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Author Topic: Cost Distributions over the Years  (Read 901 times)

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FemurLemur

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Cost Distributions over the Years
« on: September 10, 2017, 02:38:28 am »
+14

I wouldn't be surprised if this has been done before, but I couldn't find anything elsewhere. For a while now, I have felt like we see a lot more $5 kingdom cards released than in the early days of Dominion. This got me thinking about the distribution of card costs and how it may have changed over time. I found a thread discussing the average cost per set, but no threads discussing the distributions of each cost. So I set out to do exactly that.

Some background info: this ignores potions and debt. Events are not included because they are not Kingdom cards. For Split Piles, I gave them the value that the randomizer assigns them. The graph below doesn't explicitly show Walled Village or Governor in the x-axis, but that's just because I couldn't find precise release dates for them (it's a time axis, but with set icons instead of dates as labels- because graphs should be fun dangit!!) They're still in the data though; Walled Village is clumped in with Cornucopia and Governor is with Hinterlands. I also still counted the 12 cards that were removed from Base Set and Intrigue, because I will never be able to let go, even if they are mostly redundant now.

The graph shows the percentage of Kingdom cards ranging from $1-$8, with the x-axis being time and the y-axis being %. I left in some data markers for local maxima and minima (but not all of them, because it would be too cluttered), as well as the starting values and ending values, which give us some interesting insight- primarily that between main set and now, $5 cards have gone from being 28% of the cardpool to ~35% (not as high as I expected), and $4 have gone from being 40% to ~28% (much lower than I expected).

To maximize the amount of "fun" we're all having, I gave each section a background with cards corresponding to their cost. For example, the segment with Mountebank, that oh-so-handsome Jester staring longingly at you, Mine, and Emperor Palpatine is the $5 segment; whereas the segment below it with Remake, Throne Room, Island, and that oh-so-handsome Jack's Crotch staring longingly at you is the $4 segment. Good luck being able to see Poor House in the bottom sliver, or Prince/Peddler in the top  :P

Below the graph is the source data, for those interested in that sort of thing.













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Chappy7

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Re: Cost Distributions over the Years
« Reply #1 on: September 10, 2017, 04:21:31 am »
+2

Maybe someday poor house will have a friend in the $1 club... :'(
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FemurLemur

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Re: Cost Distributions over the Years
« Reply #2 on: September 10, 2017, 12:19:02 pm »
+4

Maybe someday poor house will have a friend in the $1 club... :'(

That poor house  :(
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Donald X.

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Re: Cost Distributions over the Years
« Reply #3 on: September 10, 2017, 03:42:47 pm »
+6

For a while now, I have felt like we see a lot more $5 kingdom cards released than in the early days of Dominion.
Early on I thought it was important to have $4's, because by default nothing costs $4, but there's always Estate / Silver / Duchy / Gold covering those costs. This was obviously foolish, and these days I think it's important to have $5's, because uh. They loom larger? You build towards them and they do a lot for you.

I would like the chart more with the promos not given their own bars. They're just random individual cards.
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popsofctown

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Re: Cost Distributions over the Years
« Reply #4 on: September 10, 2017, 07:35:40 pm »
0

For a while now, I have felt like we see a lot more $5 kingdom cards released than in the early days of Dominion.
Early on I thought it was important to have $4's, because by default nothing costs $4, but there's always Estate / Silver / Duchy / Gold covering those costs. This was obviously foolish, and these days I think it's important to have $5's, because uh. They loom larger? You build towards them and they do a lot for you.

I would like the chart more with the promos not given their own bars. They're just random individual cards.
I'm hoping you want every single promo to have its own bar for its own random, arbitrary existence, and not to do away with them entirely.
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LastFootnote

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Re: Cost Distributions over the Years
« Reply #5 on: September 10, 2017, 07:42:32 pm »
+1

For a while now, I have felt like we see a lot more $5 kingdom cards released than in the early days of Dominion.
Early on I thought it was important to have $4's, because by default nothing costs $4, but there's always Estate / Silver / Duchy / Gold covering those costs. This was obviously foolish, and these days I think it's important to have $5's, because uh. They loom larger? You build towards them and they do a lot for you.

I would like the chart more with the promos not given their own bars. They're just random individual cards.
I'm hoping you want every single promo to have its own bar for its own random, arbitrary existence, and not to do away with them entirely.

Every single promo already has its own bar for its own random, arbitrary existence. So I assume he means, not that.
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ackmondual

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Re: Cost Distributions over the Years
« Reply #6 on: September 11, 2017, 03:48:31 am »
+2

Maybe someday poor house will have a friend in the $1 club... :'(
You can't buy them, but Shelters will have to suffice in the meantime.
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FemurLemur

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Re: Cost Distributions over the Years
« Reply #7 on: September 11, 2017, 11:05:50 am »
+1

For a while now, I have felt like we see a lot more $5 kingdom cards released than in the early days of Dominion.
Early on I thought it was important to have $4's, because by default nothing costs $4, but there's always Estate / Silver / Duchy / Gold covering those costs. This was obviously foolish, and these days I think it's important to have $5's, because uh. They loom larger? You build towards them and they do a lot for you.

Ah that's some cool insight! I guess one relevant reason for the $4 to exist these days is for the Remodel Variants. Not like every Upgrade/Remake game even needs to have a long chain to work with, but it's pleasing when it occasionally works out that way.

One could also argue that they matter for the common 4/3 opening, because it can feel weird "wasting" that coin and just getting two $3s instead. But I mean, that's a psychological issue more than anything, so it's not like the $4s have to be well represented.

Plus, it's not like they're not being represented anymore. Just less than they used to. If we're asking the question "How many $X cards out of 10 do we expect to see in the average Kingdom?", it's actually pretty cool to see that- after rounding to the nearest whole card-  the results are almost exactly the same as when Base Set came out. The only difference is that we now expect three $4 cards instead of four (and that one empty slot is basically equally likely to either be a fourth $5 or a first $6). I don't know how much you worry about having too few $X cards or too many $Y cards when making/testing an expansion (I mean, obviously that's much lower on the priority list than making fun, well-worded, balanced cards that fit the expansion's theme), but job well done whether deliberately or by following intuition.

I would like the chart more with the promos not given their own bars. They're just random individual cards.

Totally doable. I thought of them separately because they were sometimes months apart from sets (and because I overvalue precision with data even when it doesn't matter at all). I kept the source spreadsheet on my home computer in anticipation of measuring the changes Nocturne might make, so either this evening or next I'll upload a version with all promos grouped with their nearest set for optimal graph-enjoyment


Every single promo already has its own bar for its own random, arbitrary existence.

Except Governor/Walled Village  ;)
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LastFootnote

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Re: Cost Distributions over the Years
« Reply #8 on: September 11, 2017, 11:27:51 am »
+3

If I were putting together this data, I would probably take the dropped first edition cards out at the same time I added the second edition ones. They're not being printed anymore, they're not online. They're effectively ex-canon. It would give a better view of what the cost distribution actually is right now.
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FemurLemur

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Re: Cost Distributions over the Years
« Reply #9 on: September 11, 2017, 12:10:00 pm »
+3

If I were putting together this data, I would probably take the dropped first edition cards out at the same time I added the second edition ones. They're not being printed anymore, they're not online. They're effectively ex-canon. It would give a better view of what the cost distribution actually is right now.

Yeah that's an excellent point. I still play with the removed cards IRL, so for me the above graph is an accurate view of the actual distribution right now. But for the majority of players, those cards stopped being relevant once 2nd Edition was released. Since I'm going back to adjust how promos are bucketed in the data, it makes sense to change this too.
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Holger

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Re: Cost Distributions over the Years
« Reply #10 on: September 11, 2017, 03:39:36 pm »
+3

Quote from: FemurLemur
Yeah that's an excellent point. I still play with the removed cards IRL, so for me the above graph is an accurate view of the actual distribution right now. But for the majority of players, those cards stopped being relevant once 2nd Edition was released.

You're not alone.  ;) Among f.ds and online players, you're certainly right. But I expect the vast majority of real-life Dominion copies will still contain the removed  cards for now and probably many years to come - it seems very unlikely that the base game + update packs sold more copies in the past 1 year than the old base game did in 8 years...
« Last Edit: September 11, 2017, 03:49:48 pm by Holger »
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FemurLemur

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Re: Cost Distributions over the Years
« Reply #11 on: September 11, 2017, 04:41:43 pm »
0

You're not alone.  ;) Among f.ds and online players, you're certainly right. But I expect the vast majority of real-life Dominion copies will still contain the removed  cards for now and probably many years to come - it seems very unlikely that the base game + update packs sold more copies in the past 1 year than the old base game did in 8 years...

This is true. Although the target audience here is f.ds and online players primarily. I wouldn't be surprised if the f.ds community is pretty split over whether they actually still use those removed cards or not.

When editing the post with the updated graph I may just put one version in as an image (probably the No-promo/1stE cards excluded version), then the others (No-promo/1stE included, as well as the original one graph for posterity) as hyperlinks to keep the post from getting unwieldy. I think it's reasonable that which version a person prefers will depend on their own circumstances, and I don't think it'll be too time consuming to tweak/maintain. I tried to make the first one as automated as possible since I knew I'd be updating it in a month
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Cave-o-sapien

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Re: Cost Distributions over the Years
« Reply #12 on: September 11, 2017, 05:02:39 pm »
+1

To the OP:

This is an interesting idea to explore visually, but there are several changes I would suggest:

1) While it's pretty and "fun", the background card art doesn't help convey any information. In fact it does the opposite: it makes it harder to distinguish one category from another and digest what is going on.

2)  In your post you say you want to compare the distributions of sets, but it looks like you are plotting the cumulative distribution of card costs over time. This wasn't clear to me until I looked at the data tables. While this is also interesting, it will make it harder to notice significant differences of composition in later sets as the weight of each set's contribution is diminished by increasing N. I mean, Dark Ages and Empires barely change any of the proportions. Is that because they follow the same cost distribution as the rest or just because they are dwarfed by the larger sample size of existing cards?
 
3) I'd be tempted to group the sets into four or five time periods, then compare the distributions of each of those periods to each other (both statistically and visually). For example, Period 1: Base + Intrigue + Black Market + Envoy; Period 2: Seaside + Alchemy + Stash. Or maybe Base should be on its own? If you're trying to display design decisions, then you should group these according to when they were designed; if you're trying to say something about the available card pool composition, then you could go with release date.

4) I'd also consider grouping the costs into three categories, something like: low (2 and below), mid (3-4) and high (everything else); I would also try to slot Potion and Debt costs into these bins in sensible ways (e.g. Familiar, Golem and Overlord are high; Scrying Pool, Apothecary and Engineer are mid). It would be interesting if the distribution of costs categorized in this manner varies significantly between periods. You could also test to see if there's an increasing trend in the number of high-cost cards over time.
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FemurLemur

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Re: Cost Distributions over the Years
« Reply #13 on: September 13, 2017, 02:29:19 pm »
0

the background card art doesn't help convey any information

It does actually. It conveys costs. The alternative is to have each region be a different shade of grey, which necessitates the reader consulting a legend and trying to figure out which shade of gray is the $4, which is the $5, etc. Conventional wisdom these days is that you shouldn't have a legend in your graph unless there's no alternative. Legends are an inconvenience to the reader. This hypothetical legend (which isn't really hypothetical, because I tried it originally when designing the graph) especially would be horrible because we're asking readers to distinguish between 8 different shades of the same color.

Now, it can be argued that it would be best if each region only had one card image instead of four, but that would have required stretching the card art to obnoxious proportions (or asking RGG/Donald X for a super high res image for 8 different cards that could be zoomed really far into, which (1) might not even exist, (2) I am probably not privy to even if I ask politely, because they don't know me from Adam, (3) they may not be legally allowed to disclose anyway depending on the terms of the contract between the publisher, designer, and artists, and (4) "You're asking us for this huge favor just so you can make a graph??"). The only other alternative is to make each region an unrelated color, such as having $5 = Orange, $4 = Green, etc. This is a bad move because it fails to convey how the region above it is exactly $1 more than the region below it. Also it's ugly and requires a legend. Don't underestimate the value of a visually appealing graph. People will stop looking if it's ugly, as it reminds them of math homework. A pretty visual keeps them looking long enough to digest the info.

The point is taken though. I might play with contrast to make the differences between each region pop more. You probably can't tell, but I already made it so that each region is slightly more transparent than the one below it, in attempt to make them more distinguished. All I can tell you is, if you saw the original side by side with this one, you'd know it worked. But your feedback that it's still hard to read is helpful. I'll see what I can do. But I'm not convinced that ditching background images is the right way to go.

In your post you say you want to compare the distributions of sets, but it looks like you are plotting the cumulative distribution of card costs over time

No, I didn't say that. The title of the post is "Cost Distributions over the Years", and in my post I said "it's a time axis, but with set icons instead of dates as labels", as well as, "with the x-axis being time and the y-axis being %". I think you may have just misread it. The reason the labels are set icons instead of dates is because, if the axis labels tells somebody that in October 2010 the $5 cards went from being 3.75% of the card pool to 5.71%, their next logical question is "what's the significance of October 2010?". The answer being "That's when Prosperity came out". So why not just cut out the middleman and put the set icons- the relevant information- in as the labels? It's less cluttered, more pleasing to the eye, and it answers the questions that people will naturally have anyway. This doesn't mean I'm trying to compare the distributions of each set though. One wouldn't even use an area graph for that, one would use a bar graph.

While this is also interesting, it will make it harder to notice significant differences of composition in later sets

Which is not the purpose of this graph at all. To use an analogy, that's like complaining that this graph, while also being interesting, will make it harder to notice significant differences in how each individual city or county voted. Making a graph illustrating the cost distributions of each individual set would be interesting, and I would be willing to do it if you and/or others are interested. But that's not this graph's intent.

I'd be tempted to group the sets into four or five time periods

I am not a fan of this idea. What value do we gain by washing out detail?

I'd also consider grouping the costs into three categories

Again, what value do we gain when you can just do this manually with your own eyes? The $3 and $4 regions are right next to each other on the graph. Each region is ordered by cost. So you can just add them together visually. By bucketing data, I force all readers to bucket them, whereas if I leave all data unbucketed, those who want bucketing can bucket with their eyes (at least with the y-axis. You can't do it as well with the x-axis due to the bars being spaced out, which is why I'm making another version with promos bucketed for people like Donald X who don't care to see them separated out).

something like: low (2 and below), mid (3-4) and high (everything else)

Look at the graph though, the 3-4 region would be massive. Besides, there's a non-trivial difference between $3 and $4 cards in Dominion. What do we gain by washing out detail?

I would also try to slot Potion and Debt costs into these bins in sensible ways

The only sensible way to consider Potions is by using Complex or "Imaginary" numbers (ie two-dimensional numbers). Doing that means making this graph three-dimensional, which is a no-go, especially if you're already concerned that the graph is hard to read as-is. Plus, the number of potion costing cards in the game is low enough that they would appear very small on a graph. If there were a sequel to Alchemy which added more potion cost cards, we could gain something from analyzing potion cost cards. But for now, there just aren't many of them, and that step into the 3rd dimension would cause more confusion than it's worth.
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Cave-o-sapien

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Re: Cost Distributions over the Years
« Reply #14 on: September 13, 2017, 02:41:31 pm »
0

I don't want to get in a lengthy back-and-forth here, but it appears you and I have very different ideas on a) what is interesting in this data and b) how best to convey that information. I probably will leave it there.
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