Visualizations on the Monopoly board

Two items of post from utility companies that recently dropped through our door included little graphics. There was a degree of innovation in them both. The first, from British Gas, is technically OK but probably bad on perceptual grounds:

I got a tape measure out and starting checking that they had scaled the flames and light bulbs by their area. (Sad, I know, but this is the fate that befalls all statisticians in the end.) And yes, it seemed they had – if you included the space to the little shadow underneath. In fact, someone had clearly been very careful to scale it just right, but the gap of clear space and the indistinct shadow are probably not perceived as part of the icon. I think they’re cute, but not so easy to derive facts from.

Next up from Thames Water:

This looks like a really bad idea. As if pies weren’t hard enough to judge anyway, making it into a drop is completely confusing. The categories at the top are possibly expanded in size just for aesthetic reasons. I thought I would check how much the area occupied by “day-to-day running” differed from the nominal 38/125=30%. First, to avoid confusion of colors, I brought out the GIMP and made a simplified version:

and then read it into R and counted the blue and black pixels:

library(jpeg)
drop<-readJPEG("drop_pie.jpg")
n.pixels<-dim(drop)[1]*dim(drop)[2]
is.white<-function(x){
 all(x>0.9)
}
is.black<-function(x){
 all(x<0.1)
}
white.pixels<-apply(drop,c(1,2),is.white)
black.pixels<-apply(drop,c(1,2),is.black)
n.white<-sum(white.pixels)
n.black<-sum(black.pixels)
prop.blue<-(n.pixels-n.white-n.black)/(n.pixels-n.white)

and that turns out to have 37% of the drop allocated to “day-to-day running”. Bad, bad bad…