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Evolutions in Understanding the Yomi Meta (or... Vengefulpickle Maths Again!)

Ok, I was inspired to do dumb things to try to convert a MU chart (from https://vengefulpickle.com/yomi-skill) into a tier list (in a principled way). A thought I had was: hey, if I had the Nash equilibrium of the opening blind pick, that might tell me something, right? The character that gets picked most is likely high-tier?

Turns out, @scymrian’s detective work/memory of the good-old-days brought up a similar thought experiment run by our man @deluks917, so I present both here for comparison.

First, @deluks917 based his analysis on the Princess Power MU chart.

PPMU
Arg BBB Degrey Geiger Gloria Grave Gwen Jaina Lump Mene Midori Oni Perse Quince Rook Sets Troq Val Ven Zane
Arg 5 6 5 4.5 3.5 6 5.5 6 6.5 5.5 5 7 4 4.5 5 4.5 4 4.5 4.5 4
BBB 4 5 4.5 4 4 4 4 4 3.5 4 6.5 4.5 6 5.5 6.5 4.5 5.5 4 5 4.5
Degrey 5 5.5 5 5 6 6 5.5 5.5 6 6 6 7 4.5 4 6 5 4.5 6 5.5 4
Geiger 5.5 6 5 5 5 4.5 4.5 6 5 4.5 7 5 4.5 7 6.5 4.5 6 5.5 4.5 4
Gloria 6.5 6 4 5 5 4.5 5.5 5.5 4 4.5 4.5 5.5 4 5.5 4.5 4 4 4 5.5 3.5
Grave 4 6 4 5.5 5.5 5 5.5 6 5.5 5.5 5.5 5 5.5 4.5 5.5 5.5 4.5 6 6 5.5
Gwen 4.5 6 4.5 5.5 4.5 4.5 5 5.5 4 5 4.5 4.5 6.5 4.5 5.5 4.5 4 4 6 4.5
Jaina 4 6 4.5 4 4.5 4 4.5 5 4 4.5 5.5 4.5 5.5 6 5.5 4.5 5.5 5.5 5 4
Lump 3.5 6.5 4 5 6 4.5 6 6 5 4.5 5.5 5.5 4.5 5.5 6 5.5 6 5 6.5 5
Mene 4.5 6 4 5.5 5.5 4.5 5 5.5 5.5 5 4 4.5 5.5 6 4 4.5 4 4 5 4
Midori 5 3.5 4 3 5.5 4.5 5.5 4.5 4.5 6 5 4 6 4 4.5 6 5.5 4.5 5 4
Oni 3 5.5 3 5 4.5 5 5.5 5.5 4.5 5.5 6 5 4.5 4 6 6 5.5 6 5 6
Perse 6 4 5.5 5.5 6 4.5 3.5 4.5 5.5 4.5 4 5.5 5 5.5 4.5 3.5 4 4 4.5 4
Quince 5.5 4.5 6 3 4.5 5.5 5.5 4 4.5 4 6 6 4.5 5 4.5 4.5 4.5 5 4.5 4
Rook 5 3.5 4 3.5 5.5 4.5 4.5 4.5 4 6 5.5 4 5.5 5.5 5 5.5 5 4.5 4 6
Setsuki 5.5 5.5 5 5.5 6 4.5 5.5 5.5 4.5 5.5 4 4 6.5 5.5 4.5 5 4 5 6 4.5
Troq 6 4.5 5.5 4 6 5.5 6 4.5 4 6 4.5 4.5 6 5.5 5 6 5 6 6 6.5
Val 5.5 6 4 4.5 6 4 6 4.5 5 6 5.5 4 6 5 5.5 5 4 5 6.5 5
Ven 5.5 5 4.5 5.5 4.5 4 4 5 3.5 5 5 5 5.5 5.5 6 4 4 3.5 5 4.5
Zane 6 5.5 6 6 6.5 4.5 5.5 6 5 6 6 4 6 6 4 5.5 3.5 5 5.5 5

Using that, he produced two interesting outcomes. First, a list of optimal counterpicks, depending on the match position (how many wins are still required by each player, and who is doing the counterpicking).

Optimal Counterpicks
char to CP 1 vs 1 1 vs 2 1 vs 3 2 vs 2 1 vs 4 2 vs 3 3 vs 2 2 vs 4 3 vs 3 (g1 bo5) 3 vs 4 4 vs 4 (g1 bo7)
Arg Gloria Troq Troq Gloria Troq Gloria Gloria Gloria Gloria Gloria Gloria
BBB Lump Geiger Geiger Lump Geiger Geiger Lump Geiger Geiger Geiger Geiger
Degrey Quince Troq Troq Zane Troq Zane Zane Degrey Zane Zane Zane
Geiger Zane Grave Grave Zane Grave Gwen Zane Gwen Zane Zane Zane
Gloria Zane Degrey Degrey Zane Degrey Degrey Zane Degrey Degrey Degrey Zane
Grave Arg Degrey Degrey Degrey Degrey Degrey Degrey Degrey Degrey Degrey Degrey
Gwen Lump Troq Troq Lump Troq Degrey Lump Degrey Degrey Degrey Troq
Jaina Arg Geiger Geiger Geiger Geiger Geiger Geiger Geiger Geiger Geiger Geiger
Lump Arg Degrey Degrey Arg Degrey Degrey Arg Degrey Degrey Degrey Arg
Mene Degrey Degrey Degrey Degrey Degrey Degrey Degrey Degrey Degrey Degrey Degrey
Midori Geiger Geiger Geiger Geiger Geiger Geiger Geiger Geiger Geiger Geiger Geiger
Oni Arg Degrey Degrey Degrey Degrey Degrey Degrey Degrey Degrey Degrey Degrey
Perse Gwen Gwen Gwen Gwen Gwen Gwen Gwen Gwen Sets Sets Sets
Quince Geiger Geiger Geiger Geiger Geiger Geiger Geiger Geiger Geiger Geiger Geiger
Rook Geiger Geiger Geiger Geiger Geiger Geiger Geiger Geiger Geiger Geiger Geiger
Setsuki Midori Troq Troq Troq Troq Troq Troq Troq Troq Troq Troq
Troq Geiger Geiger Geiger Geiger Geiger Geiger Geiger Geiger Geiger Geiger Geiger
Val Degrey Degrey Degrey Degrey Degrey Degrey Degrey Degrey Degrey Degrey Degrey
Ven Lump Val Val Lump Val Val Lump Val Lump Sets Sets
Zane Troq Troq Troq Troq Troq Troq Troq Troq Troq Troq Troq

Definition:

  • N vs M means the winner of the last game still has to win M games and the loser of the last game still has to win N. So 1 vs 2 gives the optimal cp in game2 of a bo3
  • The counterpicking player is the SECOND number
  • The algorinithm breaks ties by alphabetical order :slight_smile:
  • The results for N vs 1 are the same as 1 vs 1

And, the Nash-equilibrium (optimal mixed strategy) for the initial double-blind pick in a std-counterpick tournament.

Nash
Bo7 g1 Nash bo5 g1 nash bo3 g1 Nash
Arg 0 Arg 0 Arg 0
BBB 0 BBB 0 BBB 0
Degrey 0.07192 Degrey 0.07808 Degrey 0.15248
Geiger 0.29723 Geiger 0.34951 Geiger 0.367
Gloria 0 Gloria 0 Gloria 0
Grave 0.09454 Grave 0.12073 Grave 0.13853
Gwen 0 Gwen 0 Gwen 0
Jaina 0 Jaina 0 Jaina 0
Lump 0.04147 Lump 0 Lump 0
Mene 0 Mene 0 Mene 0
Midori 0 Midori 0 Midori 0
Oni 0 Oni 0 Oni 0
Perse 0 Perse 0 Perse 0
Quince 0 Quince 0 Quince 0
Rook 0 Rook 0 Rook 0
Setsuki 0.09471 Setsuki 0 Setsuki 0
Troq 0.17621 Troq 0.13513 Troq 0.13853
Val 0 Val 0 Val 0
Ven 0 Ven 0 Ven 0
Zane 0.22392 Zane 0.31655 Zane 0.20346

Now, my results for the same:

YS MU
Arg BBB DeGrey Geiger Gloria Grave Gwen Jaina Lum Menelker Midori Oni Pers Quince Rook Sets Troq Val Ven Zane
Argagarg 5.0 4.2 4.7 5.0 4.1 5.4 6.1 6.7 6.1 5.3 5.5 6.4 4.9 3.9 5.9 5.3 4.9 5.4 4.5 4.3
BBB 5.8 5.0 4.1 3.8 5.7 4.0 4.6 4.6 4.8 5.0 5.7 3.9 5.5 5.7 5.6 4.9 5.7 5.1 5.3 3.9
DeGrey 5.3 5.9 5.0 4.9 5.4 4.8 5.5 5.6 6.6 6.1 5.7 6.5 5.2 5.2 5.4 4.5 4.3 6.0 4.2 4.7
Geiger 5.0 6.2 5.1 5.0 5.6 4.2 4.9 6.7 5.1 4.5 5.8 5.4 4.7 5.7 5.3 5.3 5.5 5.6 4.5 4.2
Gloria 5.9 4.3 4.6 4.4 5.0 5.7 4.7 4.2 5.0 5.3 3.2 5.0 4.7 5.8 5.5 5.5 4.2 4.7 5.9 3.8
Grave 4.6 6.0 5.2 5.8 4.3 5.0 6.0 5.2 4.3 5.1 4.5 5.1 4.3 4.2 5.4 5.4 4.8 5.2 5.9 4.4
Gwen 3.9 5.4 4.5 5.1 5.3 4.0 5.0 5.4 3.6 5.4 4.6 4.1 5.7 5.9 4.5 5.5 3.6 5.5 5.1 4.5
Jaina 3.3 5.4 4.4 3.3 5.8 4.8 4.6 5.0 3.2 4.1 5.5 4.2 5.6 5.5 3.8 4.4 5.9 5.7 3.7 3.6
Lum 3.9 5.2 3.4 4.9 5.0 5.7 6.4 6.8 5.0 4.4 5.0 5.3 5.8 5.6 5.9 5.5 5.2 5.5 4.5 5.3
Menelker 4.7 5.0 3.9 5.5 4.7 4.9 4.6 5.9 5.6 5.0 5.0 3.9 5.0 5.2 4.5 4.4 4.5 5.1 5.3 4.2
Midori 4.5 4.3 4.3 4.2 6.8 5.5 5.4 4.5 5.0 5.0 5.0 4.8 5.3 5.9 5.8 5.2 5.0 5.3 5.3 4.5
Onimaru 3.6 6.1 3.5 4.6 5.0 4.9 5.9 5.8 4.7 6.1 5.2 5.0 5.6 4.6 5.3 5.7 6.3 5.8 5.6 5.4
Persephone 5.1 4.5 4.8 5.3 5.3 5.7 4.3 4.4 4.2 5.0 4.7 4.4 5.0 4.6 4.6 3.8 4.7 4.7 4.8 4.3
Quince 6.1 4.3 4.8 4.3 4.2 5.8 4.1 4.5 4.4 4.8 4.1 5.4 5.4 5.0 4.0 5.0 3.7 5.0 4.5 4.2
Rook 4.1 4.4 4.6 4.7 4.5 4.6 5.5 6.2 4.1 5.5 4.2 4.7 5.4 6.0 5.0 5.1 5.2 5.3 4.9 5.8
Setsuki 4.7 5.1 5.5 4.7 4.5 4.6 4.5 5.6 4.5 5.6 4.8 4.3 6.2 5.0 4.9 5.0 3.9 4.7 5.4 4.3
Troq 5.1 4.3 5.7 4.5 5.8 5.2 6.4 4.1 4.8 5.5 5.0 3.7 5.3 6.3 4.8 6.1 5.0 6.2 4.8 6.5
Valerie 4.6 4.9 4.0 4.4 5.3 4.8 4.5 4.3 4.5 4.9 4.7 4.2 5.3 5.0 4.7 5.3 3.8 5.0 6.2 4.9
Vendetta 5.5 4.7 5.8 5.5 4.1 4.1 4.9 6.3 5.5 4.7 4.7 4.4 5.2 5.5 5.1 4.6 5.2 3.8 5.0 4.7
Zane 5.7 6.1 5.3 5.8 6.2 5.6 5.5 6.4 4.7 5.8 5.5 4.6 5.7 5.8 4.2 5.7 3.5 5.1 5.3 5.0
Optimal Counterpicks
1-1 1-2 1-3 1-4 2-1 2-2 2-3 2-4 3-1 3-2 3-3 3-4 4-1 4-2 4-3 4-4
Argagarg Quince Quince DeGrey DeGrey Quince Quince Quince DeGrey Quince Quince Quince Quince Quince Quince Quince Quince
BBB Geiger Geiger Geiger Geiger Geiger DeGrey Grave Grave Geiger Zane Grave Grave Geiger Zane Grave Grave
DeGrey Vendetta Grave Grave Grave Vendetta Troq Troq Troq Vendetta Troq Troq Troq Vendetta Troq Troq Troq
Geiger Zane Grave Grave Grave Zane Grave Grave Grave Zane Grave Grave Grave Zane Zane Grave Grave
Gloria Midori Midori Midori Midori Midori Midori Midori Midori Midori Midori Midori Midori Midori Midori Midori Midori
Grave Quince Midori Midori Midori Quince Quince Midori Midori Quince Persephone Persephone Midori Quince Persephone Persephone Persephone
Gwen Troq Grave Grave Grave Troq Troq Troq Grave Troq Troq Troq Troq Troq Troq Troq Troq
Jaina Lum Geiger Geiger Geiger Lum Argagarg Argagarg Geiger Lum Argagarg Argagarg Argagarg Lum Argagarg Argagarg Argagarg
Lum DeGrey DeGrey DeGrey DeGrey DeGrey DeGrey DeGrey DeGrey DeGrey DeGrey DeGrey DeGrey DeGrey DeGrey DeGrey DeGrey
Menelker Onimaru DeGrey DeGrey DeGrey Onimaru DeGrey DeGrey DeGrey Onimaru DeGrey DeGrey DeGrey Onimaru DeGrey DeGrey DeGrey
Midori Geiger Geiger Geiger Geiger Geiger DeGrey DeGrey DeGrey Geiger DeGrey DeGrey DeGrey Geiger Geiger DeGrey Argagarg
Onimaru DeGrey DeGrey DeGrey DeGrey DeGrey DeGrey DeGrey DeGrey DeGrey DeGrey Argagarg Argagarg DeGrey DeGrey Argagarg Argagarg
Persephone Setsuki Setsuki Setsuki DeGrey Setsuki Setsuki Setsuki Setsuki Setsuki Setsuki Setsuki Setsuki Setsuki Setsuki Setsuki Setsuki
Quince Troq Midori Midori Midori Troq Troq Troq Troq Troq Troq Troq Troq Troq Troq Troq Troq
Rook Argagarg Midori Midori Midori Argagarg Argagarg Argagarg Midori Argagarg Argagarg Argagarg Argagarg Argagarg Argagarg Argagarg Argagarg
Setsuki Troq Grave Grave Grave Troq Troq Troq Troq Troq Troq Troq Troq Troq Troq Troq Troq
Troq Onimaru Geiger Geiger Geiger Onimaru Onimaru Geiger Geiger Onimaru Onimaru Onimaru Onimaru Onimaru Onimaru Onimaru Onimaru
Valerie Troq DeGrey DeGrey DeGrey Troq Troq Troq DeGrey Troq Troq Troq Troq Troq Troq Troq Troq
Vendetta Valerie Grave Grave Grave Valerie Valerie Grave Grave Valerie Valerie Grave Grave Valerie Valerie Valerie Grave
Zane Troq Troq Rook Rook Troq Troq Troq Troq Troq Troq Troq Troq Troq Troq Troq Troq
Nash
Bo7 Nash Bo5 Nash Bo3 Nash
Argagarg 0.119 0.111 0.215
BBB 0.000 0.000 0.000
DeGrey 0.000 0.000 0.000
Geiger 0.204 0.136 0.140
Gloria 0.000 0.000 0.000
Grave 0.002 0.077 0.097
Gwen 0.000 0.000 0.000
Jaina 0.000 0.000 0.000
Lum 0.000 0.000 0.000
Menelker 0.000 0.000 0.000
Midori 0.000 0.000 0.000
Onimaru 0.001 0.038 0.000
Persephone 0.000 0.000 0.000
Quince 0.000 0.000 0.000
Rook 0.000 0.000 0.000
Setsuki 0.000 0.000 0.000
Troq 0.675 0.637 0.495
Valerie 0.000 0.000 0.000
Vendetta 0.000 0.000 0.054
Zane 0.000 0.000 0.000

Now, for those of you who TL;DR’d right over all the numbers, I’ll break it down for you: Princess Power MU chart says you should start your Bo7 with pretty even mixes of Geiger, Troq, and Zane, leaning a bit towards Geiger. The Yomi-Skill MU chart says that instead, you should have a heavy dose of Troq, with some Geiger and Arg to even things out.

Why did the math come out that way?

Change from PPMU to YSMU
Arg BBB DeGrey Geiger Gloria Grave Gwen Jaina Lum Menelker Midori Oni Pers Quince Rook Sets Troq Val Ven Zane Total Change
Argagarg 0 -1.8 -0.3 0.5 0.6 -0.6 0.6 0.7 -0.4 -0.2 0.5 -0.6 0.9 -0.6 0.9 0.8 0.9 0.9 0 0.3 3.1
BBB 1.8 0 -0.4 -0.2 1.7 0 0.6 0.6 1.3 1 -0.8 -0.6 -0.5 0.2 -0.9 0.4 0.2 1.1 0.3 -0.6 5.2
DeGrey 0.3 0.4 0 -0.1 -0.6 -1.2 0 0.1 0.6 0.1 -0.3 -0.5 0.7 1.2 -0.6 -0.5 -0.2 0 -1.3 0.7 -1.2
Geiger -0.5 0.2 0.1 0 0.6 -0.3 0.4 0.7 0.1 0 -1.2 0.4 0.2 -1.3 -1.2 0.8 -0.5 0.1 0 0.2 -1.2
Gloria -0.6 -1.7 0.6 -0.6 0 1.2 -0.8 -1.3 1 0.8 -1.3 -0.5 0.7 0.3 1 1.5 0.2 0.7 0.4 0.3 1.9
Grave 0.6 0 1.2 0.3 -1.2 0 0.5 -0.8 -1.2 -0.4 -1 0.1 -1.2 -0.3 -0.1 -0.1 0.3 -0.8 -0.1 -1.1 -5.3
Gwen -0.6 -0.6 0 -0.4 0.8 -0.5 0 -0.1 -0.4 0.4 0.1 -0.4 -0.8 1.4 -1 1 -0.4 1.5 -0.9 0 -0.9
Jaina -0.7 -0.6 -0.1 -0.7 1.3 0.8 0.1 0 -0.8 -0.4 0 -0.3 0.1 -0.5 -1.7 -0.1 0.4 0.2 -1.3 -0.4 -4.7
Lum 0.4 -1.3 -0.6 -0.1 -1 1.2 0.4 0.8 0 -0.1 -0.5 -0.2 1.3 0.1 -0.1 0 -0.8 0.5 -2 0.3 -1.7
Menelker 0.2 -1 -0.1 0 -0.8 0.4 -0.4 0.4 0.1 0 1 -0.6 -0.5 -0.8 0.5 -0.1 0.5 1.1 0.3 0.2 0.4
Midori -0.5 0.8 0.3 1.2 1.3 1 -0.1 0 0.5 -1 0 0.8 -0.7 1.9 1.3 -0.8 -0.5 0.8 0.3 0.5 7.1
Onimaru 0.6 0.6 0.5 -0.4 0.5 -0.1 0.4 0.3 0.2 0.6 -0.8 0 1.1 0.6 -0.7 -0.3 0.8 -0.2 0.6 -0.6 3.7
Persephone -0.9 0.5 -0.7 -0.2 -0.7 1.2 0.8 -0.1 -1.3 0.5 0.7 -1.1 0 -0.9 0.1 0.3 0.7 0.7 0.3 0.3 0.2
Quince 0.6 -0.2 -1.2 1.3 -0.3 0.3 -1.4 0.5 -0.1 0.8 -1.9 -0.6 0.9 0 -0.5 0.5 -0.8 0 0 0.2 -1.9
Rook -0.9 0.9 0.6 1.2 -1 0.1 1 1.7 0.1 -0.5 -1.3 0.7 -0.1 0.5 0 -0.4 0.2 0.8 0.9 -0.2 4.3
Setsuki -0.8 -0.4 0.5 -0.8 -1.5 0.1 -1 0.1 0 0.1 0.8 0.3 -0.3 -0.5 0.4 0 -0.1 -0.3 -0.6 -0.2 -4.2
Troq -0.9 -0.2 0.2 0.5 -0.2 -0.3 0.4 -0.4 0.8 -0.5 0.5 -0.8 -0.7 0.8 -0.2 0.1 0 0.2 -1.2 0 -1.9
Valerie -0.9 -1.1 0 -0.1 -0.7 0.8 -1.5 -0.2 -0.5 -1.1 -0.8 0.2 -0.7 0 -0.8 0.3 -0.2 0 -0.3 -0.1 -7.7
Vendetta 0 -0.3 1.3 0 -0.4 0.1 0.9 1.3 2 -0.3 -0.3 -0.6 -0.3 0 -0.9 0.6 1.2 0.3 0 0.2 4.8
Zane -0.3 0.6 -0.7 -0.2 -0.3 1.1 0 0.4 -0.3 -0.2 -0.5 0.6 -0.3 -0.2 0.2 0.2 0 0.1 -0.2 0 0

Well, it looks like my numbers rate Arg significantly higher across the cast (+3.1, and that includes a -1.8 shift against BBB), and DeGrey, Geiger, and Troq all a bit lower across the cast. Notably, Troq loses 0.9 against Arg, and gains 0.5 on Geiger.

I’m curious to hear what you folks see in these numbers. Is Arg being slept on? Is the Bo7 Nash actually a sane way to think about a tier list?

6 Likes

I don’t understand most of that…
This kind of game theory mathematics is a bit over my head. But I agree that Arg is pretty good. I don’t know about top-3 levels of good though. Also it seems to me that optimal CPs would vary an awful lot based on the player’s skill level and player type.

Thanks for putting this up. I was considering using the Nash equilibrium to do a tier list for the Codex model once it’s mature enough, so it’s encouraging to see you and deluks917 thinking on similar lines.

I was hoping the equilibrium weights could be split into bands, to roughly give the tiers, with “never play” being Garbage Tier. It is a bit worrying that so much of the Yomi cast ends up in that tier, even if it’s assuming perfect players. (Disclaimer: I don’t play Yomi.)

Maybe it’s worth doing Best of 1 first, as a sanity check? I don’t know how the equilibrium for longer matches is being calculated, it’s not immediately obvious to me whether you’d want to always take the “greedy” approach, and take the best counter-pick for the next match. EDIT: It’s also possible that, for a multiple-match game, a character would be in the equilibrium because they allow good counter-picks later, not because they’re good themselves. Best of 1 wouldn’t conflate these.

Imo too many members of the yomi cast have too many lopsided MU and to make things worse most of them are against the same chars. Like Gloria, jaina, etc fare bad vs zane, the first because zane obliterates too much hp out of a single combat loss, the second because has few throws (and slow at that) and both of them eat their own hp as part of their gameplan. Gwen’s speed hole makes here an easy mark for any char that can poke her with 1.0 or 1.2 attacks to death. The same can be said vs troq or degrey. They have a lot of HP and a single combat win can wipe out >20 hp. In BTB, i picked only top tier chars, and players’ skill aside, i think that having only card efficient chars that have no lopsided MUs helped me. I love playing jaina, gloria or midori, but they suffer from variance too much compared to the top tiers, making them (imho) trash tier in a play 2 win enviroment.

2 Likes

I think “trash tier” is coming on a bit strong, because that leaves you with basically only two tiers:
A tier, which is the handful of characters who are a significant part of the Nash, and B tier, which is the slightly larger group of situationally relevant counterpicks. Everyone else is consigned to Trash/F, which is not a real tier.

From a strict Nash point of view there is no reason to play anyone else if we assume equal skill with all characters, so from a certain perspective you could say they are “trash tier” but that overstates their weakness IMO. A character’s position in the tier list is based on how well a character has the potential to perform, not on whether another character could do better, even if it’s to the point of obsoleting them.

E.g the existence of Zane doesn’t make Menelker “trash tier”.

2 Likes

let me elaborate. Gloria, jaina, etc have too many lopsided mus. Jaina does not fare well against degrey, zane, arg, geiger because she is a slow rushdown, has few blocks and all throw related. Gloria has too few hp and unless she finds and keeps HS she loses easily against all grapplers, persephone, zane, etc. GWen’s speed hole makes her weak againt any chars with a decent single ace poke/dodge/block. They are imo “trash tier” not because they are weak, but cuz too many mus are uber hard, while a zane or a troq has at worst a 5.5 MU. Persephone, like mene, is not bad per se but she is overly brittle. Why play a char with 70-75hp with low card eff if you can get a 90-85-char (zane degrey) with high card eff and tons of dmg?

3 Likes

Ah, I see. I misread you, I thought you were saying everyone but the top tiers were functionally F tier, but you were talking much more spesifically about a few low tiers and their spesific weaknesses.

Everything you just said is correct AFAICT.

What you said is a problem with what I wrote for assigning the Garbage Tier, though. Maybe you could do some incremental thing instead:

  1. Identify a dominant set of characters (Pick enough to represent over half of the equilibrium distribution? Split the Nash set into two clusters?). Name them as the next tier.
  2. Remove those characters, and recalculate the Nash equilibrium for remaining characters.
  3. Repeat.
2 Likes

Glad to be of a little help. I don’t have the math background to contribute to that side of the discussion.

I do want to take a second to quote Deluks once again, from the old, dead forum, so that players don’t look at this and get discouraged about their favorite characters or whatever:

The mu chart code only gives the right plays if:

  1. You play a large number of chars equally well

  2. the mu chart is exactly corrcct (this is definitely false)

The code is mabye interesting but definitely not something to worry about imo.

The game has lots of play no matter who you prefer, and ultimately is a game. Use this as a resource if it increases your enjoyment of the game. Play the way you want, and remember that characters win unfavorable matchups regularly!

3 Likes

Absolutely! My math is a fun theoretical distraction, and might have some usefulness in future balancing efforts, but in no way outweighs individual strengths and preferences.

So, this calculation is all based on perfect play (by impossibly skilled players). But also, the Nash in question is about your opening blind pick in a Best-of-X. You have to be able to back that up with the optimal counterpicks for the rest of the set. For instance, starting at the Troq-dominated Nash (for both players), each player would expect to play the following number of games of each character in the set:

Char Expected Games
Troq 1.58
Geiger 1.03
Onimaru 0.66
Argagarg 0.61
Grave 0.60
Quince 0.43
DeGrey 0.38
Midori 0.25
Persephone 0.15
Setsuki 0.12
Zane 0.12
Vendetta 0.08
Lum 0.00
Jaina 0.00
Gwen 0.00
Gloria 0.00
Rook 0.00
Valerie 0.00
BBB 0.00
Menelker 0.00

Interestingly, in the course of this, I figured out that I think I could actually add this computation to the player-specific section of Yomi-Skill, so that you could actually get customized recommendations based on who you’re playing against.

Yeah, this is all calculated based on players playing rationally during all their counterpick selections, and accounts for the expected outcome tree based on that. The only “game-theory” part comes in during the double-blind at the beginning of the match. After that, only one player is making a decision at any particular time (between games, that is), so you can compute the theoretically optimal counterpick based on what you would expect your opponent to counterpick that pick with (and so on down to the end of the set).

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Also, yes, this was a thought I had had. I think it would be interesting to figure out what portion of the cast gives most even distribution (both in the initial Nash, and the eventual games played). In theory, in a “perfectly balanced” game, you would expect to see a Nash that balanced across all of the options, and also a expected play count that was even across the whole cast (I think). Certainly that’s true for a vanilla RPS (the Nash is 33% each, and if you allowed “counterpicking”, you’d expect every option to be played evenly downstream of that Nash as well).

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Ah, so there are quite a few characters that are being used, but that aren’t reflected in the initial pick table. (Even more than the numbers on that table convey, if characters with the same frequency are ordered by name.) That’s good to know.

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Yeah, I’m not sure if there are actually any ties in the data. That would be an interesting thing to check. Right now, though, it’s just breaking ties by name.

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It is certainly possible we heavily under valued Arg. In theory arg seems strong. He actually most reminds me of degrey. He does a huge amount of dmg without needing to draw many cards.

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