Is the Police Baton Useful in Self-Defense? How to make Risk Assessment with Statistics

I was watching a self-defense channel these days, and I ended up seeing this video:

And I thought "what a great opportunity to explain how statistically based decision-making works"!

In this case "statistics" is being misused.

The dude in the video is talking about how if 99% of the time a baton isn't useful, it shouldn't be used. This is not a good use of statistics. We must take into account the outcomes of the decision, not just the probability of the outcomes occurring.

Carrying a baton vs not carrying one means having an advantage in a real fight vs not having it.

Worst case scenario, if you don't have an advantage, you lose, and you DIE.

Worst case scenario, if you do have an advantage, you win, and you get arrested.

Notice how I didn't talk about the first worst-case scenario twice, if you do have an advantage and you die, you were no better than the first case, an advantage bought you nothing.

Now, even if you have only a 1% chance of increasing your odds, that is what you should do. It makes you less Fragile, or less Concave in your exposure to risk.

By this dude's same logic, nuclear reactors only blow up 1% of the time, so why even try to increase security measures? The answer is, it's not the percentage of the possibility of failure that counts, but the actual impact if it does happen.

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