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[heron]

I was bored, so I threw together a quick ranking of cards using Councilroom stats, multiplying %+ by Win Rate With. It is sort of accurate, but even with the multiplying by %+ a few must-buy power cards are surprisingly low, like ambassador and masquerade. Also, cards that are easily acquired on spare buys, etc. display an inflated ranking. (pawn, cellar)
And then there are anomalies that I can not explain, like crossroads.

$2:
Crossroads: 78.7     
Hamlet: 78.5
Chapel: 78.477
Pawn: 66.052
Fool's Gold: 65.464
Cellar: 59.849
Haven: 58.707
Native Village: 56.43
Pearl Diver: 53.472
Estate: 45.45
Moat: 45.308
Embargo: 43.747
Herbalist: 38.311
Duchess: 35.154
Secret Chamber: 32.472

$3:
Fishing Village: 92            The highest rated card, probably due to the fact that it's bought like every game, even when worse than silver.
Silver: 86.142
Great Hall: 76.734            ...What?! I guess people buy it a lot.
Shanty Town: 73.108
Village: 71.295
Steward: 71.181
Tunnel: 70.364
Ambassador: 70.04          Apparently, it's only bought/gained 68% of the time.
Menagerie: 68.083
Swindler: 67.6
Black Market: 66.27        High, but thinking on it, BM does deserve to be higher than it gets on the Qvist rankings.
Scheme: 66.1
Masquerade: 63.315        Too low!
Warehouse: 61.098
Trade Route: 57.722
Oasis: 55.958
Smugglers: 51.597
Lookout: 44.523
Loan: 42.723
Watchtower: 37.81
Develop: 36.34
Woodcutter: 32.844
Wishing Well: 31.164
Fortune Teller: 26.315
Oracle: 25.123
Workshop: 24.795
Chancellor: 10.179

$4
Tournament: 89.507
Caravan: 89.4
Worker's Village: 84.051
Island: 82.7
Farming Village: 81.081
Bishop: 79.3
Mining Village: 75.042
Bridge: 74.593
Monument: 71.4
Spice Merchant: 71
Throne Room: 70.368
Walled Village: 67.008
Remake: 66.627
Militia: 66.429
Sea Hag: 66.352
Moneylender: 66.15
Salvager: 64.1
Conspirator: 61.5
Quarry: 57.76
Baron: 57.095
Young Witch: 57.547
Remodel: 55.48
Jack of all Trades: 54.978
Horse Traders: 54.816
Smithy: 52.92
Gardens: 52.7
Ironworks: 51.585
Silk Road: 50.7
Envoy: 48.015
Potion: 46.342
Trader: 45.477
Pirate Ship: 43.392
Feast: 42.018
Treasure Map: 38.857
Talisman: 35.844
Scout: 27.857
Cutpurse: 27.8
Noble Brigand: 27.632
Bureaucrat: 19.152
Coppersmith: 17.577
Navigator: 16.376
Thief: 16.344

More to come! If anyone has ideas on how to improve the rating system thingy, please tell me.
The major issues I notice are: Trashing is too low and villages are too high. VP cards are also rather high. Some inaccuracies may be due to newer players, but improvement is still certainly possible.

Villages being high might be okay; as a community we don't rank them highly since they're so abundant, but lots of boards change significantly if all of the villages are removed.

I'll post 4 and part of 5 tomorrow evening probably.

[blueblimp]

Your formula is interesting. It sort of makes sense to me as a measure of how much a card contributes to win rate when present in the kingdom.

You may be interested in the "Quality" field of councilroom's supply_win stats, if you haven't seen it already. It attempts to do a similar thing.

[Wingnut]

The thing to remember is that a lot of lower ranked players just don't buy certain cards because they seem weak no don't seem to have a benefit. I know Ambassador falls into that category without any question and Great Hall gets overbought by lower ranked players (I'm talking legit level 0 and such) because it is points and play another card.

This is something that could do with a level filter (I know that's hard to do), even if that is a bar like 15-20 as most of those level players have no problem figuring out that Ambassador is great and Great Hall is bad.

[rrenaud]

I don't know how much you know Python, but I essentially did the same thing you are doing a bit more programmatically to find the rankings on supply_win.  I used qvist's community rankings #1 as golden data, and tried to find a simple function of the buy/win data (and actually added a couple of card based compensation factors) that got close to reproducing the rankings.  I used some programmatic optimization to find weights that trade off the various factors.

The code is here if you want to play.

https://github.com/rrenaud/dominionstats/blob/master/card_ranker/optimize_ranks.py

Perhaps unsurprisingly, the two most important features I found were monotonic transformations of the variables you used.  I did add a correction term for a card giving VP, which helps push down great hall and other alt VP cards that are as much (or more) a symptom of winning as a cause.

[popsofctown]

Is this filtered by rank at all?  Great Hall is a card I strongly consider a noobtrap.

[rrenaud]

The raw supply win and popular buys data are not filtered by rank at all.

Note the ranking function itself rewards both gaining and winning with a card.  So if a card is gained a lot but it doesn't win a lot, it will still look mediocre according to the ranking function.

This is what supply win says when ranking cost 3 cards.  FV is way too low and warehouse is too high, but otherwise it doesn't seem that bad.

Masquerade   
Ambassador   
Menagerie      
Warehouse      
Scheme      
Swindler      
Loan         
Steward      
Silver         
Fishing Village   
Tunnel      
Oasis         
Trade Route   
Watchtower   
Shanty Town   
Lookout      
Wishing Well   
Great Hall      
Village      
Black Market   
Oracle      
Fortune Teller   
Develop      
Smugglers      
Woodcutter      
Workshop      
Chancellor      

[HiveMindEmulator]

Perhaps unsurprisingly, the two most important features I found were monotonic transformations of the variables you used.  I did add a correction term for a card giving VP, which helps push down great hall and other alt VP cards that are as much (or more) a symptom of winning as a cause.

What makes you think that low-cost VP cards are more of a symptom of winning than a cause? Why would the fact that I'm winning make me more likely to buy Great Halls?

This is what supply win says when ranking cost 3 cards.  FV is way too low and warehouse is too high, but otherwise it doesn't seem that bad.

I don't think Warehouse is (significantly) too high. At least it's not one of the things that stands out most in this list. (Lookout being so much lower than Loan is pretty surprising.) Non-terminal +3 cards is really good, and it combos with basically everything -- either you want to play particular cards more, or you need to match up certain cards or something, but drawing 3 cards is like always good, even with a net handsize decrease. It's probably under-appreciated in the community rankings.

[ftl]

What makes you think that low-cost VP cards are more of a symptom of winning than a cause? Why would the fact that I'm winning make me more likely to buy Great Halls?

Any VP cards are a symptom of winning. If I have an engine going, the end goal is to buy up VP cards, and so if I have a better engine that means that I'll probably have more of whatever VP cards there are.

I mean, it applies most to provinces, but to a lesser degree with any other VP.

[HiveMindEmulator]

What makes you think that low-cost VP cards are more of a symptom of winning than a cause? Why would the fact that I'm winning make me more likely to buy Great Halls?

Any VP cards are a symptom of winning. If I have an engine going, the end goal is to buy up VP cards, and so if I have a better engine that means that I'll probably have more of whatever VP cards there are.

I mean, it applies most to provinces, but to a lesser degree with any other VP.

You could also argue the opposite. If I'm winning, I just end the game on Provinces or piles and don't bother with silly stuff like Great Halls, but if I'm losing I have to scramble for other sorts of VP cards.

Both your argument and this counter-argument are vague and not well quantified. They may offset each other, or one effect may be more pronounced. My question is: why do we believe that it's more of the former than the latter?

[qmech]

Ambassador: 70.04          Apparently, it's only bought/gained 68% of the time.

The thing to remember is that a lot of lower ranked players just don't buy certain cards because they seem weak no don't seem to have a benefit. I know Ambassador falls into that category without any question

I've lost track of whether this is currently a contrary position, but Ambassador is frequently ignorable when there's no good engine to aim for.  So another possible explanation is that it's very good sometimes, and correctly ignored at others.  That's less likely than the above explanation though: it was well after my transition to Isotropic that I realised how strong it could be.

[rrenaud]

I don't want to get into a long and meandering debate about causality.  But if you just rank cards just by probability of buying a card and conditional winning rate of buying a card, you'll tend to over rate VP cards, as compared to the qvist rankings.

[HiveMindEmulator]

I don't want to get into a long and meandering debate about causality.  But if you just rank cards just by probability of buying a card and conditional winning rate of buying a card, you'll tend to over rate VP cards, as compared to the qvist rankings.

Okay, fair enough. So the problem may simply be that what we've chosen as the "gold standard" undervalues victory cards.