Skill factor and other calcs for DR#292

Multiplayer Discussion
1

Spreadsheet can be found here, if you’re a math nerd and want to check my work: https://docs.google.com/spreadsheets/d/1LYBGYQMHkUFJVamPEeEHbbfmY7NCjP0aIuXU3MTquC8/edit?usp=drivesdk

Polarization

Polarization is how far, on averages, matchups are from even. 0% polarization is a 50-50 matchup and 100% polarization is a 100-0 matchup. For the purposes of comparing decks against each other, two types of polarization are measured: raw polarization, which is from 50-50, and adjusted polarization, which is from the deck’s overall winrate (so for a deck with 55% overall winrate, the distance from 55-45).

Diamond 4-1 polarization
Archetype Class Adj. Pol. Raw Pol.
Reno Druid 19.02% 18.92%
Handbuff Paladin 17.40% 17.71%
Dragon Druid 16.61% 16.70%
Zarimi Priest 16.48% 18.00%
Spell Mage 16.29% 21.03%
Shopper DH 15.83% 15.16%
overall 15.79%
Reno Shaman 15.34% 14.68%
Reno Warrior 15.31% 15.13%
Pain Warlock 14.90% 14.76%
Rainbow Mage 13.68% 19.46%
Aggro Paladin 13.53% 14.09%
Rainbow DK 13.03% 14.61%
Cutlass Rogue 12.29% 14.75%
Excavate Rogue 12.25% 13.90%
Plague DK 11.60% 12.44%
Pirate Rogue 11.57% 20.29%
Token Hunter 11.44% 21.10%
Sludge Warlock 11.21% 12.62%
Snake Warlock 10.51% 10.68%
Reno Priest 10.20% 20.28%
Wheel Warlock 9.02% 12.75%
Hybrid Druid 7.58% 7.59%
Legend polarization
Archetype Class Adj. Pol. Raw Pol.
Dragon Druid 16.44% 16.53%
Reno Druid 14.84% 14.94%
Rainbow Mage 13.65% 18.12%
Aggro Paladin 13.55% 12.49%
Pain Warlock 13.18% 13.18%
Spell Mage 13.10% 18.74%
Reno Shaman 12.61% 12.86%
Handbuff Paladin 12.54% 12.85%
Reno Warrior 11.85% 10.76%
Rainbow DK 11.57% 13.43%
overall 11.26%
Token Hunter 11.20% 16.82%
Shopper DH 11.00% 9.94%
Zarimi Priest 10.96% 14.16%
Cutlass Rogue 10.46% 10.46%
Pirate Rogue 10.09% 15.50%
Sludge Warlock 9.95% 10.30%
Reno Priest 9.79% 16.18%
Snake Warlock 9.39% 9.30%
Excavate Rogue 9.13% 10.28%
Hybrid Druid 8.21% 7.76%
Plague DK 7.84% 9.89%
Wheel Warlock 7.47% 13.80%

The average game in D4-1 currently (and by “currently” I mean the 25th through 30th of last month) is 57.9% to 42.1%, which is quite polarizing. Historically, Legend is normally more polarizing than Diamond, but not this time; the average game there is 55.63% to 44.37%.

Skill Factor

Skill factor is based on the concept that overall winrate is the sum of the product of your matchup winrate against a deck and the popularity of that deck, for all decks in that meta. But what if we used the matchup winrate table for one meta, say Diamond 4-1, while using the popularity from a different meta, say Top 1000 Legend? In this way we can isolate how much winrate change is due to differences in deck popularity, and how much is due to differences in matchup winrates. Since the only thing that is changing as matchup winrate changes is the rank, and therefore the average skill, of the players, this allows for a measurement of how well a deck rewards increases in the skill of both players (so a deck that gets worse the better its opponent is, faster than it gets better from having a more skilled pilot, can have a negative value).

As far as a practical application for this measurement, the table includes a column that is the sum of D4-1 winrate and skill factor (which again, can be negative). That sum yields my best advice regarding what you should play if you are a highly skilled Top Legend player by end of month, but you are currently in Diamond or in lower Legend trying to climb.

Skill Factor
Archetype Class D4-1 WR+SF Skill Factor
Token Hunter 54.30% -5.23%
Zarimi Priest 54.02% 0.63%
Reno Warrior 53.30% -0.40%
Aggro Paladin 53.15% -2.79%
Handbuff Paladin 52.32% 0.48%
Sludge Warlock 52.11% -0.22%
Shopper DH 51.71% -0.04%
Hybrid Druid 51.10% 1.08%
Pain Warlock 49.10% -0.09%
Excavate Rogue 48.89% 3.14%
Reno Shaman 48.17% 0.43%
Snake Warlock 48.05% -2.32%
Dragon Druid 47.94% -0.38%
Reno Druid 47.10% -1.91%
Cutlass Rogue 45.29% -0.04%
Rainbow DK 44.85% -0.22%
Plague DK 43.80% -2.98%
Wheel Warlock 43.78% -0.43%
Rainbow Mage 41.71% 0.15%
Spell Mage 40.67% 0.24%
Reno Priest 40.13% -0.10%
Pirate Rogue 39.68% -0.53%

To summarize the table, if you want to just climb as quickly as possible, run Token Hunter, even though it’s the lowest skill factor deck in the meta. If you want to climb almost as quickly, but feel somewhat clever as you’re doing so, run Zarimi Priest. And if you want to feel extraordinary clever while barely climbing at all, run Excavate Rogue. :crazy_face:

2

And that’s why you don’t play sludgelock, aggro pally and hunter in top 500 legend - skill factor is too low

But you do play Zarimi priest

What happens if we subtract skill factor from adjusted polarization? What would that be a measure of?

I feel like that could be a decent measure of deck’s viability, but I’m not sure, cuz I don’t understand your table, it’s too messy xD

3

… Nothing I can think of.

Skill factor is fundamentally a measurement between ranks — that is, it condenses the difference between the D4-1 matchup winrate tables and the T1KL matchup winrate tables into a single number, in overall winrate % units. I’d imagine that for most applications you’d be interested in, you’d consider D4-1 to be a contamination if anything. I don’t think skill factor has any relevance outside of a T1KL player who happens to be at D4-1, and that’s not really a challenge in the first place unless it’s viewed from a speed running perspective. So that narrow speed running mentality is really all the practical application I can find.

I guess it also can explain the appeal of decks with poor winrate at high ranks. For example, I think it explains why Excavate Rogue is overplayed.

4

I’m not sure, I think you were onto something with that measure

I think it’s a good measure of the skill cap of the deck which explains why certain decks see much less play than their winrates suggest

5

It is intended to measure skill cap. To the extent it can be measured. Which isn’t much.

Well I do think that it is a form of “fun factor” measurement. If we’re focused on the demographic of very high level players, I do think skill factor is a measurement of how “good” a deck feels. Not how good it actually is, mind you.

Like if you remember the “Irrationality Index” thing I made half as a joke in an earlier post, I’ve calculated skill factor in previous metas and it’s normally those kinds of decks that score highest. And when the deck with the highest skill factor is Tier 1, as opposed to below 50% winrate, you always get a lot of streamers and top players calling for the deck to be nerfed, e.g. Garrotte Rogue.

6

I think this skill factor is much more useful than

at least for me

Like, skill factor explains why some tier 1 decks are unplayable in top 500 - because you lose the edge over your opponents and surrender to the luck of the draw

And when you combine that result with how I feel playing against Rogue, a high-skill-low-winrate deck, it makes perfect sense they would prefer that deck over those tier 1 decks with low skill cap because it’s impossible to play around it.

How do you play around a deck which can literally play cards from all 11 classes, with 3 mana discounts from turn 2 onwards? You don’t.

That’s how I see it. And more importantly, that’s how rogue players see it

7

I am never a fan of the word “impossible.” And although the pool is from 11 classes, and therefore a very large random pool, it is not an infinite random pool, and over the course of turns a skilled player can determine with some accuracy what a randomly generated card isn’t. For example, if it was Card X, then they would have played it instead of what they chose to play instead, therefore it isn’t Card X. So it’s not impossible to play around.

It’s more accurate to say that it’s superhuman or borderline superhuman to play around. Like you’d need to be the Hearthstone equivalent of a chess solving AI like Stockfish, to have any hope of playing around it consistently. The Magnus Carlson of card games. So yeah, I don’t. You probably don’t either. But not because it’s impossible, but because it’s ridiculously difficult.

8

I can’t believe you replied with that

Jesus you really like typing your thoughts

I suggest you keep a diary

9

Guilty as charged.

I was hoping you’d enjoy it too, though.

10

I’m not really enjoying when people take me for an idiot

I love theorizing and that’s why I’m into science

But this is sport. I look at it from more practical perspective, and that means that I don’t differentiate between impossible and superhuman/possible with some microchip from the future in our brains.

11

Saying that you’re not Magnus Carlson isn’t calling you an idiot. If you’re not THE most skilled pilot on these forums, you’re absolutely top 3. And you probably are the best. You shouldn’t feel so insecure in your position.

12

I don’t, which is why I didn’t like your comment xD It’s obvious, therefore unnecessary

Anyway, back to topic

If anyone else cares xD

P.S. I’d prefer it if I wasn’t top 3, cuz that would mean I have a person to learn from

Hell, I’d kill for a couple of more people at my rank just to compare what works and what not

13

I mean, we obviously have differences of opinion when it comes to the relationship between personal experience playing the game, and broader truths regarding the game, the role of data, etc.

But just in terms of my personal experience, you do realize that I was washing my random Sludgelock opponents just about as hard as you were washing your random Hunter opponents, right? You were very, very clearly multiple tiers above them. I really was hoping it would be that easy (although I had the sense to limit it to a hope) and you didn’t make it easy. I was, and am, truly impressed.

14

We don’t, it just takes you too much to understand my point. And I can’t believe it took a Pareto principle to realize what I was trying to say

Can’t you see how impractical and disconnected you are from normal world?

I could speak your language if I knew what it was, but you switch from statistics to economy without blinking and you confuse terminology a lot

I also noticed you like to read popular psychology books instead of scientific articles, and I can’t adapt to that

Just try to meet me halfway and be more practical xD

And I admit, being too theoretical and of too wide interests is also one of my faults, too, which is another reason why I try to avoid using specific terminology - out of fear of mixing things up

So let’s try and be more practical, less theoretical xD After all, theory is meaningless without application in practice

Without it, it’s just a game, another shot of dopamine, a drug

15

Likewise, but stop the flattering, I’m blushing here xD

Also, it would mean much more to me if you played the game and struggled with me in top ranks

Maybe it would help you to consider my perspective a bit more - and me to understand yours

16

I’ll strongly consider it.

My mom died recently. If you’ve ever seen the movie Whiplash, my mom was essentially JK Simmons’ character but female. I kinda liked her, which probably reflects something very dark about myself. But the point is, imagine how someone like that, for whom psychological manipulation enters every thought, would handle inheritance, and you can perhaps understand my current situation. I might be rich now. I might not. I have truly no idea.

But if I am rich, why not.

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17

I’m sorry to hear that

What’s dark about loving your mother? It would have been dark if it was the opposite

Yeah I’ve watched the movie, but I might have understood it differently than you, because I wasn’t as emotionally involved in the thematic

I figured, that’s what it takes to learn someone how to approach greatness.

We all have our demons and ghosts

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18

Unfortunately I fell far short of that.

But yeah, she was the sort of person who would break my nose because I used the wrong “there” in a paper for high school. She did. Watching that movie makes me homesick.

19

Yeah, sounds like narcissism, she was trying to live life through you because she had failed to live her own the way she wanted

It happens, but as I was saying, every coin has two sides.

Strong men create good times, good times create weak men, weak men create tough times, and tough times create strong men.

I’ll let you ponder on it a bit. Ofc it’s an overgeneralization, but as a theoretically inclined person, surely you’ll understand the value in it.

20

If anything you’re preaching to the choir.

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