[adammcnamara]

It's called the Elo Rating System (http://en.wikipedia.org/wiki/Elo_rating_system).

From the article, it's used to rank the relative skill of two players. It was created for chess, but I believe underpins most competitive ranking today including Xbox LIVE.

[kersny]

This is correct, and the equations in the movie were very much real. I thought it was funnily obvious when he called it "The algorithm for rating chess players", knowing what ELO was.

Here's "The Algorithm": http://imgur.com/e5myT

EDIT: In the intrest in contribution to discussion, two other methods for ranking are the Colley matrix from the BCS (http://www.colleyrankings.com/method.html) and I have used PageRank for a similar purpose before (http://michaelnielsen.org/blog/lectures-on-the-google-techno...).

[carbocation]

Nitpick: it's "Elo" because it's a man's last name, not an acronym.

Also, the Colley matrix homepage has this odd bit of text:

Please note: This method is copyright.

That's not how you protect algorithms.

[kersny]

Ah, yes, my mistake. And I wonder how that copyright works... it seems as though these guys: http://digital.ipcprintservices.com/publication/?i=34502&... used the method for their project, although I don't think they made any money off of it. That article also describes Colley's matrix very well.

[brendano]

MSR developed a (Bayesian) enhancement to Elo that apparently is used by XBox Live: http://research.microsoft.com/en-us/projects/trueskill/

[iampims]

The most comprehensive article on the subject, as far as I know: http://www.moserware.com/2010/03/computing-your-skill.html

[endtime]

Blizzard uses it for WoW and Starcraft II as well.