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That exchange describes my problem.
I'd like to be able to see the effect of one variable (let's say doing a cream ale with vs. without rice), that is, do an experiment. But inevitably, I'd also end up varying other things, too (mash temp, boiled a little longer, hops weren't as fresh and, oh yeah, I've switched from a bazooka tube to a false bottom since then).
It would actually be much more of a challenge to exactly duplicate a brew than to redo it pretty much the same.
I'm a scientist, let me weigh in a bit here. You're much closer to being able to do a good experiment than you might think.
Part of the process of doing this is in how you prepare. You already understand the main issue in experimenting like this, i.e., isolating the single variable of interest. You understand the problem of having alternative explanations (temp, boil, hop differences, etc.) of a final difference, i.e., was it the variable of interest that caused a result, or one of the other explanations?
Just did an experiment last weekend, comparing a single change. I'll report on it somewhere here when I have results, but my goal was the same as yours--two batches exactly the same except for the one variable of interest.
So I planned for that. Two batches brewed in succession. I can't do them simultaneously, which was a concern, but I did everything I could to make them identical. Same hops from the same lot. The grain was from the same lot. I crushed the grain in both cases 45 minutes before dough-in. My mash temp differed by about .7 degrees F, the pH of the mashes were 5.31 and 5.28 (and the difference might have been related to the variable of interest).
Boiled the exact same length of time, laid out and did hop additions at the same times. I used two packs of WLP001 in a 2-liter starter, which I split evenly between the batches when i pitched. My OG for one batch was 1.062, the other about 1.0615.
They are not exactly the same. As you note, that's very difficult to do. I wish I had batches were the variable was, say, a difference in yeast, because i could have split the batch and I'd know up to that point they'd be identical.
But the variable of interest goes in the strike water, so that's impossible.
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So here's the question: are my two batches close enough that there is fundamentally no difference in them due to basic recipe and technique? Is it likely we'd be able to discern a difference between 1.062 and 1.0615? Or between mash pH of 5.31 and 5.28? Or mash temp difference of .7 degrees?
I would not expect those two batches to show a difference, if I'd brewed them w/o the variable of interest. So if there's a detectable difference at the end, I will tend to attribute it to the variable, not the slight differences in batches.
Could these minor variations account for the difference? Sure, it's possible, but I have to accept them as being the same. I don't have any particular expectations for the variable of interest--I'll accept the results as true and then, at some future time, try to replicate them.
I have several "repeat" recipes. I like them, others like them, so I keep brewing them. I've got a new one, Darth Lager, that was just delicious the first time (even a blind dog finds a bone once in a while). I couldn't share the recipe until I'd done it again, and I was able to do that. Big hit. Third batch is in the fermenter right now, but I've changed that one variable. I have the 2nd batch on tap right now so some level of comparison can be made. I'm hopeful, Morrey has brewed the same recipe with that variable included, and he says it pops. So I'm hoping to find the same thing.
My point is that you are far better positioned to do this than most might be. You understand the problem, i.e., one of control. And you can control most of the variation ahead of time. Use the same hop lot, keep them in the freezer until used. Same grain lot. Same everything, using notes to record and then again follow.
I suspect many of us have variability in how we brew not because we can't do things more precisely, but because we believe such minor variations don't matter that much. If you have a 30-minute addition and you do it at 29 minutes, do you expect to taste the difference? I don't. Same with a .7 degree difference in mash temp. Or a .03 difference in pH.
When I did my experiment last weekend I was as precise as I could be. I am not normally that precise when brewing. I suspect most aren't.