Win probability for N:M case

[romovpa]

I've implemented win probability function for the special case when one team plays versus another and exactly one team wins. This case occurs frequently in my practice, I want to use those function out of the box.

The formula is proposed to me by @AVSirotkin (co-author of trueskill modifications), but it also mentioned in #1 here. Unfortunately, I cant give detailed explanation of the math behind this formula.

Usage

import trueskill

r1 = trueskill.Rating()
r2 = trueskill.Rating()

trueskill.probability_1vs1(r1, r2)  # 0.5000000150000002

r1, r2 = trueskill.rate_1vs1(r1, r2)

trueskill.probability_1vs1(r1, r2)  # 0.7732314666870078
trueskill.probability_1vs1(r2, r1) + trueskill.probability_1vs1(r1, r2)  # 1.0

trueskill.probability_NvsM((r1, r1, r1), (r2, r2, r2))  # 0.9028951782988498
trueskill.probability_NvsM((r1, r1, r1), (r1, r2, r2))  # 0.8066134315889564
trueskill.probability_NvsM((r2,), (r1, r2))  # 0.020365869935275418

[coveralls]

Coverage decreased (-1.2%) to 91.049% when pulling 1d6a204 on romovpa:master into ba42122 on sublee:master.

[coveralls]

Coverage increased (+0.1%) to 92.327% when pulling 797bdb2 on romovpa:master into ba42122 on sublee:master.

[sublee]

Thank you for the patch. But I don't think that the win probability can be a part of the TrueSkill library.

Here're the reasons:

• All other parts of this library implement only the original TrueSkill™ spec. They have been proven by Microsoft Research. But the win probability has not.
• Every TrueSkill functions should work well with any types of matches, not only 2 teams.
• In my opinion, people can find the win probability formula easily. Even though we don't provide it by ourselves.

But that's true, #1 is the most common issue on this project. So I suggest you write some note in the documentation instead of providing a code.

[Tjorriemorrie]

I would like to remark on some of those points:

3 that's not necessarily true, it took me a long time to find this, especially since I'm not familiar with stats at all, which means I'm not even sure what I'm looking for.

1 I would suggest that this is moved to an extras module. I agree it should be out of the main module, but excluding it is a bit too strict. This is also not the official TrueSkill repo. And making extra features available is what I like of python being batteries included.

2 Yes, I'm specifically looking for FFA. Currently I'm looping through every player and making two teams with the one player filling up the first team and the rest in the second team. I don't even know if that works :p

[sublee]

Algorithms in this library are all proved by the TrueSkill™ paper. But in case of a win probability function, there's no reliable reference.

I designed this library's responsibility to be limited in only TrueSkill™. If this library provides more than that by extras module, the responsibility will be expanded unexpectedly. So I reject providing batteries for TrueSkill™.

I agree with you it's not enough easy to find that the win probability function. At this point, I think a documentation about that can be enough to help people although it's not a battery.

[romovpa]

[sublee]

Don't be discouraged. Your suggestion was reasonable. Keep your passion for the Open Source culture. 👍

[lukebyrne]

@romovpa Do you have a function to calculate win probability as per this question