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State of the Game - mid 2017

These numbers are super interesting!

  1. Why is Grave chosen so often when he has a losing matchup against so many of the relevant characters?

  2. I lke how Gloria makes herself relevant as a counterpick to Arargarg, but I am curious of why so many Gloria players end up playing against Zane?

  3. Menelker players are masochistic it seems.

  4. BBB chosen as a counterpick against Rook gives him such a high rating.

Outside of that, only 4 matchups out of the 20 most popular ones does not include carousel characters.

Grave vs Arargarg
Rook vs BBB
Arargarg vs Gloria
Rook vs Arargarg

  1. Grave is secretly a high skill character. He’s picked often, but most people aren’t good with him.
  2. Because every time you see a Gloria, play Zane. Sharpo, Arkhan, LK, SirHandsome etc. etc.
  3. The life of a Menelker player is a hard one. Everytime someone sees Menelker, play Zane. Me, Ides, Copper, Mi-Go, etc.
  4. BBB is really good vs Troq and Rook. That makes him slightly relevant against grappler players.
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I’m attempting a bit of my own analysis (computer-assisted, as is my wont), but I wanted to see if I’d captured the current 20XX meta correctly as a baseline. Currently, my description is:

Blind pick: Troq, Zane, or Geiger with equal probability
Counter picks: (read “X -> Y” as pick Y if your opponent played X)

  • Argagarg -> Zane
  • BBB -> Geiger
  • DeGrey -> Zane
  • Geiger -> Zane
  • Gloria -> Zane
  • Grave -> Zane
  • Gwen -> Troq
  • Jaina -> Zane
  • Lum -> DeGrey
  • Menelker -> Zane
  • Midori -> Geiger
  • Onimaru -> DeGrey
  • Persephone -> Zane
  • Quince -> Troq
  • Rook -> BBB
  • Setsuki -> Troq
  • Troq -> Geiger
  • Valerie -> Zane
  • Vendetta -> Zane
  • Zane -> Troq

I feel like this is a bit simplistic, which is probably messing up the resulting analysis, so I’d love to hear your estimates about who the current preferred counterpicks are for each matchup (and if there are backup picks, what kind of ratio they are picked).

Based on my current estimate of the meta, a Grave opener, and Grave as a counterpick to Geiger seems to have an edge (I think because Grave has an edge over two of the three in the standard carousel, based on the historical MU chart). But I suspect that’s not actually particularly correct, and what more experienced players would say to that.

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All of that scans.

I’m pretty confident Grave doesn’t have a better MU against Geiger than Zane. Remember that these numbers are historical, and therefore not reflective of the true advantaged/disadvantaged state of a match up. The historical table contains games between experienced players, between experienced players and inexperienced players, and between inexperienced players.

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Oh, yeah, I totally misread the chart. Grave is down in the historical MUs against Zane and Troq. So, that also means my code is broken. :smile:

Your table works though. All of those are legitimate (and in most cases consensus) counterpicks.

Cool, I’ll keep using that as my baseline, then.

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You’ve got it backwards. If you see a Gloria/Menelker, pick a Zane if you have one.

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It also very clearly illustrates why having a Zane is good for your winrate, and the effect he has on the character select meta all by himself. Though honestly, for a lot of those MUs, you can just as easily put Troq as a counter pick: Argagarg, DeGrey, Grave (maybe), Menelker, Valerie, Vendetta. (And either of Zane or Geiger also CP Quince.)

It’s like 19XX: The Justificationing.

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Ok, so I checked my math, and it was wrong, as far as I can tell. Details below, but the counter meta is:

Blind pick: Grave, always Grave
Counter pick:

  • Geiger -> Grave
  • Troq -> Geiger
  • Zane -> Troq
  • whatever else you want, because in theory, on one else gets played.

The net result of that selection (against my strict meta above), is an overall expected win rate of 5.2, based on the historical MU chart ratings. Not huge, but also not negative, which makes me think there’s room for overall shifts in the meta.

The Maths

This is calculated for a best-of-3 set, but the effects are more pronounced with longer sets.

EV(C1, C2, W1, W2) means "the probability that player 1 will win the set (given that they need W1 wins vs player 2’s W2 wins required), given that player 1 is playing C1 this match, and player 2 is playing C2"

EV(Troq,Zane,1,1) = 0.650 = 0.650 * sum(1.0 * EV(Troq,Geiger,0,1)) + 0.350 * sum(1.0 * EV(Troq,Zane,1,0))
EV(Grave,Zane,1,2) = 0.804 = 0.440 * sum(1.0 * EV(Grave,Zane,0,2)) + 0.560 * sum(1.0 * EV(Troq,Zane,1,1))
EV(Grave,Zane,1,1) = 0.440 = 0.440 * sum(1.0 * EV(Grave,Zane,0,1)) + 0.560 * sum(1.0 * EV(Troq,Zane,1,0))
EV(Grave,Geiger,2,1) = 0.251 = 0.570 * sum(1.0 * EV(Grave,Zane,1,1)) + 0.430 * sum(1.0 * EV(Grave,Geiger,2,0))
EV(Grave,Geiger,2,2) = 0.566 = 0.570 * sum(1.0 * EV(Grave,Zane,1,2)) + 0.430 * sum(1.0 * EV(Grave,Geiger,2,1))
EV(Geiger,Zane,1,1) = 0.390 = 0.390 * sum(1.0 * EV(Geiger,Zane,0,1)) + 0.610 * sum(1.0 * EV(Troq,Zane,1,0))
EV(Geiger,Troq,2,1) = 0.238 = 0.610 * sum(1.0 * EV(Geiger,Zane,1,1)) + 0.390 * sum(1.0 * EV(Geiger,Troq,2,0))
EV(Grave,Troq,2,2) = 0.498 = 0.460 * sum(1.0 * EV(Grave,Zane,1,2)) + 0.540 * sum(1.0 * EV(Geiger,Troq,2,1))
EV(Troq,Geiger,1,1) = 0.390 = 0.390 * sum(1.0 * EV(Troq,Geiger,0,1)) + 0.610 * sum(1.0 * EV(Grave,Geiger,1,0))
EV(Troq,Zane,2,1) = 0.254 = 0.650 * sum(1.0 * EV(Troq,Geiger,1,1)) + 0.350 * sum(1.0 * EV(Troq,Zane,2,0))
EV(Grave,Zane,2,2) = 0.496 = 0.440 * sum(1.0 * EV(Grave,Zane,1,2)) + 0.560 * sum(1.0 * EV(Troq,Zane,2,1))

I think what’s going on is that Grave is favored enough over Geiger that it makes up for his slightly unfavorable MUs against Troq and Zane, and that once he starts down that path, the counterpicks aren’t enough to make up the difference.

More analysis (like, what, if anything, beats both of those, or how can the current meta adjust to beat the counter-meta) will be forthcoming.

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Actual step one: Get good at grave.
I never completed step one.

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Well, yes, a prerequisite to my analysis is “play all characters at least as well as is indicated by the historical MU chart”, which means that I’m not actually going to get any tangible benefit out of this in the near term. :smile:

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This is all super cool and interesting and I applaud you on this analysis.

I’ll agree with Bomber that Menelker is rough; he just loses to every one of the the main “carousel” except maybe Geiger. Zane is a terrible MU.

The one thing I wanted to question (sorry if someone already did) is the numbers on Vendetta - Troq. Those surprised the hell out of me.

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They do have a fairly low sample size, so they might end up being wrong. The same with the Jaina vs Troq numbers. But that is the life of the historical matchup chat. They could end up being right too tho, which is fun ^^

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I’m back with more math!

I realized that my previous calculations were based on an assumption that it was reasonable to counterpick the same character no matter the current win/loss record. That seemed questionable, so I wanted to investigate it.

I also observed that, assuming both players are playing optimally to the level of the historical MU chart, then they’d make identical decisions when it was time to counterpick (at the time of counterpicking, nothing is blind), so I used mini-max to figure out the optimal counterpick against each character at every wins-required combination.

In the rest of this post, X-Y means “You need X more wins to take the match, your opponent needs Y more wins to take the match”.

Some highlights (relevant to the current meta):

  • Against Zane, pick Troq (always and forever, no matter how ahead or behind you are)
  • Against Troq, pick Jaina if you only need one more win, otherwise pick Geiger
  • Against Geiger:
    • Pick Zane if you only need 1 more win, or you need 2 but are ahead
    • Pick Grave if you need 3-1, 3-2, or 4-2 (but you’re gonna have a bad time making up the deficit)
    • Pick Geiger if you’re behind 4-1
    • Pick Zane if you’re even, or behind 4-3
  • Against Grave:
    • Pick Quince if you are ahead (or at 1-1)
    • Pick DeGrey if you are behind (except 4-3)
    • Pick Argagarg if you’re even (or at 4-3, except 1-1)
  • Against DeGrey:
    • Pick Geiger at 2-2, 3-1, 3-2, 4-1, 4-2
    • Pick Setsuki otherwise

If you’re interested in following along, the code that is computing all of this is at https://github.com/cpennington/yomi-metabase (minimum requirements: some familiarity with Haskell, and the ability to tolerate my complete lack of comments).

If you’ve got specific questions, let me know and I’ll try and answer them. Here’s to a more interesting meta!

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Um? :smile:

Digging into the math a little bit, I think It basically comes down to Geiger being, of all the possible good counter picks, the one that you’re least likely to lose more with if you manage to win the game into a 3-1 situation.

Recurrence Relation for Geiger 4-1
EV(Geiger,4,1) = (Just Geiger, 0.03) = max (
  0.55 * (1 - EV(Argagarg,1,3)) + 0.45 * EV(Argagarg,4,0),
  0.31 * (1 - EV(BBB,1,3)) + 0.69 * EV(BBB,4,0),
  0.43 * (1 - EV(DeGrey,1,3)) + 0.57 * EV(DeGrey,4,0),
  0.50 * (1 - EV(Geiger,1,3)) + 0.50 * EV(Geiger,4,0),
  0.31 * (1 - EV(Gloria,1,3)) + 0.69 * EV(Gloria,4,0),
  0.57 * (1 - EV(Grave,1,3)) + 0.43 * EV(Grave,4,0),
  0.53 * (1 - EV(Gwen,1,3)) + 0.47 * EV(Gwen,4,0),
  0.16 * (1 - EV(Jaina,1,3)) + 0.84 * EV(Jaina,4,0),
  0.45 * (1 - EV(Lum,1,3)) + 0.55 * EV(Lum,4,0),
  0.51 * (1 - EV(Menelker,1,3)) + 0.49 * EV(Menelker,4,0),
  0.38 * (1 - EV(Midori,1,3)) + 0.62 * EV(Midori,4,0),
  0.44 * (1 - EV(Onimaru,1,3)) + 0.56 * EV(Onimaru,4,0),
  0.56 * (1 - EV(Persephone,1,3)) + 0.44 * EV(Persephone,4,0),
  0.39 * (1 - EV(Quince,1,3)) + 0.61 * EV(Quince,4,0),
  0.45 * (1 - EV(Rook,1,3)) + 0.55 * EV(Rook,4,0),
  0.48 * (1 - EV(Setsuki,1,3)) + 0.52 * EV(Setsuki,4,0),
  0.39 * (1 - EV(Troq,1,3)) + 0.61 * EV(Troq,4,0),
  0.39 * (1 - EV(Valerie,1,3)) + 0.61 * EV(Valerie,4,0),
  0.49 * (1 - EV(Vendetta,1,3)) + 0.51 * EV(Vendetta,4,0),
  0.61 * (1 - EV(Zane,1,3)) + 0.39 * EV(Zane,4,0))
Opponents win chances when they counterpick X
  • Argagarg: 96%
  • Geiger: 94%
  • Grave: 95%
  • Gwen: 98%
  • Menelker: 97%
  • Persephone: 98%
  • Zane: 96%
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I think the takeaway from my most recent computations is that if you’re ahead, pick characters that are stronger counterpicks against the character your opponent is currently playing (even if those characters tend to get bodied by lots of other characters), and if you’re behind, pick characters that are good against the current matchup, but also don’t lose too badly to down the road. (There’s definitely some multi-step thinking baked into the algorithm that’s hard to boil down, though).

I think that logic/thinking applies even if you don’t have the repertoire to play the “optimal” counterpick: pick aggressively when you’re in the lead, and conservatively when you’re behind (which, when I say it like that, makes some intuitive sense to me).

With that said, I’m looking forward to seeing lots more Jaina from folks who are way ahead and facing Troq!

Future analysis: what does this all mean for the optimal range during the double-blind phase?

Just keep in mind this depends on the historical results to match the “true MU numbers.” Which they won’t, by their nature.

I forget, but I’m pretty sure a while ago Ryker and I had a discussion about this and decided the correct course of action in a double blind is almost always “pick Grave” then go from there.

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