Correlation between rise time and proof time
I've seen variations of this question asked here before, and the responses generally seem to be along the lines of, "that's a meaningless question," "it's too simplistic," "there are too many other variables," etc., so I expect to get similar responses here, but I'll ask it anyway.
I'm wondering if there is any rough correlation between initial rise and proof times. Let's say that on two separate occasions, I bake a loaf using the same formula. (Let's just say for the sake of argument it's a boule, all bread flour, 70% hydration.) The first time, it rises fully (in my judgment, based on its size, appearance, etc.) in 3 hours. The second time, it rises more slowly; maybe the starter wasn't as vigorous, maybe there's some other factor at work, who knows? But it take 6 hours to get to the same point as the first dough. My question is, once I shape them, would it be reasonable to expect the second one to take longer to proof as well? Or since they were both at the same point (again in terms of volume, puffiness, springiness, etc.) when they were shaped, would they presumably both take about the same amount of time to proof? (Assume the ambient temperature and humidity levels are the same on both occasions.)
To ask the question in a slightly different form: let's say I'm following a published formula. It estimates the rise time at x hours for the dough to double in volume and be ready to shape. After x hours have elapsed, my dough clearly isn't ready, so I give it longer. It ends up taking twice as long as what the formula called for, but finally it looks like the risen dough as described and displayed in the formula, so I shape it. The formula calls for a 1-hour proof. Should I presume that since my dough needed a longer rise time, it will also need more proof time than what the formula says?
I realize that how long is long enough has to be determined by the baker, based on the appearance and feel of the dough, and can't be reduced to a simple number. It's ready to go in the oven when it's ready, and knowing when it's ready comes from experience. But my question is, in general, would longer rise times likely mean longer proof times? Shorter? The same? Or is there no relationship at all?