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More on Brier Scores: A Brief on Brier Scores | University of Virginia Library Research Data Services + Sciences, Brier score - Wikipedia, among others.

Additional Notes:

  • I’ve been asked about what happens when there’s a third party. There’s a general multi-category version of the Brier Score that allows for >2 outcomes. There’s a nice section in the first link above. I may put a mafia example in writing in this post in the future, for now here’s a screenshot of it from the article mentioned.

  • Again in reference to considering >2 possible alignments, there’s also the more straightforward solution of just having your probabilities consider town vs. not town, then you can use the simpler formulation.

  • A follow up math question that came up when I was discussing Brier Scores with a friend was “Why square? What happens when you use absolute value instead as a way of forcing non-negativity”. There’s a decent answer to this question, but it’s something that could be fun to think about on your own for a bit. Do message me if you have thoughts or just want to know why. It’s fairly interesting.


I’d be down to “compete with a friend” for some game I’m spectating here.

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There’s no competition when the foe is dan the action man

I’ll interpret that to be in my favor


That’s the only possible interpretation

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What else could it have meant dan

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You’re right there was no other way to read that, my apologies.


Edited in a couple of notes on multi-category Brier Scores (for games with more than 2 alignments) and an interesting math question about why Brier Scores are formulated the way it is.

wait wait wait

It’s pronounced “ell-EE-ber-ETH”?

I have for literal years been saying it like “ellie-bear-eth”

mind blown


I was about to ask about this and I think this is what I’d do

Could we count hypothetical town-sided third party roles as town?

Is it the fact that large outliers will have a larger impact than smaller ones?