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### Tuesday, March 24, 2020

#### Projection Hindsight Is 20/20 and It’s Totally Awesome

One of the things you have to get used to when you work with projections is being wrong. Like, All. Of. The. Time. While I’d like to believe that the projections are accurate and it’s just real life that mucked things up, that isn’t quite how they work. There are always events you didn’t see coming, assumptions you made erroneously, and just plain old irreducible error, all of which are going to thwart you.

On a basic level, you’re supposed to be wrong. Imagine a world in which you knew, for an exact fact, that every team was a coin flip to win every game. With this perfect knowledge, you’d still expect nearly a quarter of the league to win either 73 games or fewer, or 89 games or more, through nothing but luck. For the math-inclined, this is a hypergeometric distribution, not a binomial one; the coin flips are not independent because the win totals will still add up to 2,430 and one team’s win invariably is another team’s loss. Here’s a quick table for some of the win totals, showing the probability of a team winning exactly X games and how many of the teams you’d expect to have won up to X games:

....

As an example, you’d expect 3.4% of those coin flip teams to win exactly 74 games, with 15% of all teams winning up to 74 games.

But we don’t have anywhere near perfect knowledge about how good a team will be. We’re not even in the same zip code as “near perfect”; we just hope to be on the right continent. As a result, our error bars are going to be significantly larger than even the rather erroneous results you still get with omniscient projections.

One of the best courses I ever took in college was a one-off course concerning Predicting The Future- as a result, this sort of consideration is of deep interest to me.

QLE Posted: March 24, 2020 at 12:52 AM | 4 comment(s)
Beats: dan szymborski, projections, where did we go wrong

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