Just an interesting bit of design philosophy:
Hitting level 5 in D&D feels amazing. Every class, with the exception of the Rogue (who oddly gets a defensive ability) will get something that really dramatically increases their power. Pure spellcasters get 3rd level spells, which include such bangers as Fireball and Spirit Guardians, while martials get Extra Attack.
And why does Extra Attack feel so good to get (I'll lump in the cantrip progression of Eldritch Blast here as well)?
Because it smooths out the probability of landing a hit.
Analyzing "damage per round" things like I've been doing with all sorts of classes and builds is an abstraction. When you attack with a Maul, you're not really doing, like, 70% of 2d6+3 and then 5% of 2d6. You're either hitting or you're not. Probability tells you how likely one or another thing is going to happen before it does, but once it does happen, it's locked in. (This is why being "due for a win" in games of chance after losing many times is a logical illusion - before you started, you might have said that you would win after X attempts, but once you've lost in X-1 previous attempts, that model is no longer accurate).
In statistics, larger sample sizes produce more accurate results. Asking 10 people, for example, who they're going to vote for in an election, might produce a very skewed result if the actual electorate is a hundred thousand people, because you might purely by chance happen to pick all people who are voting for the yellow candidate, giving you the false impression that they have 100% of the electorate's support. If you instead had a sample size of 100, it'd be much less likely that none of the purple candidate's managed to get into the sample. Even if the purple candidate only has 5% of the electorate's actual votes (30,000) the chance that you don't get a single person who supports them in a group of 10 is 95% to the 10th power, or about 60%, but the chance you don't get one in a group of a hundred drops to about .6%.
It's the same idea: if you attack once and have a 60% chance of hitting a target (say you've got an attack bonus of +5 and your target has an AC of 14, you'll land a hit and get to deal damage... 6 times out of 10. But if you have extra attack, the chance you get to do something with an attack goes up by a lot - to 84%. Now, each attack still only has a 60% chance, but the chance you'll only miss drops from 40% to 16%. (Incidentally, the chance that you hit both times is only 36%).
Now, the good feeling of Extra Attack goes beyond this: we deal more damage on average. Indeed, we basically double our damage output. It is probably the biggest jump in power that any player characters actually experience. Even when a Fighter gets a third and later fourth attack, this is a jump of 50% and later 33%, compared to this 100% damage bump at level 5.
We often talk about tier 2 as feeling like the sweet-spot of D&D 5E, when the game feels the most balanced and satisfying. Now, comparing this with tier 3 and especially tier 4, a big part of this is because players don't have absurd solutions to every problem, like long-distance teleportation spells or great big extradimensional spaces. Saving throw DCs for players' features tend not to get to 20 or above at these levels.
But the reason I think tier 1 feels... maybe not bad, but kind of limited is that we run into these kind of binary situations - you hit or you miss, and at these levels, monster damage is high enough relative to our HP that we don't have a lot of recourse if some Incubus crits us for 26 damage (a level 4 Wizard with a +2 to Con would have 26 HP if not rolling for HP).
There's a feeling upon hitting level 5 that one has "arrived on the scene." You go from being desperate scrappers that aren't that much more powerful than the civilians you're there to save to being real professional hero-types.
Here, though, is why I think that effects like Graze are really interesting - from level 1, your attacks will always do something, but you still prefer to hit so that you can do a bit more.
It's interesting, then, to see how this principle is approached in games like Draw Steel and Daggerheart.
In Draw Steel, there is no attack roll - essentially, you skip ahead to the damage roll on any of your abilities. Thus, there's no reason for something like Extra Attack to exist, as it would purely just increase your damage. Your damage does go up, but primarily because you're accruing more heroic resources faster to spend on more powerful (and expensive) abilities, and because your gradually rising main characteristics will make it more likely to get a tier 3 result on power rolls (and less likely to get minimal tier 1 results). But I also think (theoretically) that the progression of power in that game is smoother - things like Signature Abilities don't really do more damage, but you have to rely on them less.
In Daggerheart, there's almost an opposite direction that they take: you have to roll to do anything in combat (including casting spells) but you don't get more attacks because that would make it more likely that you have to pass the spotlight back to the GM. However, instead, you wind up rolling additional damage dice based on your tier of play (or whatever the equivalent term is). Essentially, everyone has more Rogue-like scaling in Daggerheart.
I think one of the things that can be frustrating for higher-level play is that the universality of scaling breaks down. Fighters and, now, Monks, effectively get more attacks at higher levels (Monks though through Flurry of Blows' upgrade at level 10) while Paladins add a new damage die to each attack, and then Barbarians have Brutal Strikes, which brings utility but can sometimes wind up being a net damage loss if the target's AC is high enough. And Rangers... don't really get anything.
But also, while Fighters and again, sort of Monks, get this greater "damage smoothing" effect, the others don't.
