Mash Temp vs. Grain Wt.

Apologies if this has been covered here before.  When I search Mash Temp, there’s about a gajillion hits!

I have been reading way too much about this hobby over the last few weeks and I’m probably overthinking this by a mile.

Where is the fault in my understanding?

Assuming 2 exact recipes with x lbs of grain:
A low mash temp (146-149ish) would lead to a lower FG, more alcohol, less dextrin.
A higher mash temp (156-158) would lead to a higher FG, less alcohol, more dextrin.

But, all else being equal (cough, cough) if we were to increase the grain bill appropriately and mash at the higher temp, would we get the same % alcohol with more maltiness/body?

I ask because fudging the mash temperature seems like a great way to adjust the character of a beer or recipe. Certain styles might be better suited for one mash vs the other.  Or maybe that’s all imperceptible to the average beer drinker??  This is probably covered in All Grain Brewing 101, but it seems all I ever read is to just shoot for the mid-point (152-153) and take the best of both worlds.  I  guess that’s the safe play.

Basically yes, assuming you stay within the bounds of what your yeast can do (i.e. stay below the yeast’s maximum alcohol tolerance).

Apparent attenuation is defined as A=1- (FG-1)/(OG-1), often expressed as a percentage.
Alcohol by volume is roughly ABV=131*(OG-FG)

You can solve the first equation for FG and substitute that into the second equation. The result is:
FG=1+(OG-1)(1-A)
and
ABV=131
(OG-1)*A

So, if your yeast attenuation stays constant then your FG and ABV depend linearly on the OG.

Your theory is correct, but keep in mind that with most malts these days mash temp doesn’t make as much difference as it used to.

Thanks gentlemen.

I have just been wondering if there is a perceivable difference in a beer that went from 1.050–>1.010 as opposed to a beer that fermented from 1.060–>1.020, assuming the 1.060 was achieved by simply adding more of the same base malt and then mashed at a higher temp.  I would think there has to be some change of character, but I’m not sure if a rank and file beer drinker like me would notice.
It might be a more full bodied, malty beer - which could be either good or bad depending on style.
Or just a waste of money.

My experience is that there would be a difference.  Attenuation alone is not the whole story.

Also note that if your attenuation stays constant (1.050 -->1.010 gives 80%) then going up to 1.060 would finish you at 1.012, not very much different. In order to get the FG much higher you would have to go way up in OG (up to 1.100 to get 1.020) or you would have to do something to lower the fermentability of your mash to lower the attenuation. One way to do that would be to mash at an even higher temperature, and that would definitely increase the body of your beer and change the character.