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Author Topic: Data Mining: Card Impact Factor  (Read 1389 times)

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trivialknot

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Data Mining: Card Impact Factor
« on: April 29, 2018, 02:46:42 am »
+16

In another thread, I suggested that you can estimate card power by measuring how much the presence of the card impacts what cards you gain.  Well, ben_king kindly supplied some data, so I did it.

The Data

The data set consists of 140,000 game logs from Isotropic.  All games are 2 players, pro rated, no bots, and each game has at least one player in the top 100 Isotropish rankings.  It's the same data set ben_king used for this analysis, and this tooThis data predates Adventures, so cards only go up to Guilds.

The Math

ben_king's first analysis calculated "gain percentages", the probability of gaining a card given that it was in the supply.  What I'm calling the "impact factor" is a measure of how much the presence of a card changes the gain percentages of all supply piles (relative to their average gain percentage).  For instance, if the presence of Duke increases the gain percentage of Duchy by 0.2, then I add 0.2 to Duke's impact factor.

Tricky details: Contributions to impact factor are weighted by how likely it is the cards will show up together.  So Duchy makes a full contribution to Duke, because Duchy is in every game, but Count makes a much smaller contribution to Duke because Count is not in every game.  The gain percentage of Duke makes a contribution to its own impact factor, calculated as (gain percentage)*(probability Duke is not in supply).  Note that the whole calculation is based on supply piles, not kingdom cards, so I don't include Prizes or Black Market cards, but I do include Potion, Estate, Knights, etc.  Yes, the impact factor of Estate must be zero, just think about it.

I am not claiming that the "impact factor" is a measure of the "strength" of a card.  Maybe it is, maybe it isn't.  Tell me what you think.

Update: I posted another list that's calculated without any weighting, and without contribution from non-kingdom piles.

The Results

RankCardImpact         RankCardImpact
1Rebuild2.97110Throne Room1.03
2Mountebank2.55111Cellar1.02
3Goons2.46112Market1.01
4Cultist2.43113Stonemason1.01
5Ill-Gotten Gains2.38114Ghost Ship1.00
6Ambassador2.36115Remodel1.00
7Governor2.23116Oasis0.99
8University2.19117Vagrant0.99
9Scrying Pool2.17118Haven0.98
10Tournament2.16119Great Hall0.98
11Familiar2.01120Watchtower0.98
12Minion2.00121Trading Post0.96
13Swindler2.00122Doctor0.96
14JackOfAllTrades1.99123Moneylender0.95
15Chapel1.96124Lookout0.95
16Masquerade1.94125Silk Road0.95
17Colony1.94126Inn0.92
18Platinum1.94127Smugglers0.92
19Soothsayer1.87128Pawn0.91
20Fishing Village1.84129Forge0.91
21Fool's Gold1.81130Rabble0.89
22Wharf1.80131Envoy0.88
23Marauder1.80132Sage0.88
24Witch1.80133Feodum0.86
25Sea Hag1.75134Horn of Plenty0.86
26Torturer1.75135Death Cart0.85
27King's Court1.74136Vault0.85
28Black Market1.68137Trade Route0.84
29Border Village1.63138Smithy0.84
30Tunnel1.60139Farmland0.84
31Steward1.57140Expand0.82
32Forager1.57141Wishing Well0.81
33Market Square1.55142Moat0.80
34Plaza1.52143Mint0.80
35Remake1.51144Council Room0.79
36Urchin1.51145Harem0.79
37Gardens1.50146Storeroom0.78
38City1.49147Advisor0.78
39Highway1.48148Pearl Diver0.78
40Wandering Minstrel1.45149Baron0.78
41Hunting Party1.44150Hunting Grounds0.77
42Alchemist1.43151Taxman0.77
43Worker's Village1.41152Scavenger0.77
44Lighthouse1.41153Catacombs0.76
45Conspirator1.41154Journeyman0.76
46Grand Market1.40155Potion0.76
47Ruins1.40156Cartographer0.75
48Baker1.40157Nomad Camp0.75
49Peddler1.39158Treasury0.75
50Hamlet1.38159Procession0.74
51Squire1.36160Develop0.74
52Young Witch1.34161Feast0.74
53Ironmonger1.33162Loan0.73
54Herald1.31163Band of Misfits0.71
55Vineyard1.31164Mystic0.70
56Upgrade1.31165Beggar0.70
57Prince1.31166Library0.69
58Bridge1.31167Noble Brigand0.68
59Nobles1.30168Rats0.68
60Fortress1.30169Workshop0.68
61Jester1.30170Bank0.68
62Junk Dealer1.29171Spy0.67
63Festival1.28172Armory0.67
64Count1.27173Venture0.67
65Duke1.27174Duchess0.67
66Fairgrounds1.25175Poor House0.67
67Knights1.25176Cutpurse0.66
68Candlestick Maker1.24177Oracle0.65
69Butcher1.24178Rogue0.65
70Hermit1.24179Mine0.64
71Bishop1.23180Pillage0.63
72Bandit Camp1.23181Stash0.63
73Margrave1.21182Woodcutter0.61
74Walled Village1.21183Talisman0.60
75Caravan1.20184Masterpiece0.59
76Apprentice1.20185Outpost0.59
77Apothecary1.19186Secret Chamber0.58
78Hoard1.18187Merchant Ship0.58
79Bazaar1.18188Graverobber0.58
80Village1.17189Fortune Teller0.58
81Haggler1.17190Saboteur0.57
82Warehouse1.16191Tribute0.57
83Counterfeit1.15192Herbalist0.55
84Salvager1.15193Bureaucrat0.55
85Laboratory1.14194Treasure Map0.54
86Embassy1.14195Cache0.54
87Merchant Guild1.14196Philosopher's Stone0.53
88Menagerie1.14197Mandarin0.52
89Crossroads1.12198Explorer0.52
90Stables1.11199Navigator0.52
91Ironworks1.11200Thief0.51
92Mining Village1.11201Pirate Ship0.50
93Spice Merchant1.11202Adventurer0.50
94Possession1.11203Transmute0.49
95Quarry1.10204Royal Seal0.48
96Farming Village1.09205Chancellor0.47
97Golem1.08206Harvest0.45
98Shanty Town1.08207Scout0.45
99Tactician1.07208Contraband0.42
100Trader1.07209Coppersmith0.39
101Monument1.05210Counting House0.38
102Scheme1.05211Copper0.00
103Courtyard1.05212Duchy0.00
104Embargo1.05213Silver0.00
105Island1.04214Gold0.00
106Native Village1.04215Curse0.00
107Militia1.04216Province0.00
108Altar1.03217Estate0.00
109Horse Traders1.03

Edit: fixed Colony and Platinum, which were calculated incorrectly.
« Last Edit: April 30, 2018, 01:26:22 pm by trivialknot »
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Awaclus

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Re: Data Mining: Card Impact Factor
« Reply #1 on: April 29, 2018, 03:51:59 am »
+8

This data predates Adventures, so cards only go up to Guilds.


More importantly than cards only going up to Guilds, the data was collected back when everyone sucked at the game.
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markus

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Re: Data Mining: Card Impact Factor
« Reply #2 on: April 29, 2018, 05:03:00 am »
0

I don't think that this measure is useful. If I understand it correctly, it is high when you're more likely to gain all other cards in its presence.
Wouldn't that at first glance mean that the card is weak, because I'm more likely to want other cards?
Junkers make people gain Curses, Ruinss, etc, such that they end up high on the list, but not because people want to gain those cards.
Or it really favours engines, such that I want to gain a lot of different cards.

In the end, I can maybe explain why a card has a high or low impact factor, but I wouldn't know the reason, without knowing the card.

I think a more useful version would define categories for cards (Village, Smithy,...) and calculate the impact on those, e.g. am I more likely to gain Villages in the presence of Rebuild or not.
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Titandrake

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Re: Data Mining: Card Impact Factor
« Reply #3 on: April 29, 2018, 05:53:02 am »
+2

I don't think that this measure is useful. If I understand it correctly, it is high when you're more likely to gain all other cards in its presence.
Wouldn't that at first glance mean that the card is weak, because I'm more likely to want other cards?
Junkers make people gain Curses, Ruinss, etc, such that they end up high on the list, but not because people want to gain those cards.
Or it really favours engines, such that I want to gain a lot of different cards.

In the end, I can maybe explain why a card has a high or low impact factor, but I wouldn't know the reason, without knowing the card. The theory is that this is a proxy for measuring how much a card changes what you'd be planning to do.

I think a more useful version would define categories for cards (Village, Smithy,...) and calculate the impact on those, e.g. am I more likely to gain Villages in the presence of Rebuild or not.

A card is high on the list if it is likely to change what cards you gain. So the impact factor goes up both if a card's presence makes you want to gain more of a card, or less of a card.

Things that gain other cards (Cursers, Ruins givers) may be over-represented. That's probably why Tunnel is so high, for example.

idk, I think there are some interesting things in there. Colony and Platinum being so high is some interesting commentary on how strategy changes in Colony games.
« Last Edit: April 29, 2018, 05:54:09 am by Titandrake »
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markus

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Re: Data Mining: Card Impact Factor
« Reply #4 on: April 29, 2018, 05:58:46 am »
0

I missed that the absolute amount of change is added up.
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terminalCopper

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Re: Data Mining: Card Impact Factor
« Reply #5 on: April 29, 2018, 06:36:51 am »
0

Colony and Platinum being so high is some interesting commentary on how strategy changes in Colony games.

I don‘t think the presence of Colonies has a huge impact on the chosen strategy. If I understand the maths correctly, I assume that Colony games are merely longer, and therefore more cards are bought.
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markusin

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Re: Data Mining: Card Impact Factor
« Reply #6 on: April 29, 2018, 08:10:27 am »
0

Colony and Platinum being so high is some interesting commentary on how strategy changes in Colony games.

I don‘t think the presence of Colonies has a huge impact on the chosen strategy. If I understand the maths correctly, I assume that Colony games are merely longer, and therefore more cards are bought.

I don't know if Colony games are all that much longer by a number of turns metric. I think it's mostly that Colony games increase the amount you want to build, so you likely have more cards being gained overall.
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markusin

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Re: Data Mining: Card Impact Factor
« Reply #7 on: April 29, 2018, 08:11:56 am »
0

This data predates Adventures, so cards only go up to Guilds.


More importantly than cards only going up to Guilds, the data was collected back when everyone sucked at the game.

Man, forget Loan, look at Harem's placement here. Edit: okay maybe Harem wasn't so bad back before Adventures came out.

It feels like this metric is good at finding the cards that warp what you do on the board, but not so good at highlighting the cards where you naturally get one at convenience just because it's usually better than not getting it regardless of what you're doing, such as with Junk Dealer, Spice Merchant, Upgrade, Militia, and Ghost Ship.
« Last Edit: April 29, 2018, 08:20:14 am by markusin »
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trivialknot

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Re: Data Mining: Card Impact Factor
« Reply #8 on: April 29, 2018, 10:44:08 am »
0

A card is high on the list if it is likely to change what cards you gain. So the impact factor goes up both if a card's presence makes you want to gain more of a card, or less of a card.

Things that gain other cards (Cursers, Ruins givers) may be over-represented. That's probably why Tunnel is so high, for example.
Correct, it looks at the absolute change in gain percentages.  And I agree that it over-represents cards that make you gain other cards, especially Coppers, Curses, Ruins, Estates--things you wouldn't otherwise gain.

More importantly than cards only going up to Guilds, the data was collected back when everyone sucked at the game.
Also correct.

I don‘t think the presence of Colonies has a huge impact on the chosen strategy. If I understand the maths correctly, I assume that Colony games are merely longer, and therefore more cards are bought.
I don't look at the total number cards gained from each pile, just the percentage chance that at least one card was gained from each pile.  I also tried analysis where I looked at the total number of cards gained.  The number one ranked card was Ill-Gotten Gains, and well you can see which method I decided to stick with.

I think Colony is high primarily because it increases the gain percentage of 2 supply piles: Colony and Platinum.
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Re: Data Mining: Card Impact Factor
« Reply #9 on: April 29, 2018, 11:59:36 am »
0

Have you considered other normalizations for kingdom piles? How does this list change if you give them the same weight as for basic supply piles?
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trivialknot

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Re: Data Mining: Card Impact Factor
« Reply #10 on: April 29, 2018, 12:40:25 pm »
0

Have you considered other normalizations for kingdom piles? How does this list change if you give them the same weight as for basic supply piles?
Yes this is really easy to do, and I'm willing to post results for alternative analysis.  The hard part is actually just thinking out a mathematical formula that makes sense.

The current formula is:
Quote
Impact(supply pile X) = Sum over supply pile Y abs( P(gain Y|X and Y are in supply) * P(Y is in supply|X is in supply) - P(gain Y|Y is in supply)*P(Y is in supply) )

I was thinking that I could try an alternate formula like this:
Quote
Impact(supply pile X) = Sum over supply pile Y abs( P(gain Y|X and Y are in supply) - P(gain Y|Y is in supply) )
This would eliminate the weight given to base cards (or e.g. Potions in the case of potion cards), but also it would eliminate the contribution of each card to its own impact factor.  Is this calculation something people would be interested in seeing?

Another thing I wanted to do was take the impact vectors, and apply Principal Component Analysis.  This would identify a few dimensions that can be used to differentiate cards.  But I'm waffling on how I should define the impact vector.
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Re: Data Mining: Card Impact Factor
« Reply #11 on: April 29, 2018, 12:59:43 pm »
+1

This data predates Adventures, so cards only go up to Guilds.


More importantly than cards only going up to Guilds, the data was collected back when everyone sucked at the game.

And the proof is that there are cards lower than Scout.
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Re: Data Mining: Card Impact Factor
« Reply #12 on: April 30, 2018, 04:56:05 am »
+1

I don't like the own-effect of the impact factor, because the presence of the card in the kingdom shouldn't affect the average probability to gain it.

But shouldn't it be smaller for cards that show up more frequently (Platinum), as it boils down to:
P(gain X|X is in supply) * (1 - P(X is in supply)),
and P(X is in supply) is higher for Platinum? (It can be offset by a higher probability of gaining Platinum.)

The other thing that I noticed with the current formulat is that a card Y that is gained independently of all other cards, still contributes to their impact factors:
P(gain Y|Y is in supply) * (P(Y is in supply|X is in supply) - P(Y is in supply) )

In that sense, I like the alternate formula more than the current one.

Wishlist:
1) Also show a version that excludes Copper, Curse, Ruins, Estate (am I missing something?)
2) For each card, show the top 3 cards that contribute the most in a positive or in a negative way to the impact factor.
3) I (still) would like to see the impact factor (and number of cards gained from that pile) for categories of cards.

4) Analysis with games from Shuffle iT.
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trivialknot

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Re: Data Mining: Card Impact Factor
« Reply #13 on: April 30, 2018, 11:18:28 am »
0

I don't like the own-effect of the impact factor, because the presence of the card in the kingdom shouldn't affect the average probability to gain it.
It made sense to me because the idea was to see how much the card changes your gains, and surely the presence of a card changes your ability to gain itself.  But I can calculate it the other way too.

But shouldn't it be smaller for cards that show up more frequently (Platinum), as it boils down to:
P(gain X|X is in supply) * (1 - P(X is in supply)),
and P(X is in supply) is higher for Platinum? (It can be offset by a higher probability of gaining Platinum.)
Not quite.  The own-effect for Duke is about %Duke*0.95, and the own-effect for Platinum/Colony is (%Platinum+%Colony)*0.875.

The other thing that I noticed with the current formulat is that a card Y that is gained independently of all other cards, still contributes to their impact factors:
P(gain Y|Y is in supply) * (P(Y is in supply|X is in supply) - P(Y is in supply) )
That is technically true, but what I didn't tell you is that P(Y is in supply|X is in supply) is just a number I hard-coded in.  I didn't bother taking into account the fact that if X takes up a slot in the kingdom, it decreases the probability of Y.  But that's a really good point, if my formula includes such an effect, does the formula even make sense?

Wishlist:
1) Also show a version that excludes Copper, Curse, Ruins, Estate (am I missing something?)
2) For each card, show the top 3 cards that contribute the most in a positive or in a negative way to the impact factor.
3) I (still) would like to see the impact factor (and number of cards gained from that pile) for categories of cards.

4) Analysis with games from Shuffle iT.
I can do 1) and 2) fairly easily, although I'm thinking that I should also remove the other base cards and Potion.  I feel like it doesn't make sense to put synergy with Duchy on the same level as synergy with Count, because Duchy is in every game.  I could keep in Platinum and Colony because those are only 2.5x as likely to show up.

For 3) the difficulty is whose card categories do I use?  I hope that the PCA analysis, when I do it, will provide some insight into card categories.

AFAIK Shuffle IT data doesn't exist.
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trivialknot

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Re: Data Mining: Card Impact Factor
« Reply #14 on: April 30, 2018, 01:25:06 pm »
+16

Introducing the synergy factor!

The synergy factor of a supply pile is the sum of the absolute changes in the gain percentages of other kingdom piles, due to this supply pile's presence.  That means I don't count the contribution from base cards, Potions, Ruins, Platinum/Colonies, or from the card itself.  The math also ends up excluding the contribution of potion cards to Potion, and the contribution of Looters to Ruins.  Finally, I left out Prince and Walled Village because there's less data for them and it was impacting statistics in a bad way. 

Furthermore, for each card I show the top 2 synergies, and top anti-synergy.  While these are interesting, keep in mind the error margins can be larger than the differences between the top few synergies.

RankCardSynergy FactorTop synergy          2nd synergy          Top anti-synergy         
1Rebuild25.8Feodum0.25Feast0.24Laboratory-0.34
2Chapel16.9Treasure Map0.29Market Square0.14Lookout-0.42
3JackOfAllTrades16.9Feodum0.21Duke0.13Sea Hag-0.30
4Governor16.8Rats0.19Militia0.18Bandit Camp-0.34
5Cultist16.6Death Cart0.18Trader0.16Rabble-0.27
6Masquerade16.6Possession0.15Bandit Camp0.12Sea Hag-0.39
7Wharf16.6Bank0.18Quarry0.17Catacombs-0.33
8University16.1Library0.30Journeyman0.26Quarry-0.13
9Ill-Gotten Gains15.8Trader0.20Gardens0.17Festival-0.22
10Minion15.2Lighthouse0.18Horse Traders0.17Ghost Ship-0.31
11Goons14.3Quarry0.22Native Village0.22Hoard-0.26
12Fishing Village13.8Envoy0.28Smithy0.26Village-0.33
13Fool's Gold13.4Storeroom0.17Nomad Camp0.16Peddler-0.19
14Fairgrounds13.1Death Cart0.19Spy0.18Chapel-0.02
15Ambassador13.1Lighthouse0.17Native Village0.13Sea Hag-0.37
16Mountebank12.6Trader0.23Watchtower0.22Witch-0.30
17Tournament12.2Band of Misfits0.16Tactician0.10Bridge-0.21
18Prince12.0Oracle0.30Quarry0.24Jester-0.21
19Steward12.0Bandit Camp0.10Bazaar0.10Lookout-0.26
20Forager11.9Poor House0.18Fool's Gold0.16Trade Route-0.37
21Sea Hag11.9Moat0.17Lighthouse0.17Familiar-0.32
22Border Village11.8Rabble0.26Journeyman0.24Nobles-0.13
23Torturer11.7Lighthouse0.17University0.14Rabble-0.27
24Remake11.5Poor House0.32Fortress0.13Moneylender-0.28
25King's Court11.5Saboteur0.27Woodcutter0.21Bank-0.17
26Scrying Pool11.4Storeroom0.21Woodcutter0.21JackOfAllTrades-0.17
27Urchin11.4Fortress0.16Lighthouse0.10Lookout-0.26
28Wandering Minstrel11.2Workshop0.21Armory0.19Farming Village-0.30
29Walled Village11.2Hunting Grounds0.24Council Room0.23Advisor-0.19
30Hunting Party11.2Altar0.15Horn of Plenty0.15Laboratory-0.26
31Plaza11.0Library0.22Watchtower0.18Mining Village-0.31
32Gardens10.9Beggar0.39Workshop0.26Apprentice-0.13
33Swindler10.7Masterpiece0.30Chancellor0.28Fool's Gold-0.16
34Tunnel10.5Storeroom0.28Embassy0.22Militia-0.19
35Fortress10.4Procession0.20Develop0.19Worker's Village-0.15
36Black Market10.3Fairgrounds0.17Quarry0.13Smugglers-0.18
37City10.2University0.18Bridge0.16Cartographer-0.18
38Worker's Village10.2Catacombs0.21Torturer0.21Mining Village-0.21
39Witch10.2Lighthouse0.15Trader0.14Torturer-0.26
40Highway10.1Talisman0.21Ironworks0.18Mystic-0.19
41Familiar10.0Transmute0.25Golem0.20Witch-0.13
42Vineyard9.9Herbalist0.24Rats0.23Cultist-0.18
43Baker9.9Altar0.11Count0.09Treasury-0.18
44Festival9.6Hunting Grounds0.22Watchtower0.21Market-0.17
45Ironmonger9.6Workshop0.22Ironworks0.17Farming Village-0.23
46Bazaar9.4Smugglers0.18Smithy0.16Treasury-0.14
47Village9.4Rabble0.18Smithy0.18Shanty Town-0.11
48Soothsayer9.4Lighthouse0.15Watchtower0.13Witch-0.24
49Marauder9.3Lighthouse0.13Death Cart0.12Militia-0.16
50Bridge9.3Native Village0.20Inn0.11Nomad Camp-0.25
51Squire9.1Torturer0.20Rabble0.19Native Village-0.14
52Margrave9.1Village0.15University0.15Ghost Ship-0.16
53Hamlet9.0Library0.21Smithy0.19Native Village-0.25
54Young Witch8.9Tunnel0.15Band of Misfits0.13Expand-0.23
55Herald8.9Armory0.26Workshop0.25Mining Village-0.13
56Grand Market8.9Quarry0.26Vault0.21Hoard-0.18
57Embassy8.8Tunnel0.11Farmland0.07Catacombs-0.18
58Bandit Camp8.8Envoy0.19Hunting Grounds0.16Festival-0.18
59Farming Village8.7Torturer0.20Hunting Grounds0.16Mining Village-0.20
60Upgrade8.5Rats0.31Poor House0.28Apprentice-0.18
61Colony8.5Mine0.13Taxman0.12Duke-0.24
62Platinum8.5Mine0.13Taxman0.12Duke-0.24
63Duke8.4Beggar0.21Bureaucrat0.15Possession-0.11
64Conspirator8.3Sage0.14Ironworks0.13Bank-0.11
65Junk Dealer8.3Market Square0.11Quarry0.09Trading Post-0.26
66Butcher8.3Rats0.23Fortress0.12Remodel-0.18
67Caravan8.2Workshop0.26Ironworks0.23Advisor-0.22
68Market Square8.2Apprentice0.17Vineyard0.11Worker's Village-0.15
69Mining Village8.2Torturer0.18Rabble0.16Fortress-0.16
70Lighthouse8.2Mint0.11Horn of Plenty0.08Moat-0.20
71Bishop8.1Fortress0.19Rats0.18Gardens-0.18
72Laboratory8.0Altar0.15University0.15Mystic-0.15
73Salvager7.9Rats0.19Fortress0.12Remodel-0.20
74Native Village7.8Bridge0.19Torturer0.15Pearl Diver-0.16
75Knights7.8Moat0.16Rogue0.15Duke-0.17
76Apprentice7.8Rats0.30Fortress0.16Gardens-0.13
77Envoy7.7Inn0.14Worker's Village0.09Nomad Camp-0.14
78Horn of Plenty7.7Spy0.16Journeyman0.15Workshop-0.05
79Stash7.7Envoy0.15Scavenger0.13Market-0.11
80Hermit7.7Market Square0.12Wishing Well0.11Sea Hag-0.17
81Stables7.6University0.11Altar0.09Mystic-0.16
82Trader7.6Feodum0.38Duke0.11Sea Hag-0.18
83Quarry7.5Market0.16Forge0.15Trader-0.09
84Crossroads7.5Torturer0.17Great Hall0.14Native Village-0.14
85Alchemist7.4Possession0.22Transmute0.17Smithy-0.12
86Tactician7.4Storeroom0.18Secret Chamber0.16Soothsayer-0.11
87Peddler7.4Worker's Village0.13Salvager0.12Fool's Gold-0.09
88Monument7.4Golem0.12Band of Misfits0.10Scavenger-0.16
89Menagerie7.3Ironworks0.14Outpost0.13Envoy-0.12
90Ruins7.3Fairgrounds0.09Watchtower0.09Baron-0.12
91Haggler7.1Mining Village0.14Spy0.13Rogue-0.11
92Count7.0Duke0.18Grand Market0.05Trading Post-0.16
93Candlestick Maker7.0Vineyard0.16Peddler0.12Pawn-0.21
94Ironworks7.0Silk Road0.23Gardens0.21Armory-0.19
95Merchant Guild6.9Quarry0.10Golem0.09Nomad Camp-0.12
96Embargo6.9Stash0.11Venture0.10Pawn-0.11
97Golem6.9Apothecary0.17Saboteur0.12Throne Room-0.07
98Throne Room6.8Armory0.13Band of Misfits0.13Mining Village-0.08
99Procession6.8Adventurer0.17Catacombs0.15Horn of Plenty-0.06
100Apothecary6.7Possession0.20Golem0.19Loan-0.11
101Altar6.7Stash0.16Mystic0.16Expand-0.10
102Spice Merchant6.7Fool's Gold0.11Market Square0.09Moneylender-0.24
103Militia6.6Band of Misfits0.12Lighthouse0.11Cutpurse-0.18
104Counterfeit6.6Fool's Gold0.10Envoy0.10Loan-0.14
105Ghost Ship6.6Farming Village0.14Lighthouse0.13Militia-0.11
106Feodum6.6Masterpiece0.41Trader0.30Throne Room-0.10
107Market6.5Quarry0.19Conspirator0.11Band of Misfits-0.10
108Horse Traders6.4Tunnel0.11Gardens0.10Nomad Camp-0.15
109Warehouse6.4Tunnel0.17Treasure Map0.12Oasis-0.18
110Rabble6.3University0.12Village0.12Library-0.10
111Shanty Town6.3Rabble0.14Council Room0.13Wishing Well-0.12
112Doctor6.3Venture0.09Merchant Ship0.08Lookout-0.20
113Jester6.3Spy0.09Native Village0.08Rogue-0.12
114Watchtower6.2Festival0.13Rats0.11Oracle-0.11
115Nobles6.2Quarry0.20Trade Route0.13Harem-0.14
116Courtyard6.2Worker's Village0.08Bandit Camp0.07Pearl Diver-0.17
117Moneylender6.2Venture0.09Stash0.09Cutpurse-0.14
118Inn6.1Torturer0.13Hunting Grounds0.13Cartographer-0.10
119Vault6.1Grand Market0.10Tunnel0.09Envoy-0.12
120Lookout6.1Mystic0.09Treasure Map0.09Loan-0.18
121Silk Road6.0Workshop0.16Baron0.14Laboratory-0.08
122Hoard5.9Harem0.13Silk Road0.12Conspirator-0.09
123Smugglers5.9Apprentice0.10Duke0.09Workshop-0.07
124Vagrant5.9Vineyard0.09Harem0.08Pearl Diver-0.24
125Trading Post5.9Feodum0.12Grand Market0.10Altar-0.11
126Possession5.9Apothecary0.20Alchemist0.17Conspirator-0.09
127Island5.8Ironworks0.20Hoard0.10Remodel-0.11
128Haven5.7Envoy0.10Treasure Map0.08Pearl Diver-0.21
129Forge5.7Rats0.12Catacombs0.10Gardens-0.11
130Beggar5.7Gardens0.25Counting House0.13Fortress-0.08
131Journeyman5.7Horn of Plenty0.07Bank0.07Council Room-0.12
132Masterpiece5.6Feodum0.32Gardens0.15Cellar-0.08
133Remodel5.6Rats0.14Fool's Gold0.13Horn of Plenty-0.08
134Stonemason5.5Catacombs0.10Feodum0.09Altar-0.07
135Cellar5.5Tunnel0.12Bureaucrat0.08Pearl Diver-0.15
136Smithy5.5Festival0.09Village0.09Envoy-0.18
137Workshop5.4Gardens0.15Silk Road0.13Stonemason-0.08
138Feast5.4Stash0.09Witch0.07Fortress-0.07
139Storeroom5.2Tunnel0.12Tactician0.10Woodcutter-0.11
140Pawn5.2Vineyard0.11Stash0.09Pearl Diver-0.19
141Catacombs5.2University0.10Bank0.08Journeyman-0.13
142Scheme5.2Conspirator0.12Armory0.09Wishing Well-0.16
143Nomad Camp5.2Golem0.09Highway0.07Woodcutter-0.10
144Rats5.2Apprentice0.14Butcher0.14Spice Merchant-0.07
145Expand5.2Rats0.09Marauder0.08Bank-0.09
146Library5.2Festival0.09University0.09Envoy-0.10
147Armory5.2Advisor0.12Vineyard0.12Workshop-0.12
148Venture5.1Altar0.09Bank0.08Graverobber-0.10
149Trade Route5.1Band of Misfits0.08Scrying Pool0.07Develop-0.11
150Baron5.0Silk Road0.10Cartographer0.07Nomad Camp-0.11
151Treasury5.0University0.09Expand0.08Mystic-0.10
152Hunting Grounds5.0Native Village0.10Worker's Village0.09Council Room-0.09
153Sage5.0Trader0.07Golem0.07Wishing Well-0.11
154Advisor4.9Armory0.19Ironworks0.14Spy-0.09
155Scavenger4.9Stash0.20Lookout0.07Navigator-0.12
156Council Room4.9Bank0.11Village0.09Library-0.07
157Wishing Well4.9Mystic0.08Horn of Plenty0.07Sage-0.10
158Moat4.9Harem0.07Festival0.07Pawn-0.10
159Develop4.9Rats0.15Poor House0.13Envoy-0.10
160Oasis4.8Tunnel0.13Soothsayer0.07Wishing Well-0.12
161Woodcutter4.8Ill-Gotten Gains0.08Gardens0.08Baron-0.06
162Pirate Ship4.8Oasis0.10Merchant Ship0.08Envoy-0.12
163Adventurer4.8Stash0.08Venture0.08Peddler-0.06
164Cutpurse4.7Hoard0.08Band of Misfits0.07Navigator-0.09
165Great Hall4.7Ironworks0.19Silk Road0.13Sage-0.10
166Talisman4.7Feodum0.11Highway0.09Smugglers-0.07
167Taxman4.7Harem0.09Soothsayer0.08Moneylender-0.08
168Bureaucrat4.6Feodum0.11Duke0.09Vineyard-0.06
169Secret Chamber4.6Stash0.09Tactician0.08Poor House-0.07
170Herbalist4.6Philosopher's Stone0.14Stash0.09Moat-0.07
171Cache4.6Monument0.07Young Witch0.07Conspirator-0.07
172Loan4.6Venture0.08Baker0.07Oracle-0.07
173Mystic4.6Altar0.08Rebuild0.07Tribute-0.10
174Band of Misfits4.6Duke0.07Margrave0.06Bishop-0.10
175Mint4.5Fool's Gold0.08Harem0.06Trading Post-0.08
176Transmute4.5Trader0.08Apothecary0.08Stash-0.06
177Thief4.5Venture0.10Familiar0.08Stonemason-0.07
178Harem4.5Silk Road0.13Hoard0.09Ironworks-0.07
179Farmland4.5Trader0.09Silk Road0.07Band of Misfits-0.06
180Philosopher's Stone4.4Herbalist0.14Duke0.09Throne Room-0.11
181Mine4.4Harem0.09Catacombs0.08Band of Misfits-0.05
182Bank4.4Venture0.12Tactician0.07Vineyard-0.07
183Harvest4.4Hoard0.07Duke0.07Highway-0.05
184Chancellor4.4Envoy0.10Stash0.10Quarry-0.04
185Cartographer4.4Tunnel0.12Moneylender0.06Bazaar-0.09
186Oracle4.4Ill-Gotten Gains0.09Venture0.07Fortune Teller-0.09
187Rogue4.3Soothsayer0.08Doctor0.07Candlestick Maker-0.07
188Pearl Diver4.3Cartographer0.07Jester0.07Lighthouse-0.09
189Noble Brigand4.3Beggar0.09Venture0.07Ironworks-0.05
190Duchess4.3Stash0.12Venture0.07Workshop-0.08
191Contraband4.3Expand0.09Envoy0.08Festival-0.06
192Spy4.3Doctor0.08Golem0.07Quarry-0.07
193Outpost4.3Trading Post0.07Navigator0.07Horn of Plenty-0.05
194Saboteur4.3Embargo0.07Sage0.07Armory-0.07
195Royal Seal4.2Cartographer0.08Venture0.07Stash-0.07
196Navigator4.2Tunnel0.08Farmland0.08Oasis-0.07
197Tribute4.2Ghost Ship0.09Familiar0.07Pillage-0.05
198Treasure Map4.2Chapel0.07Sea Hag0.07Throne Room-0.08
199Death Cart4.1Rats0.11Band of Misfits0.07Nomad Camp-0.08
200Scout4.1Harem0.08Band of Misfits0.07Quarry-0.06
201Counting House4.1Beggar0.10Treasury0.08Tactician-0.05
202Poor House4.1Vault0.09Island0.06Remake-0.09
203Mandarin4.0Mint0.07Familiar0.07Envoy-0.07
204Fortune Teller4.0Ill-Gotten Gains0.07Mystic0.06Poor House-0.05
205Merchant Ship4.0Marauder0.06Inn0.06Harvest-0.06
206Coppersmith3.9Apothecary0.07Council Room0.06Quarry-0.07
207Pillage3.9Alchemist0.08Hoard0.06Saboteur-0.06
208Graverobber3.9Rats0.08Marauder0.07Possession-0.06
209Explorer3.9Duke0.07Silk Road0.06Envoy-0.08
210Potion3.2Herbalist0.08Woodcutter0.07Quarry-0.04
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AJD

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Re: Data Mining: Card Impact Factor
« Reply #15 on: April 30, 2018, 02:08:21 pm »
+1

I don't like the own-effect of the impact factor, because the presence of the card in the kingdom shouldn't affect the average probability to gain it.
It made sense to me because the idea was to see how much the card changes your gains, and surely the presence of a card changes your ability to gain itself.

Yeah, to put it another way, if, in a game with Counting House, you're not much more likely to gain Counting House than you are in a game without Counting House, that's evidence that Counting House is a fairly low-impact card whose presence on the board doesn't usually matter.
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ben_king

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Re: Data Mining: Card Impact Factor
« Reply #16 on: April 30, 2018, 03:09:25 pm »
+3

I love that Swindler's top synergies are terrible cards that you get Swindled into.
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markus

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Re: Data Mining: Card Impact Factor
« Reply #17 on: April 30, 2018, 05:11:41 pm »
+1

I don't like the own-effect of the impact factor, because the presence of the card in the kingdom shouldn't affect the average probability to gain it.
It made sense to me because the idea was to see how much the card changes your gains, and surely the presence of a card changes your ability to gain itself.
Yeah, to put it another way, if, in a game with Counting House, you're not much more likely to gain Counting House than you are in a game without Counting House, that's evidence that Counting House is a fairly low-impact card whose presence on the board doesn't usually matter.
But that runs against the idea of "how much does the presence of the card change the gain probabilities of cards?". By that definition, the presence of Counting House doesn't affect the probability of gaining Counting House conditional on it being present.

I wouldn't call it "synergy factor", if it sums up the absolute values of synergy and anti-synergy.
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markusin

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Re: Data Mining: Card Impact Factor
« Reply #18 on: April 30, 2018, 05:31:37 pm »
+2

Remake's top synergy card: Poor House  ;)

Looking at the stats, it's a higher synergy pair than everything except Gardens/Beggar, Trader/Feodum, and Masterpiece/Feodum.
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markus

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Re: Data Mining: Card Impact Factor
« Reply #19 on: April 30, 2018, 06:39:37 pm »
0

For 3) the difficulty is whose card categories do I use?  I hope that the PCA analysis, when I do it, will provide some insight into card categories.
I know, that people can argue what defines a Village. I would suggest that you pick whatever definition you like. Given that most villages are uncontroversial, it shouldn't matter too much for the results.

I'm skeptical that PCA will deliver anything useful, but I'd be happy to be wrong about that.
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trivialknot

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Re: Data Mining: Card Impact Factor
« Reply #20 on: April 30, 2018, 06:49:09 pm »
0

Now that I have both these lists, here are my thoughts on interpretation.

The "Impact factor", while not perfect, is the best objective measure of "card strength" that I have seen so far.  In the gain percentage list, the top three cards were Tournament, Governor, and Border Village; here they are Rebuild, Mountebank, Goons.  And that seems to me a little more on point.  I bet if you compared this to the 2014 Qvist rankings you would find that they are a closer match.

But there is an obvious bias towards cards that either force or incentivize you to gain copper/curse/estate/ruins/potion.  I think dumping 10 curses into players decks should rightfully be considered impactful, but maybe not quite this much.

The synergies and anti-synergies are very interesting, and you can think up a reason for why almost every card on that list is there.*  I'm not sure the sum absolute value of synergies is especially meaningful though.

*ok, I have no idea why Duchess promotes Stash.

The synergy factor looks like the most promising data for PCA.  My prediction is that the first principal component will be "terminals vs villages".  The most villagey cards will be strong villages that encourage even weak terminal draw and weak terminal payload, while discouraging weak villages.  The least villagey cards will be strong terminal draw that encourage even weak villages, while discouraging weak terminal draw.
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Donald X.

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Re: Data Mining: Card Impact Factor
« Reply #21 on: April 30, 2018, 06:53:36 pm »
+2

For 3) the difficulty is whose card categories do I use?  I hope that the PCA analysis, when I do it, will provide some insight into card categories.
Hey you can use your math to figure out categories.

1. Each card determines a category. You won't actually do each card, because we care about e.g. villages rather than e.g. Poor Houses.
2. So, pick a card, e.g. Village.
3. Iterate through all other cards.
4. For each card, calculate the sum of the absolute value of the differences between gain percentages for Village and the other card, for all other cards. For example, for Poor House, first you say, okay how much does Village change the gain percentage for Ironworks, how much does Poor House change the gain percentage for Ironworks, take the absolute value of the difference; then, Forager, how much does Village change the gain percentage for Forager, how much does Poor House change the gain percentage for Forager, and so on. In the end you have this number that says, how similar in changing gain percentages is Poor House to Village.
5. Sort from lowest to highest; the ones at the top are the most similar to the chosen card, e.g. Village.
6. Draw the line where it looks like it goes.

This of course includes power level; a card we recognize as a village might be so weak that it's beaten by cards we are sure aren't villages. Still, could be fun.
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samath

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Re: Data Mining: Card Impact Factor
« Reply #22 on: April 30, 2018, 09:42:40 pm »
0

For 3) the difficulty is whose card categories do I use?  I hope that the PCA analysis, when I do it, will provide some insight into card categories.
Hey you can use your math to figure out categories.
In other words, you have a matrix of interaction strengths. Treat each column (or row, or some combination to account for interactions in both directions) as a vector, and run a clustering algorithm on the results. (Donald suggests measuring distance with the 1-norm, but you could probably use any reasonable norm. You might need to lower the dimensionality by random projection first.)
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Awaclus

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Re: Data Mining: Card Impact Factor
« Reply #23 on: May 01, 2018, 03:01:01 am »
+1

*ok, I have no idea why Duchess promotes Stash.

I do! When you gain a bunch of terminals for free, you don't have so much terminal space left so you'll buy Stash or Venture instead of a terminal $5. I don't think this effect would be at all visible today, but I'm like 90-93% sure that was really the reason in 2014.
« Last Edit: May 01, 2018, 03:02:08 am by Awaclus »
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Bomb, Cannon, and many of the Gunpowder cards can strongly effect gameplay, particularly in a destructive way

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markusin

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Re: Data Mining: Card Impact Factor
« Reply #24 on: May 01, 2018, 02:25:59 pm »
0

*ok, I have no idea why Duchess promotes Stash.

I do! When you gain a bunch of terminals for free, you don't have so much terminal space left so you'll buy Stash or Venture instead of a terminal $5. I don't think this effect would be at all visible today, but I'm like 90-93% sure that was really the reason in 2014.

Or like, on board where you go for a Stash deck and you buy Duchy, Duchess is a "might as well" addition. Or am I misinterpreting the statistic.
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