Limited resources are part of the game, so we should take them into account, making some effort to average out their impact over the course of the day.
As for AC, they likely are going from 17 to 18 over the course of tier 2. That's slightly ahead of rogues, non-Hexblade warlocks, and non-Valor bards, but that's about it (even wizards and sorcerers, who have no reason to get into melee, can sit at 16 and bump that to 21 when they need it). Warlocks and bards can take a feat, dip one level of something, or use a magical secrets pick, to boost their defenses. That has opportunity cost, to be sure, but it's at least an option. Rogues have a lower opportunity cost than monks to avoid getting attacked (either staying at range, possibly hiding, or disengaging for free), because their ability to maintain their baseline level of damage doesn't require their bonus action to the same extent that monks do, and on top of that they can halve damage from one hit per round completely at will.
Even a fighter that specs entirely for offense and invests nothing in defense except for gold (which, let's be honest, isn't a major bottleneck in most campaigns after tier 1) can usually have an 18 for most of tier 2. So monks focusing on offense are slightly behind on defense compared to other characters focused on offense... and for doing that they gain... ell, is their offensive output in that case actually on par with other offense-focused martials, even those who don't take -5/+10 feats?
Ok, I guess We are doing this?
No magical gear. Just rough math of maxing AC.
Barbarian: Half-Plate for 17/ 19 with shield (lowers damage). 22 if they max stats, 24 with shield (not counting reckless)
Bard: 17 if they max dex or 19 if Valor (Half-Plate)
Cleric: Between 19 or 21 depending on domain (Half or Full Plate)
Druid: 19 (Half-Plate and shield)
Fighter: Between 18 and 21 (Full Plate and Shield with defensive)
Monk: 20 (25 when using patient), 22 and 27 if Kensei
Paladin: Between 18 and 21 (Full Plate and Shield with defensive)
Ranger: Half-Plate for 17/ 20 with shield and defensive
Rogue: 17 if they max dex. Does have a lot of tricks
Sorcerer: 15 if they max dex, 18 for dragons, bumping to 20 and 23 if they use shield
Warlock: 18 if they max dex with armor of shadows. 17/19 if they go hexblade with shield
Wizard: 15 is they max dex, 18 for mage armor, 23 if they use shield
So, I know there are a lot of problems with this list (I didn't account for ASI's, if they are this race they can do this, by the level this would happen everyone is in magic gear)
But at 20/25 the monk is doing better than everyone on that list. 20 alone puts them equal or above every caster except a forge domain cleric. And a lot of those casters I have maxing their dexterity, which they would never do.
Even just the 18 for a more reasonable 20 dex 16 Wis is better than a lot of options on this list. And that happens by level 8.
Their resourceless damage is on par with that of a featless greatsword-wielding champion through tier 2, and then when you take into account the fact that champion doesn't have any resources to spend to boost that, then yes, monk comes out ahead.
Actually, I showed them on par with a Battlemaster with no feats, using their superiority dice on every attack. I mean a single point of average damage below, but a monk using flurry and a Battlemaster with Greatsword and dice were right next to each other by level 5.
Oh, and if the Battlemaster didn't afford Plate by Level 5? Then they have the same AC or worse than the monk.
What happens when a monk boosts their defense? They can spend their bonus action and ki to dodge, which functionally gives them an AC of about 21-22 on those rounds, which is on par with a fighter with a shield and the defense style, for those rounds. But the opportunity cost they're paying to do that is higher than the fighter, because (a) that leaves the monk with that many fewer chances to stun someone, and (b) on rounds when they use their bonus action to do something other than attack, they're left doing about 2d8+10 potential damage, which is equal to a sword and board fighter who uses no resources or bonus action whatsoever, and is less than a defense fighter who uses that extra ASI they got at 6th (or who is a variant human) to pick up polearm master to do 2d6+1d4+15 with a spear or staff with no resource cost at all (if they're variant human they might have sentinel on top of that, resulting in them doing even more damage due to extra reaction attacks, and/or drawing attacks away from allies more effectively than the dodging monk).
I'm sorry, I want to get this straight. You want to tell me that the fighter who picked their Fighting style, which can never be changed, and is using a shield which takes time and effort, and reduces their damage output, is facing less of an opportunity cost than a generic monk who decided to spend a single ki this one round.
Also, breaking down your numbers (using your +5 mod)
Monk with no subclass, feat, or race using Patient Defense: 2d8+10 = 19 average
Fighter Sentinel feat, possibly variant human for sentinel: 2d6+1d4+15 = 24.5
Monk with no subclass, feat, or race on a standard no resource turn 2d8+1d6+15 = 27.5
Monk with no subclass, feat, or race on a flurry of blows turn = 2d8+2d6+20 = 36
So.
The same monk has three choices. They can spend no resources and have an 18 AC. They deal more damage than that fighter. They can spend to deal even more damage than that fighter. Or they can spend to have the same AC as the fighter for 1 round of combat and do less damage that round.
And that fighter? Has no option to change their play. I mean I guess they could doff their shield (1 round) and two-hand their spear. Then they could at least keep up with the monk's damage.
And this monk has no build. This is just a faceless undefined monk. Who can spend resources to match your defense mister specialization, and without doing that, beats your damage potential. By a lot if they choose to spend the resources on it.
Add the fighter's hitpoint advantage and hopefully you are starting to see why some of us are saying that defense-oriented monks are lacking in offense compared, not to offense-oriented fighters, but to defense-oriented ones.
Nope. You showed that a monk choosing to patient defense lacks offense that turn, but that only applies to the that specific turn. The monk can choose to just have their AC of 18 (if it is good enough for a heavy weapon fighter, why is it too low for monks?)
1) No ki. Some of your examples are using Ki. The goal here is to show that the monk, without appropriate short rests is behind.
I literally started with no ki. That is the first analysis I did, since you seemed to have missed it.
Monk
without spending any ki or resources
level 1 does 1d8+1d4+6 = 13
level 5 does 2d8+1d6+12 = 24.5
AC 16/17
And then the two fighters, also with no resources (and no feats)
BM fighter Longsword+Shield and Dueling Style
Without spending any resources
Level 1 1d8+5 = 9.5
Level 5 2d8+12 = 21
AC 18
BM Fighter Greatsword
Without spending any resources
Level 1 2d6+3 (assuming style is +2 damage on average) = 12
Level 5 4d6+8 = 24
AC 16
So. No resources spent. The monk is ahead of all of them until 5th where the Greatsword Fighter catches up.
2) No flurry. Action bonus to attack is available to all BUT GW users save for the PM. Without his flurry, the monk is behind. It doesn't take a mathematician to see it. Treantmonk proved it already. With his flurry, the monk barely keep up at low level. The fact that I said that monk have only two attacks refers to ranged attacks. I should have mentionned it again but I thought it was implied.
I don't care about Treantmonk's analysis. He didn't compare these classes, he compared them to a EB+AB+Hex build. Which, by the way would be
1d10+1d6+3 = 12
2d10+2d6+8 = 26
Which loses to the Monk at level 1, and beats everything by level 5.
And since we now want to add in PAM fighter
2d10+1d4+9 = 22.5
This was assuming they did that at level 4 instead of an ASI, and it puts them back behind the monk. So, maybe if it is a Variant Human who took PAM at level 1... but we've kind of gone beyond just "Battlemaster fighter" by this stage.
3) Though the Monk's attacks are magical, they bring no bonuses. So a fighter with a simple magical sword will do better and hit more often than the monk of an equivalent level.
So now to beat the monk (which supposedly sucks) we are giving the fighter the advantage on magical +1 gear and the monk nothing.
4) A shield can be used to attack with a bonus action. It is only a d4, but it is there. Since it becomes an improvised weapon that comes into play after the main attack(s), the shield still counts toward the AC of the fighter. The bonus action is seperated from main attacks. In this, the monk's advantage is in that he can still add his stat (dex) modifier to his rolls. This also mean that the dueling style still applies.
Really? Not only is this heavily DM dependent, on multiple levels, but this is a lot of stretching. Especially since a longsword isn't a light melee weapon and can't be dual-wielded.
But sure, we will give the Fighter Dual-Weilding, heck, lets do it as a variant human.
So, Variant human with dueling style applied to an improvised shield weapon that is using a feat in a way you need permission from your DM to even attempt
1d8+1d4+7 = 14
2d8+1d4+14 = 25.5
Congrats. You beat the monk by a single point in both categories.
5) In hand to hand, without Ki, the monk will make only one more attack, that much is obvious. At any but high level this bring the monk on par with most martial classes save the fighter. With his AC, (15 before level 4, assuming 14 or 15 wisdom and 16 up to level 7 and 17 from level 8 to 11)
The baseline assumption has been 16 AC. from 16 Dex, 16 Wis. I have no concept why you are lowering their AC. Especially since it doesn't even help.
The monk will stick out of the range of melee attackers since patient defense or dodge as an action is out of the question. The same sword and board will be at 20 AC, even the barb will be better at around if he is using a shield (barbs in my games, tend to carry a one hand weapon and a shield when out of rage capabilities. I have seen this quite often at other tables, so I think it is something that is done relatively often).
So, the barbarian will spend one turn dropping his big weapon to pull out his small weapon and put on a shield. Nice turn. The monk actually took their turn to do something.
Also, again, unless you are using massive cheese, the sword and board fighter isn't doing more damage. The PAM fighter is, but they have comparable AC (Only 18 if a 5th level fighter is getting full plate [and this makes me wonder what the monk spent their money on])
In addition, the monk will possibly be in long range for using thrown weapons, thus bringing itself in the disadvantage roll to attack.
Literally why? By 5th level a monk has 40 ft of movement, daggers have 20 ft of range. That means I need to be within 45ft to run in, attack and run out. There is absolutely no reason to assume the monk will be at long range.
Heck, using the daggers was just for ease of carrying, they could use Javelins and get 30, meaning they have a range of 55.
And again, this is going under your own assumption that they don't want to be in melee.
Unless the monk take time to put ASI into wisdom, he will not be at 16 until level 12. In this, the GW user can wear plate, making him an 18 AC. Even the two hander can have a better AC than the Ki-less monk. Some races can be a bit higher but I stick with the non variant human.
Standard array gives us a 15, 14. A wood elf Monk would have 16/16 by level 1.
If you want to stick by a worse array, that's on you, but everyone has been assuming a +2/+1 race for this since the beginning. In fact, that was Treantmonk's standard.
That is a chance! I sure hope the monk will have a few. But he would not throw them around for nothing. Most monk throwing weapon I have seen were darts (shuriken) that would give a lot more munitions than daggers. At 2 daggers per round, you require 10 daggers for a 5 round fight. All of them will be magical???? I doubt it.
I can't find the bracer of daggers at the moment (maybe it was adventurer specific) but that creates endless magical daggers. Or, they just need two daggers of returning,
But frankly, by this point we are assuming
1) The monk has no ki
2) The monk wants to stay at range
3) They are fighting an enemy with damage resistance
4) the other classes have magic weapons
If this is what it takes to prove monks suck, I wonder how anyone can stand playing a spellcaster.
Yes, I know. But the fighter doesn't get the benefit of their style, and they use a lower damage die, and they have a harder time getting in and out of range.
Save for sword and board users that will not see that much of a change when out of resources compared to the monk. The monk uses hit and run for good reasons. Without ki to fuel his Patient Defense or Step of the Wind, the monk would be a fool to go hand to hand.
So, GW fighters are all fools?
And, your point was that they would take multiple AO's from moving. Which means that instead of stopping next to a single enemy, they stopped in the middle of a group of them. That is frankly stupid if your plan is to run away.
And you know I've proven that without massive cheese, your S+B fighter is also doing significantly less damage until level 11
Edit: And I see that your GW Fighter just becomes a sub-par Sword and Board fighter instead.
You must love the shadow monk. But if that monk is in bright light? We are talking in general here, not specific subclasses. Since there are a lot of factor, lets keep to the basics shall we? And if the big sword user (or whatever big weapon) is in trouble, I am absolutely certain that it is not a morron. The BW user will have a one hander and a shield to improved his survivability. I know my players do it. It is not their first choice, but they know when to adapt to the situation. So should fictionnal example of characters that are in deep sh*t... They will use the most effective manoeuvers and tactical decision. It is just that the monks' options are a bit weaker in general. Yes, there are exceptions, like the sun soul monk that will shoot rays of light for no Ki at a range of 30 feet. But again, we are speaking of baseline character. Monk will not have a wisdom of 16 until level 11 in most cases (again specific races may change this). So we work with the baseline. Just like Treantmonk did.
Which is why I mentioned it was an option. I also said it was possible they attacked a weaker enemy and killed it, allowing them to flee for free.
And, I'm guessing you are talking about switching weapons and shields before the fight even starts, because they can't do that mid-combat without wasting a turn.
I brought up the shadow because, like you said, it starts to depend on what they can do. You've wanted to take a monk, with no subclass, a subpar racial group, take away over half of all their abilities at these levels, and make assumptions that put them in the worst possible position.
And even with all that, they are still performing right at level with fighters until level 11.
I'd like to see a wizard do the same if we took away all his spells and forced him into melee.
