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Tiny documentation error with explanation of beta parameter#11

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opened this issue Dec 29, 2015 · 5 comments
Closed

Tiny documentation error with explanation of beta parameter #11

opened this issue Dec 29, 2015 · 5 comments

rsimmons commented Dec 29, 2015

 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. The text was updated successfully, but these errors were encountered:

sublee commented Dec 30, 2015

 Thank you for the report. I agree on your opinion. Should we describe Beta as `76.025% (Φ(1/√2))`? Or `approximately 80%`? Which do you prefer?

sublee commented Dec 30, 2015

 Which win probability formula you used? If you used the last one, should the simple formula be `Φ(1/√(2β))` instead of `Φ(1/√2)`? ``````Φ(delta of μ÷√(players×β²＋sum of σ)) → Φ(β÷√(2β²＋0)) → Φ(1÷√(2β)) ``````

rsimmons commented Dec 30, 2015

 I think there's a mistake in that simplification: `Φ(β÷√(2β²＋0))` has `√(2β²)` in the inside denominator, which simplifies to `β√2`, so we get `Φ(β÷(β√2)) → Φ(1/√2)`. 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 :)

sublee commented Dec 30, 2015

 Oh, you're right. I had a mistake. Thank you for letting me know. Would you give me a pull request to add you to the contributor list? If you don't care about the contributor list, I'll update the document myself.

mentioned this issue Dec 30, 2015
closed this as completed Dec 31, 2015

sublee commented Dec 31, 2015

 I released TrueSkill-0.4.4 with your patch. http://trueskill.org/#version-0-4-4