Shoe sizes, the investigation part 2.

1. US Men's sizes are always 1 greater than UK sizes.

Taken literally the answer would be "No", but the statement is not too far from the truth, in fact an answer of "Almost" fits better - we shall see, as with all things shoe size related it's not completely straightforward. First off let's corral the data and as usual we'll try and lean on graphics, we all prefer a picture right?.

  • Scatter diagram showing the relationship between UK and US shoe sizes

So we've got a nice compact uniformish linearish (if they're not words then they should be :) chart and we can see the longest line which itself defines the boundaries of the scales and sits indeed on the vector that represents US = UK+1, check it out, for example a UK size 2 is a 3 in US sizes and right at the other end a UK 18 is a US 19. Alas there are two more parallel lines running alongside our original, these represent where the US is half a size greater than UK sizes and the last line - furthest from the first is where the UK and US sizes actually have parity, interesting. If you've read my notes on the official / historical line then they should in fact only be a quarter(¼) of a size difference but as we've seen that's clearly not followed. OK so we've got three solutions but which is the most popular. For that we need a new style of graph which explains why it took a few days to get this published (programming isn't my strong point).

Behold the awesomeness of my 2D graph with some pseudo 3D stacks on it, OK it's not great but it serves it's intended purpose.

  • Scatter diagram showing the relationship between UK and US shoe sizes, the use of a third dimension now highlights the popularity of XY pairs.
  • A close up of the previous diagram, this just highlights that there is no pattern in shoe type regarding the manufacturers decision to favour US=UK+1

So if we consider each pair of US vs UK sizes as a vote by a manufacturer then we've clearly got a winner, in a democracy then US sizes are indeed one size larger than UK sizes, in fact only one manufacturer (from my data - set) has them as the same. The problem comes from the number that use a half size up there's nearly 20% in this category so chances are you've got some in your collection like this - a half size up/down. To try and understand these better we need some other dimension and that's where the colours come in, I've categorised the manufacturers into groups, Green is for Trainers/Sneakers/running shoes, Blue are for formal shoes, Pink are for Sandals, Yellow for casual/Soft and finally Red for manufacturers that make styles across multiple types. I was hopeful for a nice separation but whilst there's only predominantly Red and Green in the half size up group Red being manufacturers that make multiple types means we can't really draw any conclusions from this. As I mentioned before, I've started with the major manufacturers so these charts are representative but as I add more manufacturers these will change, for now though the conclusion has to be "Generally the US is one size greater than the UK, but there are appreciable variances to this, particularly regarding half a size up".