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[allenciox]

Just about all of you know about the link to the Councilroom "Popular Buys" page at  http://councilroom.com/popular_buys .  Looking at that, it struck me as interesting that a lot of very popular cards actually don't fare that well, if you compare "win rate with" to "win rate without" that card.  So I thought I would calculate an overvaluation rating, to indicate the cards that are often bought but have poor win rates.  Using the equation:

overvalue=p/(1-p)*(win_rate_wo-win_rate_with)

where p=pct. of time card was bought, here are the top ten overvalued cards, starting with the most overvalued (keep in mind that these stats precede Dark Ages and Guilds, so none of those cards are considered here):

1. Silver: pct.=87.8%, win rate with=.98, win rate wo=1.13.   Interestingly, those situations where silver is not bought does much better than when silver is  bought.  What does this mean?  I guess, think twice about buying silver if there are other good options available.  Perhaps it is generally better to buy two kingdom cards then buying that silver on your first two turns.   Does anybody else have a better interpretation of this?

2. Highway: pct=82.9%, win rate with=.98, win rate w/o=1.09.  Highway is deceptive.  Even though Highway is rated right in the middle at 25th out of 48 5-cost cards on latest Qvist rankings, Councilroom evidence is that the rare individual that stays away from it does much better.  Why?  I guess it is no better than Peddler without a source of buy, and at a cost of 5, there are likely better choices in the kingdom available at the 5 cost point.

3. Worker's Village!: pct=84.9%, win rate with=.99, win rate w/o=1.07.  Considered one of the best villages, what a surprise this one is!   By itself, it takes care of two of the necessary items for an engine: +actions and +buy.  But does that justify its use 85% of the time?  It is rated 17th out of 53 of the top 4-cost cards in Qvist rankings. 

4. Throne Room: pct=73.4%, win rate with=.96, win rate w/o=1.12.  Interestingly, while the stats show that King's Court is generally an excellent buy, it's younger brother should generally be skipped.  Throne Room is ranked 15th in the top 4-cost cards in the Qvist rankings.  Why is it so overrated?  Well, I can only speak for myself... it is alarming how often my Throne Room appears in a hand with no other actions, in which case it is a dead card. 

5. Black Market: pct=71.0%, win rate with=.95, win rate w/o=1.13.  Black Market may be the "funnest" card in the game, but if you are playing to win, evidence shows that most of the time you should pass it by.

6. Bridge: pct=77.0%, win rate with=.97, win rate w/o=1.10.  Hmmm, are you starting to notice a pattern here?  All of the cards so far, including this one, are used heavily in engines.  Perhaps the temptation to build engines when they are not the best choice is too high?  Bridge is rated all the way up to 10th out of 53 4-cost cards in the Qvist rankings. 

7. University: pct=63.8%, win rate with=.92, win rate w/o=1.13.  Another village good for engines, it requires a side step to buy a potion as well.  It is doubtful that that should warrant a 63.8% usage rate, especially considering the 21% win rate difference between those using it and those not. 

8.  Pirate Ship: pct=52.1%, win rate with=.84, win rate w/o=1.16. A whopping 32% win rate difference shows what a trap card this can be.   I guess "boys" like to be pirates.  Then they get whipped by the men on the other side of the table.

9. Festival: pct=83.1%, win rate with=.99, win rate w/o=1.06.  What a surprise this one is to me!  On a card that is almost always better than silver.  But people are likely to bypass better 5-cost cards, I guess.  I suspect that people are buying it too often, this card might be better passed up unless building an engine.  Festival is rated 28th out of 61 5-cost cards in the Qvist rankings.

10. City: pct=80.9%, win rate with=.99, win rate w/o=1.06.  Until one or more stacks are emptied, this is just an expensive village.  City is rated 34th out of 61 5-cost cards in the Qvist rankings.

Honorable Mentions: (11th-15th, in order): Great Hall, Village, Smugglers, Walled Village, Farming Village.

General comments:  Notice that the top 15 has 7 villages and almost all the cards are best used in engines [and the next eight includes 3 more villages].  I suspect that people are trying to force engines on boards that are best suited to "big money", since engines are fun to build.  At least I know that I am oriented this way.  It doesn't mean that these cards are never good.  Thirteen of the fifteen cards are bought at least 70% of the time.  Perhaps people are assuming that by themselves, they make an engine, rather than that all the pieces are there. 

I would be interested in other's take on these statistics.  By the way, this is my first post on these forums!

Jim

[SirPeebles]

1. Silver: pct.=87.8%, win rate with=.98, win rate wo=1.13.   Interestingly, those situations where silver is not bought does much better than when silver is  bought.  What does this mean?  I guess, think twice about buying silver if there are other good options available.  Perhaps it is generally better to buy two kingdom cards then buying that silver on your first two turns.   Does anybody else have a better interpretation of this?

My interpretation is that Silver usually a good buy, but if you can spot those relatively rare instances in which Silver is unnecessary, then you are more likely to win.  Alternatively, the games in which one doesn't buy Silver may correspond disproportionately to games where one receives at 5/2 open, thereby gaining a key $5 card without opening Silver. 

[jsh357]

Welcome.

Well, one thing to keep in mind nowadays is that CR is based on only isotropic games and doesn't factor in Dark Ages, Guilds, and more importantly, players being better at the game than they were back then.  Highway stands out as a card that seemed so great when Hinterlands came out but has settled in to its value over time.  I would say that engines are stronger now than they were, at least in most games.

Also, with cards like Silver and Worker's Village: these are cards that you'll pick up in most games regardless, so the win rates are definitely hard to make conclusions out of looking at stats.  It's unwise to see Silver having a high loss rate and assume you should avoid it whenever possible.  There are plenty of games where it's a necessary component.  And of course, cards like Black Market and Pirate Ship tend to be ones that are best played with a concrete plan or are very swingy, which might make them appear overrated when they are simply misplayed.

[allenciox]

Thanks for your comments, jsh.  You make an excellent point that play has improved since Isotropic ended.  I also agree that Dark Ages makes engines more viable.  The only thing I would question is the statement that silver and Worker's Village are cards you will pick up in most games regardless.  I would think that these stats indicate that  lot of these cards (e.g. Worker's Village) should not be always acquired, perhaps unless you are building an engine and an engine is the best choice on that board.

[toaster]

1. Silver: pct.=87.8%, win rate with=.98, win rate wo=1.13.   Interestingly, those situations where silver is not bought does much better than when silver is  bought.  What does this mean?  I guess, think twice about buying silver if there are other good options available.  Perhaps it is generally better to buy two kingdom cards then buying that silver on your first two turns.   Does anybody else have a better interpretation of this?

My interpretation is that Silver usually a good buy, but if you can spot those relatively rare instances in which Silver is unnecessary, then you are more likely to win.  Alternatively, the games in which one doesn't buy Silver may correspond disproportionately to games where one receives at 5/2 open, thereby gaining a key $5 card without opening Silver.

Silver buys also sometimes indicate that a player has failed to hit a key $5 on their second shuffle, which can also spell doom for them.

[jsh357]

Thanks for your comments, jsh.  You make an excellent point that play has improved since Isotropic ended.  I also agree that Dark Ages makes engines more viable.  The only thing I would question is the statement that silver and Worker's Village are cards you will pick up in most games regardless.  I would think that these stats indicate that  lot of these cards (e.g. Worker's Village) should not be always acquired, perhaps unless you are building an engine and an engine is the best choice on that board.

Well, my point is that the cards are acquired whether or not the player wins, which makes the stats hard to evaluate.  The same can be said for City and Festival, which also appear on the list.  A Village is useful in a good engine and usually found in a bad one too.  Certainly knowing how many villages you need is important, but you'll surely want some unless there are just no terminal actions worth buying on the board.  I agree it's useful to look at the hard numbers, but at least for me when I'm running a deck I don't think of it that way.  I think of whether or not the village is good for me or a wasted buy in that particular case.

Short version: Depends on the board, I guess.

[ftl]

Soon soon soon cr will be updated with goko things and then these numbers will be better! one of these days...

Just about all of you know about the link to the Councilroom "Popular Buys" page at  http://councilroom.com/popular_buys .  Looking at that, it struck me as interesting that a lot of very popular cards actually don't fare that well, if you compare "win rate with" to "win rate without" that card.  So I thought I would calculate an overvaluation rating, to indicate the cards that are often bought but have poor win rates.  Using the equation:

overvalue=p/(1-p)*(win_rate_wo-win_rate_with)

where p=pct. of time card was bought, here are the top ten overvalued cards, starting with the most overvalued (keep in mind that these stats precede Dark Ages and Guilds, so none of those cards are considered here):

1. Silver: pct.=87.8%, win rate with=.98, win rate wo=1.13.   Interestingly, those situations where silver is not bought does much better than when silver is  bought.  What does this mean?  I guess, think twice about buying silver if there are other good options available.  Perhaps it is generally better to buy two kingdom cards then buying that silver on your first two turns.   Does anybody else have a better interpretation of this?

I don't think this number, in particular, is an indication that "it is generally better to buy two kingdom cards than silver". Remember, you're calculating that it's overvalued, not that it's bad! I would agree that this may be an indication that you should skip silver more than 12.2% of the time, but that's still a low number - maybe you should skip silver entirely in one out of every 6 games rather than one out of every 8, or something.

Or it could be that the actual truth is a little more subtle. It means that when people deliberately skip silver, it's part of a deliberate strategic choice, whereas silver is sort of a default thing that you get when you don't know what you want to do and lose to someone who immediately goes for more focused cards.

[scott_pilgrim]

Interesting list.

I suspect that people are trying to force engines on boards that are best suited to "big money", since engines are fun to build.

I'm guessing that this is the main reason for most of the cards appearing on this list.  If you include DA and Guilds, most of the cards on the list become substantially better, just because of the increase of engine viability.  Before DA and Guilds existed, it seemed like there were a lot of players who would play engines on every board, even though so many boards just weren't good for engines.

It's not at all surprising that University, Pirate Ship, and City appeared on the list.  New players tend to really overrate these cards; I'm not sure why.

The big questionable card on the list is Silver, and I think SirPeebles's explanation is good.  Many (perhaps most?) games where you don't get Silver are games where you open 5/2, and most games where you open 5/2, and then never get a Silver for the rest of the game, are probably games in which a 5/2 opening is dominant.  The other games in which you don't get Silver are probably heavy engine boards, and it makes sense that there would be better options than Silver on those boards.

Bridge and Highway I'm guessing are both on the list because they tend to lead to a temptation to set up something super-awesome, where that thing is just not all that great or takes too long to set up.  In particular, trying to set up KC+bridge with no support, or highway+gainer with no +actions or +buy.

WV and Festival are probably on the list because players overrated engines before DA and Guilds came out.  I generally tend to think that Throne Room is an overrated card, so now I have a statistical measure to back me up.  And Black Market is probably purchased because people get more excited about the cards that they could be buying in the BM deck, whereas in reality, the odds are that you're not going to find what you need in the BM deck.  It especially becomes a temptation for players to buy lots of terminals from the BM deck, even if there's no good source of +actions on the board.

[eHalcyon]

Silver really is something that you get in almost every game.  Even when there are key $5s on the board, it is likely that you need 1-2 Silvers in order to get that first $5 card.  As has been pointed out, the fact that it is often gained by both the winners and the losers means that the win rates with and without are harder to evaluate.  Other scenarios have been mentioned -- maybe someone luckily opens 5/2 and is able to skip Silver and quickly jump to Gold (or whatever is important), and maybe someone who gets a bad shuffle (e.g. missing $5 before second reshuffle) takes Silvers as consolate prizes but never manages to catch back up.

I'm not sure how the win rates are calculated -- does it weight on how many of the cards are acquired?  If so, the win rate without on Silver may indicate the opposite of your overall conclusion -- people are playing too much big money (read: buying too many Silvers) when engines are viable.


Highway is possibly overrated.  Certainly price reduction sounds really great, but you need +Buy and quite a few Highways before it is actually meaningful.  I'm sure that there are some players who don't even realize that Highway is just Peddler without +Buy.


Throne Room is a tough card to play properly.  You say that you often draw TR with no other actions -- I submit that this suggests you are not playing TR properly.  You usually don't want TR unless you have decent action density.  If you ARE playing properly, then your statement may just be a case of negativity bias.


Black Market is a weird card.  You may be right that people are buying it simply because it is "funnest".  It may also be affected by the same thing that affects Silver -- that is, on weak boards, the best strategy may be to cobble something together out of the Black Market.  Every player goes for it but only one can succeed.  Also, I'm sure there are people who will go for Black Market hoping to pull something amazing and missing out on the nice reliable strategy that is available.


Bridge is only really worth it when you can play a fair amount of them.  I expect this is like Highway, where price reduction is shiny.


University is probably overrated by newer players.  Gaining $5 cards just sounds so great.  But it can be very slow to go with University, especially since it is less reliable as a Village given that it doesn't draw.


Pirate Ship is almost certainly overrated.  It is one of the top cards that look OP due to group think.  People play 3p/4p IRL and they think PS is powerful.  Everyone gets it and they destroy each others' decks until the only way to make any money is with PS.  It's a self-fulfilling prophecy.  Then they go online and play 2p against someone who knows what's up.  They go for PS and the other player thanks them for clearing out the Copper.


I would peg Festival to the same Silver problem.  It is almost always a better buy than Silver, and if you keep hitting $5 then Festival is a pretty safe, decent buy.


City is almost certainly overrated too.  Some people work hard to get lots of Cities and empty a pile (maybe City itself), but by the time they do the other player already has 5 Provinces.





Overall, the question is how you are defining "overrated".  You have Pirate Ship on this list, but IIRC it wasn't rated very highly on Qvist's list.  Even if I gain a lot of a card doesn't mean I rate it highly.  For example, I highly rate Chapel but I'll never buy more than one.  Cards like Caravan and Ironmonger are decent but not really standout, yet I will happily gain many of them and on plenty of different boards. 

[allenciox]

eHalcyon asked how I was defining overrated... it was from the formula I posted.  Basically, it is taking cards that have win_with_rate < win_without_rate, and multiplying that difference by an inverse of the percentage.  In English terms, it is going to favor cards that are most often played and that have a win_with_rate significantly lower than win_without_rate.  I think it indicates in many places that those cards are generally being played a greater percentage of the time than they "should" be.  It completely ignores number of times a card was acquired (or how it was acquired) just whether it was acquired at least once.

[eHalcyon]

Well I'm more confused about how CR does the win rates with and without.  I mean, you have rates there > 1.0, so does that mean greater than 100%?

My stupid may be showing here.

[allenciox]

If you go to the link I included in the first post, you can see their definitions... here is an excerpt copied from that link:

"% +" refers to the percentage of decks in which the card was bought or gained at least once.
Win Points are a measure of success. Players receive 0 for a loss, # players for a win, and draws are split evenly between the winners.
"Win Rate with" is the number of Win Points per game you get when you buy or gain at least one of this card.
"Win Rate without" is the number of Win Points per game you get when you never buy or gain the card.

[eHalcyon]

Ahhh.  So it gets bumped up due to 3p and 4p games.

FWIW, that makes this stuff even harder to evaluate.  Some cards are great in 2p but not as good with more players (e.g. many attack cards that don't stack, also cards that are only great if you manage to get lots of them).  Some other cards are bad in 2p but matter more with more players (e.g. Pirate Ship, especially in certain groups).

[allenciox]

You said, "it gets bumped up due to 3p and 4p games."  Not quite.  In a two person game with one winner, one person gets 2 points (since number of players is 2), and one gets 0 points. So the average is 1 point for each player.  In a four player game, the winner gets 4 points, and everyone else gets 0.  So the average is still 1 point for each player.  Across all cards, the average win_with_rate will be 1, and the average win_without_rate will also be 1.  Since the cards in my ranking are all played the majority of the time, the win_without_rate is always farther from 1 than the win_with_rate.

I completely agree that I wish they had separate ratings for 2 player vs. multiplayer games, as some cards, such as Pirate Ship, are much better multiplayer.  I just have to work with what I've got.  But still note that Pirate Ship has a huge difference in win rates, even though multiplayer games are included.

[eHalcyon]

You said, "it gets bumped up due to 3p and 4p games."  Not quite.  In a two person game with one winner, one person gets 2 points (since number of players is 2), and one gets 0 points. So the average is 1 point for each player.  In a four player game, the winner gets 4 points, and everyone else gets 0.  So the average is still 1 point for each player.  Across all cards, the average win_with_rate will be 1, and the average win_without_rate will also be 1.  Since the cards in my ranking are all played the majority of the time, the win_without_rate is always farther from 1 than the win_with_rate.

I completely agree that I wish they had separate ratings for 2 player vs. multiplayer games, as some cards, such as Pirate Ship, are much better multiplayer.  I just have to work with what I've got.  But still note that Pirate Ship has a huge difference in win rates, even though multiplayer games are included.

Eh?  That doesn't sound right.  In a 4p game, not every player will be counted for win_rate_with unless they all bought the card in question.  Likewise for win_rate_without, unless they all skipped it.  Or am I missing something?

[Beyond Awesome]

I know jsh brought it up, but old CR stats don't tell us as much about the game as we would like. The information is valuable but DA and Guilds really changes things. But, also having Shelters also shakes things up a lot. We really need a new CR to properly disseminate this kind of stuff.

[allenciox]

In a 4 player game, let's label the players a, b, c, and d.  Suppose a wins the game.  Each of the cards that player a acquired during the game will get a win_with score of 4.  Each of the cards that were possible to buy in that game that player a did not acquire will get a win_without score of 4.  No other cards get any points for any of the players.

So you are right that the 4 player game will "weight" the cards for the winner more heavily than a 2 player game will --- in fact, twice as much.

[StrongRhino]

I know jsh brought it up, but old CR stats don't tell us as much about the game as we would like. The information is valuable but DA and Guilds really changes things. But, also having Shelters also shakes things up a lot. We really need a new CR to properly disseminate this kind of stuff.

Hint hint 

[Awaclus]

I don't find it surprising that people overbuy splitters. Having your terminals collide is more annoying than having too many splitters, so people will rather have too many splitters because it makes them feel better.

[WanderingWinder]

Correlation does not imply causality.

[DG]

Silver has always been marked as an overbought card in the Council room. The alternatives to silver are usually cards like warehouse and wishing well that give an increase in deck cycling. This allows a much fast speed of deck development, better use of the starting cards (copper), and can also support an endgame strategy later. Silver is is an extra card in the deck to cycle through, is an extra card to clog up card combinations, doesn't add much if you are gaining cards instead of buying them, and is even worse in colony games.

I put together a nugget of Dominion wisdom once that isn't so far from the truth. Beginners first need to learn the value of gold. As they get better they find ways to deal with copper. As they master Dominion they may finally learn more about silver.

[SCSN]

These stats mean absolutely nothing as most games are played by atrocious players. When I started out I played every board as if it had Fairgrounds on it, and since I hadn't yet read How to Use the Village in Dominion, I needed extraordinary shuffle luck to not have terminal collision. Most players never progress beyond that stage.

[ConMan]

There are plenty of reasons why Silver could wind up so high. As well as the arguments already discussed, there's mid-to-late-game points where it may be better to pass your buy on a $3 hand, but it feels wasteful to do so (and hence the better players will be the ones who do pass), and other situations where a strong opponent has decimated your deck such that you need to rebuild your economy to have any chance of recovering (but even then it's probably not enough).

If we had some of these statistics over time, I suspect you'd see a lot of cards having a big jump in their win rates with and without a short time after their first appearance, as the more experienced players get over the "shiny new thing" mindset quicker and figure out how best to use them, while the lesser players are still mucking around with them.

[jomini]

You need to make a lot of assumptions to make any use out of this statistics. You are assuming that "strength" alone determines win rates. I'd submit that as important, and much more likely more are "ease of execution" (% of the time a player will make correct decisions for playing the optimal strategy), "obviousness" (% of the time the player will see a strong or optimal strategy for this card), and "resiliency" (how much this card reduces the impact of shuffle luck/opponent interference).

First and foremost, let's look at the player population pool. Say 10% of the player population is really good with Dominion allowing to accurately weight card strength and that this population played 3x as many games per player as the other 90%. That means that we have 40:90 ratio and hence good players were involved in 30.8% of games and other players were involved in 69.2% of games.

This means that in 42.6% of the game, you will have a Strong vs Weak player match-up. This means that in those games it is more important to minimize luck than to optimize card strength. Yeah the Remodel - Militia - Market - Village - Smithy engine beats big Money/Smithy, but as a strong player against a poor opponent (e.g. say just someone who buys Smithy/Market), you maybe should go for a more resilient Militia deck. Likewise, a poor player spamming village buys will often make the "optimal" counter strategy move from on card set to another. E.g. Hop decks are phenomenally strong, but against a village idiot you may not be able to get enough uniques in play to power up the Hop's - swap to BM/something resilient and clean up. Certainly cards that respond better to superior opponent play (Possession, Smugglers, Tribute, etc.) will get heavily depressed in these types of matches.

This also means that in 47.9% of games we have two poor players going at it. Here the winning set of cards may not actually show raw power, but rather ease of execution and obviousness. Take something like Smithy again. BM/Smithy is strong and +3 cards is obvious in its power and ease of play. Something fiddly, like Remodel -> Engine is a lot less obvious and a more difficult to pull off (when do I remodel a copper to a useful 2 and go from a gold to a semi-useful 5?) so even if one player sees the stronger combo (with "perfect" play) execution may push the win rates over to the easy to use cards. If poor players can quickly see that a card is strong (like Witch), they will use it more often than strong, non-obvious cards (like Mint).

It is only 9.5% of games where we'd really expect strong card strength effects when playing the cards "optimally" would show their strength. This is a pretty weak signal in a lot of noise. Further even here things get complicated. Take the silver case. Win rate without gets inflated by boards with viable Trasher/X openings with silver-less engine setups. Say something like Chapel/Market Square or Fishing Village/Steward shows up, of course Silver is going to give up win rate without. This doesn't say anything about Silver vs Chapel or Silver vs Fishing Village ... it does say a lot about Silver vs a combo.

Now of course I'm just making a WAG about where to draw the line between the players who actually know card strength and players who don't ... but the point remains. Most of council room data will reflect situations where other concerns - like an opponent nerfing a combo (and hence a cards win rate with/without) by nerfing their deck or cards being easy to execute - may well dominate the game and hence the data. I can completely see something like Highway being correctly rated ... but execution faltering (I grab an Herbalist too soon/late); I can also see something being correctly rated ... but not being as resilient against less skilled spam play (e.g. Trader is much stronger against less skilled players who still get attacks). Certainly I'm going to put for more weight into the elite community ratings than into the raw stats for what is properly rated.

The cards noted here seem to fit well into this paradigm. Highway - has a low ease of execution. Worker's village - has low obviousness (+buy is terribly underrated by new players, also if you see a player open Wv/just about anything without Peddler on the board you should often swap to something "weaker" but more resilient). Throne room - horribly low ease of execution. Black Market - low ease of execution and poor resiliency. Bridge - low resilience, low obviousness, and low ease of execution. University - everything about Bridge, but more so. Pirate ship - likely generally overrated by lower ranked players. Festival - low ease of execution and higher variance. City - likely overrated, but still has low resilience and non-trivial ease of execution. Silver is the big surprise, but I strongly suspect that just shows that Engine openings like Trasher/X or Potion/X can let people win a lot over more obvious strategies (like BM/B-crat).