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Calculating Shoe Sizes: A Look at the Data

As a member of Sizeadvisors, you can get your shoe size calculated when you provide the measurements of your feet. Currently, you get your shoe size for the UK, US, and EU systems. Others may follow later.

There's just a small problem.

Some men think these numbers cannot possibly be true.

In the following post, I'll try to show why these numbers are about right, and why some men think they are definitely wrong.

The difference between rated and calculated UK/US sizes

Given the data of Sizeadvisors, it's easy to compare the shoe sizes members rated, on the one hand, and their calculated shoe size, on the other hand. You just need to subtract one from the other.

For example, if you rated a pair of shoes in (UK) 8.0 as "really comfortable" and your calculated shoe size is (UK) 8.0, the difference is zero. Thus, we should see zero differences in most cases if the current calculation is correct.

So, here's the data for all UK sized shoes rated to fit fairly or really comfortable (ie. "3" or "4"):

Histogram UK Differences, rated good

Note that in graphs like these the area of each rectangle indicates frequency, not the height. Since every rectangle is 0.5 units wide, you need to divide by 2 to get the frequencies.

In other words, for about 33 percent of all UK-sized shoes being rated, there's no difference to the calculated size of the critic.

This indicates that the UK sizing method is correct, on average.

And here are the differences of US-sized shoes rated to fit fairly or really comfortable:

Histogram US differences, rated good

Again, for most ratings the calculated size appears to be correct. There's no difference to the calculated size of the critic for about 25 percent of all US-sized shoes being rated.

What does seem to be true, though, is that the right size **does not guarantee** to get shoes that fit. You can see this clearly, when looking at the difference to the calculated size for shoes that members found to fit slightly or really uncomfortable (ie. "1" or "2"):

Histogram UK/US differences, rated bad

For this image, I combined UK and US sizes, since the difference is measured on the same scale. Again, most members tried shoes in sizes, Sizeadvisors calculates. Since this is about badly fitting shoes, though, it makes clear that you can't (only) rely on shoe sizes.

In other words, trying shoes in your 'true' size may be a necessary condition for a good fit, but it certainly is not sufficient.

Where do the differences come from?

The above analysis used ratings to look at the differences between rated and calculated shoe sizes. You could say, this is as if shoes would be looking at the men who wear them. The differences could then be due to either:

  1. the shoes "themselves", or
  2. the men who judged their fit, or
  3. both.

Of course, there's also a fourth option: Sizeadvisors' data is not a true random sample, and data is never perfect. The above differences may simply be due to errors such as typos, mis-measurement, or misunderstandings. Some of them are easy, others are impossible to detect. For the later, I can just assume that they cancel each other out, on average.

Provided errors in the data just have a minor effect, what's the more influential or likely cause?

If it's the first case, shoe makers differ in how they determine size, and the above graphs reflect these differences. In other words, some shoes simple don't fit "true to size".

If you follow (online) discussions about shoe sizes, some men seem to favor this explanation.

But there's no economic incentive for shoe makers to use a different sizing method (or apply existing methods differently). Without an economic incentive, what's left? Ignorance?

This seems to be a rather unlikely explanation. After all, we're talking about premium brands. It doesn't seem reasonable to trust them to make quality shoes, but not to label them with the correct size.

If it's the second case, men differ in foot shape and how they judge fit. Their feet may be wide or narrow, they may have a high or low instep, or wide or narrow heels. In other words, some men simply deviate from their "true" size.

And shoe buyers do have an economic incentive to do so.

For instance, to search for fitting shoes in your correct size can take more time, unless your feet are close to average. It also rules out many shoes you may like to wear. It's even harder if you're not willing to pay any price even if a particular pair would fit perfectly.

Also, many buyers determine shoe size by trying shoes in a store, only. They may not have used a measuring device for years. Some may not even be aware there is such a thing as a correct size. Some don't know that shoes are made on lasts, nor have they ever tried to test how different lasts influence fit.

Expressed differently, there are reasonable explanations for shoe buyers to deviate from their calculated sizes. Reading numbers you don't expect must be rather surprising.

It was for me, at the very least.

So, if you think the shoe sizes calculated by Sizeadvisors are definitely wrong, you may like to reconsider.

In the posts to follow, I'll provide more information about shoe sizes, what they mean, how they are calculated by Sizeadvisors, and how shoe sizes help you to make better decisions when buying shoes.

Meanwhile, what's your take? Do your deviate from your calculated size? If so, do you think this is due to your shoes or your foot shape?


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