How did manufacturers decide which sized pots & caps to use?


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I'm just asking a naive question.
I know for single coils they recommend 250k pots and for humbuckers it's 500k.
And in cap size it's generally .047 for single coils & humbuckers .022.
I 'get' that it's 500k/.022 for humbuckers because that's a double equation to the single coil formula & there's two coils in a humbucker.
But I'm curious to find out if the original 250K pot/.047 cap was done to meet some electronic maths formula, coinciding with the pickup's DC voltage and Inductance?
And what's thrown me the curve ball for all this, is that I have Jazzmaster pickups that I know would sound much more open using 1M pots and .033 cap yet they are single coil?
So I guess I'm asking: Is there some mathematic equation/formula used to arrive at a certain ideal range number?
I suppose Leo originally used 250K pots because that was probably all that was available. But is there more to it?
This is a factor of taste rather than science. Many guitar factories are constantly copying iconic vintage guitars, because most great guitar rock songs are from the 1960s, and that becomes “taste standard” to copy that traditional recipe more than scientific calculation.
However, there are still some technical indicators and the relationship between treble reduction to music style link to pickup type. You can refer to this video.

no rules that stop you use other pots value
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Just to add on, I'd like to know what effect two tone pots in use simultaneously in the 2 and 4 positions of a Strat-style guitar has on the circuitry and overall tone control.
To understand the issue with pot resistance and tone controls, firstly you need to understand the electrical resonance of the pickup. Each pickup has a particular inductance and capacitance which determines the natural resonance frequency. However the pickups natural resonance doesn't tell the whole story. What's more important is the resonance when the pickup is wired to the electronics of the guitar and the added capacitance of the instrument cable and amplifier input. There are two basic qualities of the resonance, 1) Frequency, and 2) Q factor. To tune the Frequency of the resonance, different cables can be used which have different capacitance. Changing the pickups will shift the resonance frequency because the inductance and capacitance will change. The "Q Factor" is tuned using the guitar's tone control, and the choice of pots will have a major effect. There are many other aspects that affect the tone and brightness of the guitar, but that is a really long list!
I suspect it was mostly trial and error. While you can certainly calculate the roll-off frequency of a R-C network, other loads all effect the final result. Electric guitar wiring evolved alongside amp development. The earliest guitar amps ('30s) had no controls, volume (and eventually tone) was controlled at the instrument. Fender settled on 250K and .5 mfd, and then voiced the amps to complement the guitars; Gibson and Valco voiced their amps around the existing guitar tone as well.

Feel free to experiment. I prefer .033uF caps in Teles, it lets me roll off the top end but keep the upper mids for a more P-90-esque type tone from the bridge PU (and the Tele neck Pu is rarely too bright). Though, i will say, I've never liked 1M pots in anything, pure icepick to the ear, IMHO.
It could be the early manufacturers chose the pot value first, then they wound their pickups to get the right tone when using those pots.

In that case, the volume pot value is chosen so they can drive enough signal into the instrument cable without losing the high frequencies. That issue comes up when the volume control is Not set to maximum.