zslastman comments on 0 And 1 Are Not Probabilities - Less Wrong
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"When you work in log odds, the distance between any two degrees of uncertainty equals the amount of evidence you would need to go from one to the other. That is, the log odds gives us a natural measure of spacing among degrees of confidence."
That observation is so useful and intuition friendly it probably deserves it's own blog post, and a prominent place in your book.