Bringing this back to the original question. Do you take your boot width into account when choosing your skis due to your explanation above? Or does the boot width have a negligible affect on the performance? I'm completely on board with the fact that wider skis take more leverage to get onto edge; but I don't think your boot width has a large enough impact on that leverage to constitute considering your boot width for your ski width choice.
It's the width of your foot, not the width of your boot (these correlate, but are not the same), and yes.
A ski that's the same width as your foot (aka the point where power transmits from the boot to your body) feels different than a ski that's narrower or wider. The bigger the difference in relative width between the ski and the foot - the bigger the amount of mechanical advantage you gain/lose.
Someone with a 82mm wide foot on an 86mm wide ski has lost mechanical advantage. This is a "wide" ski *
for that foot*.
Put someone with a 90mm wide foot on that 86mm ski and they will gain mechanical advantage over the ski. This is a "Narrow" ski
*for that foot*.
I am explicitly *not* arguing for an absolute amount of difference that a millimeter makes. I'm trying to demonstrate that there *is* a difference in leverage and it comes from the ratio of foot width to ski width.
I can personally feel a dramatic difference between 2mm of ski width difference (78 vs 80 mm, a 2.5% difference in ski width), your mileage may vary depending on your kinesthetic awareness.
However, I 100% consider my binding choice based on the width of the skis it's going on...a wider ski performs better with a wider binding IMO.
You ski real skis that are not infinitely rigid from side to side. That is why you are completely correct that a wide binding skis better on a wide ski.
Personally, I think this is oversimplifying the leverage, pressure and pivot points of your ski.
@Saintsman is correct and his is the right model to use when trying to analyze leverage between where the snow applies force (at the ski edge) and where your body resists that force (in your foot, and *technically* along the length of your leg shaft inside the boot but that is effectively constant since we're holding the leg in question constant and only varying foot width in our model.).
The pressure applied to a ski is not just on the edge of your foot, it's distributed across the entire thing (albeit not necessarily evenly). So it's not just a force times distance equation, like in high school physics. In order for that 10-15% difference in width to make a non-negligible difference in leverage, all of your weight would have to be located at that pivot point. In reality, probably 80-90% of a person's weight is located somewhere along the 70-ish millimeters under the boot lug (not at the very edges of their boot width). I do agree that there would be SOME difference, but I believe it is completely negligible when you are choosing the width of your skis.
The foot stands on the bootboard, which is connected to the boot lug, which touches the binding, which attaches to the ski. When modeling the question of leverage, all of this can be pretty darn accurately modeled as a rigid system with two interface points (ski to snow, and boot to foot). That forms a triangle, and that triangle's shape/size tells you whether you have advantage over the ski or the ski has advantage over you.
None of what you're referencing (which is maybe necessary to simulate a ski moving in three dimensions) applies to the question of "Do I have leverage over it, or does it have leverage over me). We don't care about the fore/aft balance here (we're explicitly ignoring it, because it'd be constant for all situations). We *do* care about where their center of mass is relative to the ski edge when we go from the static to the dynamic - but again, you're drawing a triangle from the CoM Straight down, then over to the ski/snow interface.
If this is a foot: __||__
And this is space so things format correctly: ---
And this is a foot over a wider Ski:
------__||__
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And this is a foot over a Narrower ski:
__||__
--_
Surely you can see at a glance that there's a change in leverage?
If your argument is simply "no one can tell the difference between those two scenarios", then I can only respond - I have never met someone who can't feel the difference between a 22m radius cheater GS ski that's 65 underfoot and a 22m radius 95 underfoot ski while making a railroad track turn.