Think of it this way too - though it's a meat grinder because it's INF on INF warfare....
You have your standard 20-width division (10x INF).
The standard width for attacks one province on one province is 80.
Your standard 20-width infantry division (10xINF) can have 4 divisions attacking without penalty - that's 4 targets, each target getting 10 INF attack.
Those same divisions, under the Mass Assault Doctrine, can get 5 divisions attacking without penalty (16*5=80). That's 5 targets, each getting 10 INF attack.
Add an extra province attacking, that adds 40 combat width. Your standard 20-width infantry division now can get 6 divisions attacking without penalty - that's 6 targets, each getting 10 INF attack
With the Mass Assault Doctrine, you can now attack with 7 divisions without penalty, with an 8th being at 50% - forgetting where the cutoff is where it won't allow you to bring another unit into the battle, but at worst, that's 7 targets (still one more than otherwise) and possibly 8 targets. You'll be able to break the enemy faster with the extra (though pure inf are probably the last unit I'd want to be throwing into attacks if I can avoid it)
If you go up to 24 width (12xINF), that's the 19.2 width, and you gain 2 extra INF per division - so attacking on an 80 width front, that's 4x12=48 infantry brigades attacking 4 targets.