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I played many sports in my youth, but to my loss almost never soccer. As my kids and wife have recently gotten into it, however, I have started to learn more about it.

In every sport I'm aware of the rules around equipment and gear are intricate and precise in areas that affect play. In baseball the specifications for gloves, ball and bat are fairly rigorously defined. Football of course had Brady's DeflateGate, and rules around substances like Stickum. Racing bikes go through rigorous approvals. Rims in basketball and the ball itself are measured carefully and have defined bounce characteristics.

Soccer shoes, however, seem to have no rigorous definition except apparently around the safety of the cleats.

An obvious gap to my naive mind is not in the cleat but instead in the upper.

Having hardened/carved components on the shoe, or even inside, would seem to offer the player who could utilize them an advantage, in better catching the ball on the inside, conveying the leg action more efficiently on the kick, etc.

I can find no mention of these even in concept, no products for sale, no reports even of surreptitious use or anything.

What's the deal? Is this just not a thing? What am I missing?

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I think you have a minor issue with physics here. It's not 100% clear to me what you're describing, but there are two ways you could 'harden' the shoe:

  • A solid mass between the upper and the foot (imagine, say, a roll of coins)

    This would hurt. A lot. Brass knuckles do hurt the fingers that wear them when not braced properly, and I doubt you could brace this sufficiently - even if it did impart an advantage, which it wouldn't.

  • A stiffer upper in general - at its extreme, an iron upper.

    Unless this were actually metal, it seems like it would most likely defeat the purpose - the upper would absorb force from the boot, spending some of that force bending. It also seems like it would cause the ball to come off at a less precise angle, again unless you had something like a golf club for a shoe...

At the end of the day, you have a certain amount of force that comes from the foot - from the mass of the foot/shoe system itself, and then from the speed imparted from the muscles, leading to the equation F=ma. The most force you can impart is F, and for the most part that F is pretty similar to what comes off from a direct kick. The shoe exists primarily to protect the foot from the effects of that F, which does reduce it some, but the shoe for the most part isn't really changing the force - and it certainly cannot increase it. This is not golf, where the club is a lever that is being used to drive the ball - the foot and leg are the driving force itself, the only leverage coming from the length of the foot from the hip, and that isn't really something they can make rules about...

Ultimately, if someone had figured out a way to make a shoe that somehow increased the force of a kick dramatically, you're undoubtedly right that there would be rules related to it, similar to how Golf, Tennis, etc. have rules about their various implements - which are mechanical in nature (a lever, which is what both a tennis racquet and a golf club are, is a simple machine!) and thus must be constrained.

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