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More Math about the Meta


I’ve been wondering for a while what the effect of using a Fantasy Strike-style randomized stable might do to the overall Yomi meta. So, I did some math!

The crux of my analysis was to use all of the historical tournament data (thank you, @mysticjuicer), and build out violin charts for each of the characters based on their matchups. This shows the spread of each characters matchup numbers, and the number of matchups at each part of the range.


As expected, we see the big three at the top (sorted by average matchup number). You can also see how Zane has the bulk of his matchups up at around 6-4, with a tail of matchups down to 4-6.

The next step was to figure out, based on two teams of characters, what the expected outcome of a Fantasy Strike-style stable game would be. (As a reminder, for each match in a set, a random character is picked for each side. The winning character is removed for the set, and the losing character is set aside until all other characters have been played). With a function to compute that in hand, I computed all 1.29M matchups between 3-character teams, and again plotted the violin chart.

It turns out, the full image with all ~1K teams on it is too big for the forums, so here are the top and bottom teams (again, ordered by average MU rating).

The big takeaway here is that you can’t escape The Meta. I was hoping the randomization might lead to some unusual teams, but just using the Big 3 means you end up with a team that only has ~10 MUs that are worse than 5-5, and their worst MU is 4.5-5.5.

So, the Fantasy Strike match play isn’t a silver bullet out of character dominance, sadly.


Jaina plays the world’s tiniest :violin:.


What’s the best team against specifically Troq/Zane/Geiger?


I looked it up, but don’t recall off the top of my head.

This question has prompted me to try and find the Nash Equilibrium for both single-character tournaments (the easy case) and for 3-character teams (the case that’s going to melt my CPU for a while). More math to follow when I have time.


Well, I wasn’t able to find a Nash for the team setup (needs more time, or a faster algorithm).

Geiger/Troq/Zane is beaten by Oni/Rook/Troq 51.3% of the time (and that’s the best response!)


Rook is meta boiz


Interesting! I guess the benefit of having 3 positive match-ups against Zane is more important than having a better match-up against Troq (by subbing in Midori for Rook, for example). Hmm.