or by seeing when it breaks?
There might be deflection in the actual 12" diameter roll, but my guess is that it would come after something else has already broken.
The rolls are usually turned down at the ends, and put in bushings or bearings- so it makes sense that, before a 12" cylinder would deflect significantly, the 6" diameter end shank would bend or break.
Not to mention gear trains, adjusting bolts, cross bracing, and all the other parts that make an older set of rolls work.
Many many people overwork their rolls. Its human nature, I suppose- and its easy to assume that, if it will roll 14 feet of 3/8", then it should be able to roll 4' of 3/4", right?
And, sometimes, especially with older machines, they are enough overbuilt that they do it.
But it is not without cost. Its possible to spring rolls, break teeth off gears, bend frames, and lots of other bad stuff, some of it subtly over time.
I have a friend who has a big set of Lown Rolls, that she is sure are 3/4" rolls- after all, she has rolled pieces of 3/4" plate in em. But when I did some research, I found out they were rated by Lown for 12 gage at full width. Its a testament to their construction that they havent blown apart yet, but I sure wouldnt recommend repeated rolling of 3/4" in them.
And even though these rolls seem incredibly herky with 12" diameter rolls, most likely they were only designed to roll 3/8" mild steel.