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making probabilistic predictions, continued

There’s a post about the NFL predictions game that I had my students try here. Although they were making predictions every week, I didn’t integrate it into the class at all. (I considered having them figure out how the scores were determined and then discussing it in class–using scaled Brier scores, which is kind of interesting. But I decided there wasn’t time.) I did, however, send the email below after they had been making predictions for a few weeks.

What made me think of sending the email was seeing that a student had predicted that some team had a 100 percent chance of winning (and they lost). As a gamble, selecting 100 percent might be worthwhile sometimes, but, since it is an inductive inference, there can actually be a 100 percent chance of anything happening. I don’t think that I mentioned to that student or the class how I got the idea for the email, but another student said that she found thinking of each prediction as an argument helpful. (I was a little skeptical that it could be that helpful, but she did crush it the weekend that I sent the email.)

 

Class,

First, don’t forget to make your NFL predictions. Now that you’ve been doing them for a few weeks, let me point out that, for each one, you’re basically creating an argument. For instance, the first game tomorrow is Minnesota versus Cleveland. Depending on what information you have, you might have different premises. But one simple argument goes like this:

[P1] After weeks 1 – 7 of the 2017 season, the Minnesota Vikings’ record is 5 wins and 2 losses.

[P2] After weeks 1 – 7 of the 2017 season, the Cleveland Browns’ record is 0 wins and 7 losses.

[P3] In week 8 of the 2017 season, the Minnesota Vikings and the Cleveland Browns are playing each other.

[C] Therefore, the Minnesota Vikings will win.

Or you could have this conclusion: Therefore, the Cleveland Browns will win. But after you’ve settled on a conclusion (i.e., selected a team that you think will win), you have to determine how likely the conclusion is. That’s the probability that you’re picking. The higher the probability, the stronger the argument. Then, after the game is over, you get scored on how well you estimated that probability.

No matter what, though, it’s an invalid argument, so the conclusion can’t (or shouldn’t) be 100 percent. (For a valid argument, if the premises are true, then there is a 100 percent chance that the conclusion is true. But these are not valid arguments.)