Shoe size calculator

Discussion in 'Classic Menswear' started by niklasnordin, Mar 5, 2013.

  1. niklasnordin

    niklasnordin Senior member

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    A question to claus though.

    The data used to rate your size. Does it use any linear correlation of larger and smaller sizes or does it just do a proximity 'check'.
     


  2. niklasnordin

    niklasnordin Senior member

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    lol, nice trolling sir :)
     


  3. gaseousclay

    gaseousclay Senior member

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    clearly you've never purchased shoes online, let alone shoes from a non-US shoemaker. and as someone already pointed out, a lot of English/Italian/French shoemakers do not have a presence in large parts of the US, unless you live in L.A. or NYC, thus making your argument very weak.

    I provided measurements for my feet to AFPoS and their size recommendation was spot-on when my shoes arrived.
     


  4. Claus

    Claus Senior member

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    Niklas, I'm glad you like it. :)

    Right now, the method based on measurements uses a mere proximity check. I have already started a branch to use size deviations, so proximity will then be based on foot shape deviations. I guess this comes close to what you mean by 'interpolations'. This introduces some noise, but a Bayesian ordering ought to keep this in check.

    Not having enough members in close proximity is still a problem for some people. Any rating with a typo can get too prominent in the result list. Which is probably the reason there are some unexpected sizes in your recommendations.

    I see your foot length increased quite a bit compared to your above number. I already thought so, but the magnitude is still surprising. Also, the 1 star rating seems a bit odd.
     


  5. niklasnordin

    niklasnordin Senior member

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    I had to re-measure the length, cause the first numbers I put in was just off the paper. So the size was way off, but measuring them properly produced better result.
    The 1 star is because the instep for that model is too small. I bought it on a pretty cold day and the fit was really snug, but if Im warm and my feet are slightly swollen. It hurts when I use them...hence the 1 :)

    What I was planning to do was to come up with a simple linear model so that it uses all the parameters from all sizes to guesstimate your size.
    That way, input inaccuracies and other errors would eventually be irrelevant.
    For instance, starting with the simplest model approximation it could be something like this.

    Assume that your size you feel most comfortable with = a_1*(param_1 - b_1) + a_2*(param_2 - b_2) + ... + a_n*(param_n - b_n)
    Using all the statistics from one last and doing a least square fit to find a_i and b_i would hopefully give you a good and accurate model for approximating the size.
    Size is not just the length of your foot, sometimes you go up cause your foot is too wide or too high, and this would be reflected in the non-zero a_i coefficients to those parameters.

    This would also make it possible to then create a recommended size for all lasts, for instance it would be possible to answer
    the (to this site very common) question - I wear size X in C&J, what is my Carmina size for the Rain last.

    That was my plan anyways :) You have the data so maybe you can do it instead.
     


  6. DWFII

    DWFII Bespoke Boot and Shoemaker Dubiously Honored

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    The thing to remember is that the foot can feel 1/16" in circumference. Full length sizes are calibrated in 1/3 of an inch (more or less) from what is almost always an arbitrary baseline depending on the last. Width grades roughly 3/16" per size at the treadline and half of that at the heel seat. it's actually more complicated than that because last grade up in length for each increase in width. But these can be critical factors in proper fit esp. with regard to length and width in the forepart of the shoe.

    Then too, some people have dense feet, some have flaccid feet. Some people have strong connective tissue, some not so much. Some people hold more or less fluid in their feet. Do you know how to pull the tape measure to get a girth measurement that you can send off to someone with full confidence that the resulting size will address the type of foot you have? Do you know what kind of foot you have?

    Does this system address heel seat width? Does it address treadline/joint width?

    Does it address the fact that the length measurement...esp. as take the way this system suggests...will hardly ever accurately predict the correct shoe size, simply because some people have long toes, some have short toes--the only accurate way to find the proper shoe size is to measure the heel-to-ball length.

    I don't doubt that this is clever and nor do I doubt that in many cases it will be close enough...but there's an old saying in the Trade that has application--"The shoemaker that says that he has never had a misfit is either lying or needs a new standard of fit." Most people buying RTW shoes have never had a really really good or accurate fit. The upshot is that unless your system addresses the issues I've outlined above, it is really not much better that a person just trying a pair of shoes on and going with what feels OK.

    Bottom line is that without a standard of fit that is universally recognized from one maker to the next, one last model to the next, among all customers, self fitting is probably the closest thing to infallible...esp. when you consider that probably half of fit has no bearing on the foot at all but is rather in the customer's head.
     


  7. niklasnordin

    niklasnordin Senior member

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    I agree with you 100%, but when you see a beautiful shoe online that you have no way of trying before buying it...what to do?
     


  8. Claus

    Claus Senior member

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    If I understand you correctly, param_1, param_12, etc. would be foot measurements. Unfortunately, they are highly correlated. A Least Square estimation could result in a rather artificial foot shape that nobody has.

    However, I could try over the weekend. Is there any particular last you're interested in? Maybe, one you could test in the following week?
     


  9. Claus

    Claus Senior member

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    DWFII,

    I understand your ideal fit as a custom shoe maker is something that the system will never attain. But I doubt it can be reached with RTW, anyway, unless one is really lucky.

    The market today favors RTW and most people are only interested in getting the shoe they want in a somewhat comfortable size. When the latest SF frenzy starts, people simply buy a Carmina, or Meermin, or Vass, or whatever. Could this be possible if they really cared about 1/16" differences in circumferences?

    I appreciate the input, though. :)
     


  10. niklasnordin

    niklasnordin Senior member

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    yes, thats what param_1 means. Its true that they are correlated, so it could present problems, in which case I guess it would be safe (well pretty safe) to exclude that parameter.

    I have a EG in last 888, could be a good trial last.
     


  11. DWFII

    DWFII Bespoke Boot and Shoemaker Dubiously Honored

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    Well, the point I was making in my above comments is not that everyone will appreciate a bespoke fit. You're correct, RTW is the name of the game. But think of what that means--it's all down to subjective perceptions. Even in bespoke work, if a fitter's model is done, the customer still tries it on and either accepts or rejects the fit based on what is still probably, entirely, subjective perception.

    So...if it's all subjective, there doesn't seem to be any point in trying to codify fit from a limited, and limiting, set of even more subjective (the untrained customer taking his own) measurements.

    And I suspect that's the reason, after all these decades and centuries, the amount of standardization in lasts and last grading is almost immaterial.

    PS...not trying to diss you or make light of your ideas...simply pointing out the remorseless facts. BTW, if you want to get semi-accurate measurements from a foot...there's already a computer based scanner out there that will do everything but compensate for types of feet and/or subjective perceptions.

    --
     
    Last edited: Mar 6, 2013


  12. Claus

    Claus Senior member

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    Ah, there's the other problem. Least Square requires enought data to estimate the vectors a and b. I don't have enought ratings for EG's 888 last.

    I'll use the 348 by C&J in E and report back after the weekend.
     


  13. niklasnordin

    niklasnordin Senior member

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    ah, crap :)
    348 will do fine,

    cant wait to see what will pop out.
    cheers
     


  14. Claus

    Claus Senior member

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    Niklas, I'm back, as promised. Beware, this is going to be a bit geeky…

    If I understood your suggestion correctly, the goal is to find a, well, "reasonable" shoe size for a given last-width combination (hereafter called 'last') based on one's foot measurements.

    Given the goal, Multidimensional Least Squares seems somewhat plausible: Instead of using only foot length as it's traditionally being done, it also considers the potential influence of ball width, heel width, etc.

    Since Sizeadvisors uses 6 measures for each foot and there's also a fixed term, we need to estimate at least 7 parameters. Which means, we need at least 8 data points for any last. Which means somewhere between 4 and 8 ratings of 3 or 4 stars, depending on whether the measurements differ for the left and right foot.

    Using left and right measurements (in Millimeter) separately, Least Squares yields

    Code:
    Foot length:   0.100271900057
    Ball girth:    0.0125457488365
    Ball width:   -0.0379630679714
    Heel width:   -0.0241301798012
    Instep girth: -0.00839712226414
    Heel girth:    0.017940791048
    Constant:    -20.2175416295
    Consequently, your measurements result in an suggested shoes size for C&J's 348-E last:

    Code:
    Left:  5.75438715856
    Right: 5.75438715856
    According to this, you should try a 6.0 UK for this last. For comparison, using Sizeadvisors formula based on foot length alone, would result in the following suggestion:
    Code:
    Left:  6.03
    Right: 6.03
    Since shoe sizes are rounded up, this would yield a 6.5 UK which I guess is more appropriate given your other ratings. A 6.5 UK is also the recommendation for you under 'Similar fittings'.

    So, considering only this example, Least Squares doesn't seem very promising. However, it should be noted that you didn't measure very carefully. While every algorithm has the "junk in, junk out" problem, some are more forgiving. Least squares can capture the mistakes made by others to some degree, but it can't capture your own mistakes.

    It's also a black-box method. There's no way to interpret the results in any meaningful way, other than stating that some dimension are relatively more influential, while others may even have a negative influence. Each parameter thus probably catches some of the "real" weights if there is such a thing but each also catches

    • the influence of converting the measurement scales (from mm to shoe size).
    • the average preferences of all raters of the particular last.
    • some measurement errors if their distribution differs from the assumed distribution.
    • other factors that may exists.

    That doesn't mean Least Squares can't be helpful, but it's probably more useful for large samples to extract factors that influences a recommendation.
     


  15. niklasnordin

    niklasnordin Senior member

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