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Tiny documentation error with explanation of beta parameter #11
The documentation describes beta as "the distance which guarantees about 75.6% chance of winning". I think the correct percentage should be 76.025% (rounded however you wish). While the difference is trivial, it might confuse other people.
I was curious where the 75.6 magic number came from so derived what it should be, using the formula for computing win probability (mentioned in another issue). If you consider a match of two players, with the player sigmas and draw margins being 0, and the difference in rating means equal to beta, the win probability simplifies to cdf(1/sqrt(2)), which is about 0.76025.
I think there's a mistake in that simplification:
I would probably describe beta as "the distance which guarantees about 76% (specifically Φ(1/√2)) chance of winning".
Also, thanks so much for your work on this project. When I discovered the TrueSkill site/papers I was excited to use it but the thought of implementing it from scratch made my heart sink a little :)