Ten-Minute Talks: Thinking Probabilistically

This semester, I’ve been taking a class in Applied Probability. It’s a graduate level course for the ORIE department here At UT, so it’s a bit more rigorous than the typical probability and stats course taken by engineers.

One of the first things we did was discuss predictions for the 2016 election, looking at models that predicted some probability of Trump or Hillary winning. Of course, most of these models predicted, with a lot of confidence, that Hillary would win.

So were those models bad? My immediate intuition was to say yes. I mean, they said Hillary would win!

But if we’re being rigorous, the model doesn’t spit out a binary “Hillary” or “Trump” result. It gives a probability. So maybe the model is “good,” but we’re playing in that 10% range where Trump wins.

This pattern’s repeated itself pretty often through the semester.

A first example: a friend of mine was on an intramural soccer team. In the elimination bracket, they landed opposite the best team in the competition; if they played it would be in the finals. My friend wasn’t happy about this. He wanted to get that game out of the way, since they were going to have to play them in the finals anyway (like I said, that other team was the highest seed). But I realized there’s more to it. Every game is like rolling the dice; you have some probability of winning but there’s no guarantee. Don’t get me wrong, having the best team in the competition on the other side is advantageous because it increases your chance of winning. But even if that team had a 75% chance of winning each game (arguably a pretty one-sided probability when it comes to intramurals), their chance of getting to the finals (winning 3 in a row) was just 42%.

I see the same thing now that I’m applying to graduate school. It’s tempting to think there’s a “dream school” that I’m just destined to go to. They’ll read my application, rush to accept me, and I’ll wonder why I ever applied anywhere else.

But, of course, it doesn’t work that way. Many students get multiple admission offers, and most programs accept more people than end up attending. Every application I send out is like rolling a set of dice. Having a strong application improves my odds of a good roll, but doesn’t guarantee it. So instead, I’ve opted to just roll the dice a bunch of times, casting a wide net of applications.

My wallet will have to learn to forgive me for these application fees.

Each week, I meet with 7 other people. Each of us has committed to the time we chose, but, we just about alternate between having everybody and not. At first I was irked, but then I thought about probability. Let’s say we each show up 90% of the time. The chance of all of us being there on any given week is only 42%.

Growing up in Houston, I’ve had plenty of with brisk driving. Sometimes it’s other people, other times it’s me (sorry Mom). But 5 mph faster or slower, running a yellow, or cutting in front of someone going slow hardly makes a difference; I almost always end up at the red lights with people I’d been passing just a minute before.

This isn’t a normative post. I’m not trying to convince you to change your behavior (I still drive “briskly"). Consider this post an invitation to think less in binary. Even if your life doesn’t make an enormous change, it’s interesting to see how shallow our immediate intuitions can be.