Guild Wars 2

I really don’t understand how Glicko ratings work, how they’re calculated, and how upsets affect scoring. So if any maths experts are out there, hypothetically, what would happen if a #4 rated team beat the #1 team with technically a 250 points difference? I wonder because Anet manually adjusted the ratings, so I’m confused with how artificial increases factor into the overall calculations.

The #4 team gains a larger amount of glicko from the #1 team. In order for the #1 team to gain anything they’re expected to win by a certain amount, but that clearly isn’t happening. Adjustments aside, #1 is currently losing to #4.

https://en.wikipedia.org/wiki/Glicko_rating_system#Step_2:_Determine_New_Rating

A formula guaranteed to give non-mathematician and non-engineers nightmares.

The fact that the servers are #1 and #4 doesn’t directly matter to Glicko at all. What’s important is that the #1 server has a rating of 2036.4021, and the #4 server has a rating of 1921.0294.

The way Glicko works, the difference in ratings is used to establish an expectation. Because the servers are over 100 points apart, Glicko expects the higher-rated server to win by a significant amount. If the servers were only 5 points apart, Glicko would still expect the higher-rated server to win, but not by a large margin.

If a server does better than their rating would predict, they gain points. If they do much better they gain more points. If a server does worse than predicted, they lose points. This can happen even if the server wins, if they win by less of a margin than was expected.

This week, the #1 server is expected (by Glicko) to beat the #4 server by a lot. Instead what has happened is the #4 server is winning (not a blowout, but they are solidly ahead). So #1 is going to lose rating points (26 points or so), and #4 is going to gain rating points (32 or so).

These rating changes are not going to be enough to change the rankings (#4 will stay #4, and #1 will stay #1) because Glicko knows that even good players or servers can have a bad game sometimes. So ratings will change, but in order to change enough to switch places in the rankings #4 has to do consistently better in multiple matches (and #1 has to do consistently worse in multiple matches).

If #1 and #4 get matched up again next week, the rating difference will probably be only around 50 points. So Glicko will still expect #1 to win, but not by as much (Glicko will expect it to be a closer game). If #4 wins again, by the same amount, #4 will gain rating points again (but not as many as this week) and #1 will lose some. The amount gained/lost will be fewer than this week because the ratings are closer together, so even though #4 would still be expected to lose, a win next week would be “less unexpected” than this week’s win was.

-ken