Serial Correlation: Patriots Win

The Patriots (that’s my team) beat the Falcons, Tom Brady is the GOAT, Bill Belichick is the GOAT.

How could this have happened?

ESPN’s model had the Patriots as having 0.3% chance of winning at one point, at <1% at more than 20 points.

However, ESPN’s model and many others aren’t properly factoring in serial correlation. Or at least I doubt it, I don’t actually know the inner workings of the model, other than that they use other games in similar situations to project the results.

Serial correlation is essentially the momentum effect. The application in football is thus: it’s unusual for equally matched teams to be separated by a lot of points early in a game, but because it’s a high variance sport, that can happen whether the teams are equally matched or whether one team or the other is superior.

Once one of the teams begins a comeback, if they are actually better than their opponent, they’ll be much more likely than statistics based on other similar games would show to finish the comeback. And there’s a snowball effect, if a team comes back from down 10, they’re likely to be better than their opponent, so more likely to be able to come back from down 14.

That’s because all of the actions the Patriots had to take to come back are related to each other, they’re all team A vs team B, but a sample of similar games played by various teams is going to include more closely matched teams or outmatched teams. But once team A has come back vs team B, it’s more likely that team A is actually beating team B, and will continue to do so. The probabilities have fat tails.

Anatomy of Missing the Point

The entire election and what appears to be at least the next four years have/will be dominated by the same two halves of the country talking past each other in a way that neither of them quite understand.

Let’s use a hypothetical to illustrate the point.

Let’s say the POTUS, a Democrat, were to make a statement comparing the United States to a steaming pile of shit, and assume for the sake of argument, we all agree that’s pejorative.

Now, that President’s detractors, Republicans, are going to say, “whoa whoa whoa, that is simply un-American, and perhaps not true”. Democrats support their leader and point out that while it might be hyperbole, there are certainly things that could be better.

Now the next POTUS, a Republican, makes a statement comparing the United States to Russia, and assume for the sake of argument, we all agree that’s pejorative.

It might not seem like it, but the conditions are in place for a total meltdown of the brains of both sides.

Now the Democrats say, “whoa whoa whoa, you told us that was un-American! Also, that’s un-American!”. The Republicans respond, “It wasn’t so un-American last time, it was an accurate representation of the facts, you have changed your mind to suit the narrative”.

Both sides have now made both arguments, but more importantly, they’re now making the argument that the other side has played both sides of the coin and is either a) now wrong or b) inconsistent and therefore idiotic/puppets of their party. Neither side considers door c) which is of course that the other party is now correct and was incorrect before (and that their idiocy isn’t an unforgivable sin which makes them wrong even when they are right).

We are now stuck in a loop. Welcome to the next four years.