I wrote this library: https://www.npmjs.com/package/openskill

It's open-license, handles complex matchups (e.g. 5 vs. 3 vs. 4), comparable in predictive accuracy, and is up to 20x faster than TrueSkill. The implementation is also much simpler.

This is excellent. I love how simple the API is.

They can't patent the general idea, so just base something off the information in the Wikipedia article. At time of writing, I don't think doing that would infringe their patent.

Is your project non-commercial? You can use this[1] official bsd-licensed[2] library for non-commercial projects.

[1] https://trueskill.org/

[2] https://github.com/sublee/trueskill/blob/master/LICENSE

If it's BSD licensed, how do they limit it to non-commercial use?

BSD doesn’t have a patent grant, so it would still be protected by patent, even if there’s no copyright restriction on commercial entities using the code.

Glicko

Glicko (1 and 2) don't handle complex matchups well (as in, anything that's not 1v1). Trueskill was specifically designed to extend the Bayesian concept of Glicko in a more general way which allowed this type of use-case.