I've been watching a lot of videos of mid-stakes regs having overbets in their strategy. And so, i was wondering, from a more theoretical standpoint, why it's good to have overbets in your arsenal in the first place.

I think i do know the reason, but please correct me if im wrong.

Basically, from what i know, it gives our opponent's less of an attractive price to make a call, thus giving us more fold equity, and forcing him to have stronger hands in general. And as long as we figure out what price we are laying him, we can figure out the amount of value:bluff combinations that we must have in order for him to be indifferent towards either calling or folding.

So for simplicity sake, let's take a river situation where villain is OOP with pure bluffcatcher vs our nuts/air. We make an overbet to 1.5x pot, meaning he has to continue at least 40% of the time so that we don't instantly profit off all of our bluffs. And it also means that he's being laid 37.5% pot odds, so that's how often he has to be right when he calls.

Given his pot odds, it means that we are allowed a 62.5 to 37.5 ratio of value hands to bluffs. If he calls when we hold that ratio, he will break even on his call, so now he has to fold all of his bluffcatchers, and we essentially win the pot every time that we bet. And if compared to a PSB, which would give us a 66:33 value to bluff ratio, the 37.5 represents an extra 4.5% of hands that are bluffs, that can win the size of the pot.

So having an overbet is key when you show up with more bluffs in a potential spot, to give those hands +EV. And in other cases, when you show up with alot more value hands in a particular spot, you'd generally bet smaller since villain would pretty much never call an overbet in that spot, but you don't lay the price SO small so that he has a profitable call with all of his bluffcatchers.

Does this sound about right?

Bluffs are usually around 0EV, no matter the bet size.

in a perfectly polarized GTO river spot, the EV of our betting range is POT, and the EV of our checking range is 0. The bigger that our bet size is, the larger portion of our range we'll be betting, therefore the EV of betting bigger is larger than the EV of betting smaller with whole range.

Basically, the main reason to bet big in poker is to get more value.

But in truth, because we've made him indifferent to calling or folding, you could also say that he'd just be folding against our entire range. So then we wouldn't actually be making more "value" off of our value hands, the EV of our entire range would become the size of the POT for every combo in our range.

And to add to what i was saying, it also looks like turn overbets may be more effective, in turns of number of combos of bluffs we can add than when compared to the river, so long as we make him indifferent on the river with all of his bluffcatchers.

I think it's more to do with how polarized your betting range is, and how elastic villain's calling range is when faced with various bet sizes.
If you have a LOT of "thin value" hands, then betting small (and not bluffing at a high frequency) makes sense, since you want/expect to get called often. If you have a bunch of "fat value" nutted hands that only get called infrequently, betting large maximises their value, while also creating fold equity for an appropriate number of bluffs.

In short, if you have a clear "nut advantage" that will make villain fold a lot, go large with your nuts and air. If you have a range that is only "slightly better" than villain's calling range, betting small (but usually at a higher frequency overall) for thin value makes more sense.

I overbet when I have some nutted hands + a lot of draws for example when I'm on the button in a SRP and the board is:
AK46
We can have all sets, all 2prs, and many good bluffs. While villain can not have all sets or 2prs.

So if I understood you right, I think it makes sense.

If you're overbetting the flop or turn, do you also have alternate ranges that bet the flop at a smaller sizing?