EXTREME novice here. How do people (mathematicians, physicists, engineers, etc.) come up with their own formulas?

That's just a weighted average.

Suppose you want to average two numbers, X and Y. Normally you'd do this: (X + Y)/2.

But what if you want to give more weight to X than to Y? Well, then you can assign them different numbers, say r and s, and then the weighted average is (rX + sY) / (r + s).

Those numbers can be any positive number? All that's important is their relative sizes. The bigger number will have more weight in the average.

If the weights are equal, r = s, then it reduces to the normal average.

So the IMDB rating is a weighted average of R and C, and they've used those things v and m as weights. I don't know what v and m mean exactly so why they thought that made sense to use as weights. You can weight in any way that makes sense to you.
The Drake Equation is also a very simple idea. That's just taking a fraction of a fraction. All these things have to be true for there to be an alien species capable of making themselves known to us. How many planets even have life on them? Well, estimate how many stars there are, how many of those have planets, how many of those could have life, how many of those actually DO contain life, etc.
This seems to be a weighted average.

In Mathematics and Physics, most formulas come from equations. In Engineering, "model fitting" is the popular one next to equations and in subjects using maths more recently like neuroscience and economics, it's almost entirely model fitting.

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