Finally caught up, a few things with some hyper-basic math and all that jazz.
First. Can we please acknowledge that "I can buy a horse" is the worst counter-argument for the monk's mobility ever conceived? I feel like I'm alone in remembering the first UA for the Cavalier where pretty much everyone agree that building a subclass based on mounted combat was a terrible idea, because horses lose effectiveness in all the places Adventurers go.
I played a paladin with a mount, being mounted is awesome, but I also could rarely utilize it, because you don't ride your mount around the city, and you have to leave it behind when crossing a ravine, or going down a ladder, or any of the millions of other things that Adventurers do constantly.
To give just a basic example to highlight what I mean. Level 9 monk in a marketplace, along with his Cavalier horse buddy. I'm even going to assume that instead of stabling the horse, they are riding the horse through the market place.
Assassin fires a crossbow bolt from a rooftop and begins fleeing.
The monk gives chase moving approximately 150 ft, running up the walls of the buildings to get to the roof and begin leaping the rooftops to catch the assassin.
The mounted cavalier... can't get to the rooftops, so they will have to take a more circuitous route. They also are at half speed because of the crowds (not a problem for a single person to slip through, but a large horse, much harder), so are only moving 60 ft....So, no, the monk's mobility is not copied by buying a horse.
Also, I'd like to talk a bit about Deflect Missiles. Let us assume that a part of 4 is facing five archers. Immediately, I have to ask, are all 5 archers targeting a single player? No. Most DMs will spread that out, not focus all of that damage on a single player. Especially at low levels such as 5 and below, where five ranged attacks can drop a player pretty quickly,
Assuming Monk AC of 16, and archers have a +5 to hit, they hit about half the time. So, DM gives that extra shot to the monk. Two attacks, one misses, the other hits. The attack is a heavy crossbow let's say. That is 1d10+3. The Monk's deflect missiles is 1d10+6 minimum. Meaning they are very likely to take zero damage from that exchange. If this is 5th level? 1d10+8 is likely. Meaning that is the monk rolls a 1, the enemy still needs to roll a 7 or better to deal any damage at all.
Now, let's say that you are suffering from "DM hate's me-itis" and all five attacks are going at you. If we give the monk a turn to dodge, that takes their 16 AC to 21 (approximately) We'll say that drops the attackers chances of hitting to 30%. That means... Out of 5 attacks, it is likely only 2 hit, and of those two, one did zero damage.
This is very powerful.
But, now for the meat. DPR/AC/Ect.
One thing that is annoying me is not only the baseline (which is very high) but how a lot of this gets tilted around. So, I'm going to throw my own analysis down, and point out a few things that I think people are overlooking or ignoring.
I am assuming +4 to main stat (because I did that math already) and that everyone has about the same Con. I am using no daily resources, no feats, no subclasses. Just the base numbers. I will acknowledge here, Barbarian has best HP, followed by fighter, and rogue and Monk essentially tie.
Fighter Dual-Wielding AC 15 Damage at levels 1/5/11 double shortsword 15/22.5/30
Fighter Great Weapon Master AC 16 Damage at levels 1/5/11 Greatsword (assume style is +2 total) 13/24/35
Fighter Dueling Style AC 18 Damage at levels 1/5/11 Sword and Board 10.5/21/31.5
Fighter Defensive AC 19 Damage at levels 1/5/11 Sword and Board 8.5/17/25.5
Monk AC 17 Damage at levels 1/5/11 Staff and single martial arts 15/24.5/25.5
I had barbarian and rogue, but I started running out of time, so I cut it short. Note that in my analysis At level 1 the Monk is tied for best damage, level 5 they have the best damage, and they drop sharply at 11. And in terms of AC, they are comfortably in the middle.
But, I hear the hew and cry, my analysis is all wrong. Why aren't the fighter's wearing plate? Or using magical weapons.
And that is point 1 that I would like to address. While it is true that fighter's can spend gold to increase AC, that leaves a weird deficit in the party, because if we assume equal loot, the monk is getting a lot of gold, and nothing to use it on. They have to be buying something with all that gold, but we don't know what it is.
But, these is part of the problem with monks that isn't any problem of the monk design, but rather the rest of the game. If we assume the Fighter is getting +3 Plate, +3 weapon and +3 Shield, then the monk falls behind everywhere, because they don't have any good magic item support. Monks don't really have any way to increase their AC through magical gear that isn't also available to everyone else. Which means that they are going to fall behind by default. Not because they are poorly designed, but because the other classes have access to things that support them and their styles.
Now, that all being said, I did make a recommendation on a different site that I am going to leave here too, because I think it is painfully obvious that monks fall off the cliff at level 11. But, I just want to acknowledge that if we are assuming the other classes can use their gold to improve past their starting gear, but leave the monk with nothing to spend their gold on that helps in anyway, then of course they are going to look worse.
So, the solution might simply be, make Monk Gear.
Now, this is a massive drop off [talking about 11th level damage], I fully agree with that, but I also note, that everything is below his baseline yet again. I can see a fix of increasing the monks bonus action attacks here, letting them do 2 naturally and 4 with ki...
That would make the monk doing 4d8+16 = 34 baseline, and then spending their ki could bring it to 51... which is pretty decent actually. But, I think his baseline is still far too high
Edit: People reminding me that short rest recovery is a thing. Maybe do something a little more complex, but have the second set of attacks be a die size lower? Probably still too good if you really focused on making them shine, but they do need a big boost in damage to stay competitive with even basic builds at this level.