LOL. Sorry. Here it is in less mathy / fraternity terms:

The ranking system used by Microsoft assigns a Skill Level to every player, which fluctuates up and down as he plays games, but eventually settles within a narrow range. For example, after 30 games, I might be on average a Level 30 AGOT player, and you might be a Level 20 AGOT player.

However, because we are playing in different metas, my Level 30 can't be compared to your Level 20. You may actually be better than me, but because your meta has more highly-skilled players than mine, you don't win as often as I do.

So far, that's pretty obvious intuitively. Here's where it gets interesting: If I travel to your area and you whomp me several games in a row, the system adjusts: For example, I might change into a Level 23, while you might become a Level 25. (Behind the scenes, the system will also adjust another figure that shows the uncertainty of the previous calculations; that's what thebraz was writing about, but I'll ignore that for now.)

However, now my Skill Level can't really be compared to my old meta anymore either. Pretend that before my trip, my brother had a Skill Level of 26. But after the trip, my Level has dropped to 23, while his is unchanged. Now I appear to be a worse player than he is, which would be galling....

Furthermore, your new Level 25 can't really be compared to your old meta anymore either, for the same reason.

With time, if we each continue to play exclusively within our metas, our Skill Levels will return to a new equilibrium. But then they won't be comparable to each other anymore, once again.

Why is this important? It's not, really. As thebraz pointed out, every ranking system has similar problems if there's not a lot of "inter-league play." It's really only important as a warning not to take rankings too seriously -- a warning which I think most people in these forums don't need.

(Oh, yes: It may also be relevant to Sithlord's decision on how much time he wants to spend managing the ranking system. That was actually my original motive for joining the conversation.)

Can you weight the inter-meta events, read regionals and worlds. Maybe make those games worth double. Those events would be the ones which would give the best idea of where people lie skill level wise across the board. The other question is if in the above example entire meta scores could be altered by the loss of their top players against people outside of their metas. If John is lvl 30 in the Littlestfinger Meta and Quinn is lvl 20 in the Orphans of the Green Bay, and Quinn beats John 2 out of 3 games would the people who John dominated in his meta go down also and will those who dminate Quinn go up?

As mentioned, the information from the inter-meta play *does* carry back to the home meta and the equilibrium reached (if there is one) is not the same, but it is *closer* to a true comparison than before. This is an incredible gain on ELO.

dormouse said:

A real statistician could perhaps apply a weighting system to give more weight to inter-meta matches.... maybe. To be honest, I don't know whether that can be done in a statistically sound way.

I have to give the same answer to your second question, about using the results of John vs. Quinn to adjust the weighting of entire metas. This one I think is at least theoretically possible, but the plug-in-the-numbers tool on Microsoft's web site can't do it, so it would require a real statistician.

thebraz said:

Thebraz made a good point here. When John and Quinn go back to their home metas and play more matches, John will drag the scores on the Littlefinger Meta down, and Quinn will drag the scores on the Orphans Meta up. So indirectly, even without a statistician, some inter-meta adjustment will occur.

The real question is, how much inter-meta play is necessary to calibrate the various metas with each other naturally? My intuition says "a fair amount," but that's no more than a guess. Furthermore, it's possible that the cross-fertilization can depend on something other than volume. There's a great book called "The Tipping Point," that talks about the power of Connectors (people with many connections). Applying the ideas in that book to this problem, I would guess that the metas could theoretically synchronize quickly through the power of a single person who connects regularly to multiple Metas (through travel or Internet play) -- if such a Connector existed.