Welcome back to my irregular series Weird Facts from MTG JSON, using data made available by Robert Shultz on his site.
It is a truth universally acknowledged that the Magic creative team tends to give cards a dominant color scheme that corresponds to their Color. How can we test this this hypothesis?
The mtgimage site provides easily available images of the art for every card. There are far too many cards to practically apply this method to the whole history of the game so we’re going to take a look at a limited section of them. Since the core sets have no particular theme I expect they’ll be less influenced by the artistic tone of a given block.
Between them the last several core sets have more than one thousand cards. We will adapt some code from the is.R() blog on tumblr to extract the images.
library(jpeg)
library(RCurl)
library(MASS)
a <- AllCards[AllCards$set == 'M10',]
b <- AllCards[AllCards$set == 'M11',]
c <- AllCards[AllCards$set == 'M12',]
d <- AllCards[AllCards$set == 'M13',]
e <- AllCards[AllCards$set == 'M14',]
f <- AllCards[AllCards$set == 'M15',]
l <- rbind(a,b,c,d,e,f)
w <- l[l$color == "W",]
u <- l[l$color == "U",]
b <- l[l$color == "B",]
r <- l[l$color == "R",]
g <- l[l$color == "G",]
l <- rbind(w,u,b,r,g)
code <- l$ID
urls <- paste("http://mtgimage.com/multiverseid/",codes,"-crop.jpg", sep="")
Running the actual extraction takes a while but we only have to do it once.
jpglist <- list()
for (i in 1:length(urls)) {
jpglist[[i]] <- readJPEG(getURLContent(urls[i]))
}
This next complicated bit of code comes again from the is.R() blog. You can read more about it there. The idea is that is the color information from the raster image is can be averaged in order to produce coordinates in color space.
meanRGB <- t(sapply(jpglist,function(ll) {
apply(ll[,,-4],3,mean)
}
cardDistance <- dist(meanRGB)
cardDistance[cardDistance <= 0] <- 1e-10
MDS <- isoMDS(cardDistance)$points
Bind the color and name of each card to its position in color space then save the data so we don’t have to run the loop in the future.
col <- as.character(l$color) name <- l$name posCol <- data.frame(MDS,col,name) save(posCol,file="posCol.Rdata")
There is now a file in R’s working directory called posCol.Rdata which you can load directly into R with the load() function.
Then we make a simple scatter plot and make all the colors line up with appropriate Colors. The goal here is simply to be able to identify clustering if there is any. In order to deal with the fact that the cards are ordered by color we’ll randomize them.
posCol <- posCol[sample(nrow(posCol)),]
p <- ggplot(posCol,aes(x=X1,y=X2,color=col))
p + geom_point(size=2) +
scale_color_manual(values=c('black','green','red','blue','white'))
You can see some distinct regions of dominance in the image. Red and Blue are are mostly separate, but White shares space with them. Green shares a lot of space with Black.
We can go a bit deeper into this analysis, rather than just rely on what I conclude by eyeballing the scatterplot. The mean position for each color is easy to calculate (if not terribly robust) and we can then compute a distance matrix.
x <- with(posCol,tapply(X1,col,mean))
y <- with(posCol,tapply(X2,col,mean))
mean.pos <- data.frame(x,y)
round(dist(x,y),3)
B G R U
G 0.082
R 0.154 0.094
U 0.135 0.084 0.161
W 0.196 0.115 0.123 0.101
The matrix suggests that Green and Black (or maybe Green and Blue) are the most similar Colors in terms of the color palate used for them. By far the most dissimilar are Black and White, although both Red and Blue and Red and Black are close follow ups. By a couple of different metrics it is apparent that Black has the least variability in color while Blue has the most.
We can do a better job of visually checking the variability of the colors positions as well.
We can also use ggplot2 to draw contour lines with the geom_density2d() layer that estimates the density in two dimensions. This makes seeing a middle for each plot much easier.
This makes the incredible similarity in color palate between Green and Black the most apparent. Perhaps surprising for enemy colors.
Intuitor 