I apologize. I meant that at level 8 or 12 you wouldn't notice the difference between a PC with an 18 and 20. That +1 means so little in the overall aspect of the game. And the fact that really intelligent people still debate it is mind boggling.
People debate it because it's not really true and you foolishly said "10 hours of combat" not "an hour of combat". If you'd said the latter, sure no-one would be arguing.
It does depend on how many rolls are made, how many PCs are involved, and how much information we have. But I think you haven't thought this through as carefully as you think you have.
But if we had 100% information EXCEPT that the stat values were hidden and we only get to see the totals rolled, not the math, which seems to be the scenario you're presenting, I'm pretty confident we could determine, particularly by looking at outliers of rolls, what people's stats are, simply because:
A) We'd know if any +X weapons were involved.
B) 5E D&D doesn't use many plus or minus modifers - almost none - it uses Advantage and Disadvantage.
Advantage and Disadvantage don't modify the outliers, in fact, they create more outliers, making the number MORE clear than they would be otherwise.
You're acting like this is 3E, 4E, or Pathfinder. In any of those, your position would be unassailable. There are so many little bonuses and penalties that constantly come into things (even PF2 has them) that would indeed be very difficult to determine the actual stat values.
But this is 5E. We have bounded accuracy. The to-hit roll is very simple in almost all cases. It's simply PB (known) + Stat mod (unknown in this case) + weapon bonus if any (known). Thus you look at the outliers, Scott. The lowest and highest numbers rolled. Let's assume 4 players, and they complete a round of combat in 10 minutes (which is actually kind of slow, in my experience, but not super-slow - maybe the DM has complicated monsters). Let's assume the class in question has 2 attacks from the Attack action, and makes some other Bonus Action or Reaction attacks, to average 2.5 attacks a round. That means in 10 hours they're likely making 150 attacks. Again this is a pretty conservative estimate. 10% on average of those will be 1s or 20s, the outliers - so 15 of them.
From those 15 attacks, you can work out the missing number. Even if we got very unlucky and were say, only 6 outliers, you could still do it. What are the lowest and highest numbers? The only way* it would break is if, in 150 rolls you roll NO 1s and NO 20s at all. Not even a single one. Because that's all we need to work this out - one outlier. One. That's assuming no Advantage and Disadvantage too - every time either one comes up, that makes our job easier, because we get more rolls, and therefore more outliers.
Do you understand this? Our confidence couldn't be perfect, because technically rolling no 1s or 20s is possible, but it could extremely high, well over 95%. So long as in 150 rolls at least one 20 or 1 is rolled.
Now there is a way you could really mess with us though. It's a little spell called Bless (I'm assuming you'd hide the results of the Bless spell roll). But if we know bless is going on, we can still trying. We might get lucky and get an get outliers where we could could work out they were either +1 on a 1 or +4 on a 20. Also we'd know which rounds Bless applied to, and we'd probably get enough outliers from rounds when it wasn't on that we could work it out regardless. Bardic Inspiration could get in there too, but we'd know it was being used so could factor in the variance on the very few rolls it applied to. Again not a real problem unless every single outlier occurred at the same time as Bardic Inspiration (very unlikely). Indeed, if the Bardic Inspiration was maxed on a 20 roll, or minimized on 1, we could still work it out from one outlier.
If you disagree, I'm going to need to you to explain the logical and mathematical principles on which you disagree. Otherwise it's not actual disagreement, it's just being a sore loser!
And to be fair, again, if this was 3E or 4E, you would be right, period. I could not argue with you. I could not reliably work it out. There are too many bonuses in play. But this is 5E, and they killed the bonuses.
* = Or if every single outlier had an unknown Cover modifier on it, but it has to be
every single one. And if we know that the cover modifier applies to the roll it's easy to remove.
Thanks for giving me a really nerdy problem to think about though lol.