The Mythic Limited Rating Problem


Thanks to @twoduckcubed for reading my previous work and being familiar enough with high-end limited winrates to see that there was likely to be a real problem here, and there is.  If you haven’t read my previous work, it’s at One last rating update and Inside the MTG: Arena Rating System, but as long as you know anything at all about any MMR system, this post is intended to be readable by itself.

Mythic MMR starts from scratch each month and each player is assigned a Mythic MMR when they first make Mythic that month.  Most people start at the initial cap, 1650, and a few start a bit below that.  It takes losing an awful lot to be assigned an initial rating very far below that, and since losing a bunch of limited matches costs resources (while doing it in ranked constructed is basically free), it’s mostly 1650 or close.  When two people with a Mythic rating play in Premier or Quick, it’s approximately an Elo system with a K value of 20.4, and the matches are zero-sum.  When one player wins points, the other player loses exactly the same number of points.

Most games that Mythic limited players play aren’t against other Mythics though.  Diamonds are the most common opponents, with significant numbers of games against Platinums as well (and a handful against Gold/Silver/Bronze).  In this case, since the non-Mythic opponents literally don’t have a Mythic MMR to plug into the Elo formula, Arena, in a decision that’s utterly incomprehensible on multiple levels, rates all of these matches exactly the same regardless of the Mythic’s rating or the non-Mythic’s rank or match history.  +7.4 points for a win and -13 points for a loss, and this is *not* zero-sum because the non-Mythic doesn’t have a Mythic rating yet.  The points are simply created out of nothing or lost to the void.

+7.4 for a win and -13 for a loss means that the Mythics need to win 13/(13+7.4) = 63.7% of the time against non-Mythics to break even.   And, well, thanks to the 17lands data dumps, I found that they won 58.3% in SNC and 59.4% in NEO (VOW and MID didn’t seem to have opponent rank data available).  Nowhere close to breakeven.  ~57% vs. Diamonds and ~63% vs Plats.  Not even breakeven playing down two ranks.  And this is already a favorable sample for multiple reasons.  It’s 17lands users, who are above average Mythics (their Mythic-Mythic winrate is 52.4%).  It’s also a game-averaged sample instead of a player-averaged sample, and better players play more games on average in Mythic because they get there faster and have more resources to keep paying entry fees with.

Because of this, to a reasonable approximation, every time a Mythic Limited player hits the play button, 1 MMR vanishes into the void.  And since 1% of Mythic in limited is only ~16.5 MMR, 1% Mythic in expectation is lost every 2-3 drafts just for playing.  The more they play, the more MMR they lose into the void.  The very best players- those who can win 5% more than the average 17lands-using Mythic drafter- can outrun this and profit from playing lower ranks- but the vast majority can’t, hence the video at the top of the post.  Instead of Mythic MMR being a zero-sum game, it’s like gambling against a house edge, and playing at all is clearly disincentivized for most people.

Obviously this whole implementation is just profoundly flawed and needs to be fixed.  The 17lands data is anonymized, so I don’t know how many Mythic-Mythic games appeared from both sides, so I don’t know exactly what percentage of a Mythic’s games are against each level, but it’s something like 51% against Diamond, 29% against Mythic 19% against Plat, 1% Gold and below.  Clearly games vs Diamonds need to be handled responsibly, and games vs. Golds and below don’t matter much.

A simple fix that keeps most of the system intact (which may not be the best idea, but hey, at least it’s progress) is to assign the initial Mythic MMR upon making Platinum (instead of Mythic) and to not Mythic-rate any games involving a Gold or below.  You wouldn’t get leaderboard position or anything until actually making Mythic, but the rating would be there behind the scenes doing its thing and this silliness would be avoided since all the rated games would be zero-sum and all the Diamond opponents would be reasonably rated for quality after playing enough games to get out of Plat.

Constructed has the same implementation, but it’s mostly not as big a deal because outside of Alchemy, cross-rank pairing isn’t very common except at the beginning of the month, and even if top-1200 quality players are getting scammed out of points by lower ranks at the start of the month (and they may well not be), they have all the time in the world to reequilibrate their rating against a ~100% Mythic opponent lineup later.  Drafters play against bunches of non-Mythics throughout.  Cross-rank pairing in Alchemy ranked may be/become enough of a problem to warrant a similar fix (although likely for the opposite reason, farming lower ranks instead of losing points to them), and it’s not like assigning the initial Mythic rating upon reaching Diamond and ignoring games against lower ranks actually hurts anything there either.

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