden) = 25%

• So I think that of Biden’s 15% chance of being out of the race almost all of it (80%) comes with Trump also departing:

  • p((~Biden & ~Trump) | ~Trump) = .15 * .80 = 12% from a total of 15%

  • this has two elements: Trump’s exit causes Biden to exit and Biden exits independent of Trump even though Trump does exit

• And I think that of Trump’s 10% chance of being out of the race only a small fraction (25%) coincides with Biden departing:

  • p((~Trump & ~Biden) | ~Biden) = .10 * .25 = 2.5% from a total of 10%

  • this also has those same two elements just with the names switched

Note that I have only made four predictions. The rest are implications that mathematically result from them.

• p(Biden) = 85%

• p(Trump) = 90%

• p(~Biden | ~Trump) = 80%

• p(~Trump | ~Biden) = 25%

If you find yourself questioning these four predictions, I am glad. At least it got you thinking about it. But as you question, remember to have some base-effect guidance. If you think there is “no way it is not Trump vs. Biden”, consider how high those probabilities have to individually be for the joint probability to be extremely high.

If you want it to be 99% likely that it is T vs. B, that limits you to something like a 99.5% chance each are there at election day. Are you sure there is that high a chance for each of two elderly “gentlemen” to even be alive in about 9 months? What probability do you assign to health problems short of death? What about removal for cause (Biden from the presidency and Trump from enough ballots)?

Strange things can happen when the powers that be would rather things be different—no, I’m not talking about deep-state nefarious (murderous) activities. I am thinking power brokers in smoke-filled rooms finally reasserting themselves for the good of their party interest to cut deals that move people off the ballot.

It will be entertaining to watch as events develop to see how these probabilities will need to change. At least we can have fun watching the train wreck.

1. I am trying to be specific without having some technical loophole here. I mean the plain-English version of this guy is the guy who might get elected U.S. President in the 2024 election. I’m sure there are some technical differences between a nominee, person on the ballot, blah, blah. And not being on a few particular states’ ballots, a possibility I find fairly unlikely anyway, is not relevant here.

2. At first blush I wanted to make this something different (higher) thinking that the conditional probabilities explored in the next group in the post impacted the likelihood. They do not, but they do entail something about the implied conditional in the last bullet point.