But... that's precisely why we need an integrated analysis?
If you want to precisely measure it, I guess, but it takes only a few moments of consideration to realize that their damage is decent until level 11, unless you are including limited resources or the -5/+10 feats. And that their AC is fairly decent compared to every class out there.
Add in the fact that monks don't need to purchase anything (meaning that the 1500 gp the figher spent on plate to equal the monk's AC is still in the monk's pocket for something) and they have the same Spell DC as any half-caster tends to have... and well it is generally easy to see the rough shape of what a full "test every class" set of data would tell us.
I do not agree. At high level a fighter will have more attacks. Any fighter type will.
Stop.
You said "the monk without ki has two attacks".
That is 100% false. A monk without ki has 3 attacks while in melee. Nothing you say about high level fighters or anything else changes that fact. In melee, with zero Ki, a monk can make three melee attacks.
Continue.
But at low and mid level it is even worse, the monk does not do that much damage. It does not have that high of an AC too. All the while, the BM will be in plate (chainmail at the minimum) and with a shield (unless two handed). At higher level, it also means that the BM will have more attacks, better AC (not counting magical items) and better HP. So the monk will be stuck with two attacks unless it takes the risk of going melee with a low AC (no Ki remember?) and relatively low HP compared to a BM (or any fighters for that matter). The monk will, however, have potentialy more attacks than the paladin, ranger and barb but if the paladin and rangers have a shield or an off hand weapon, they can use their bonus action to have exactly the same number of attacks than a monk. And if they are PM, then they can use their bonus action too for better effect. So the monk isn't winning on this side. If Flurry of blow was off the Ki spending, it would be way better.
Okay, so you just threw a whole lot at there with little or no supporting numbers. So, I'm going to have to add in the context myself it seems.
Once again.
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
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. Zero resources spent. The Monk is doing more average damage than both fighters, and has more AC than the Greatsword fighter. Since we have made this a battlemaster fighter, I'm going to make this an Open Hand monk.
Offense
Spending some ki for Flurry?
level 2 does 1d8+2d4+9 = 18.5
level 5 does 2d8+1d6+12 = 32
Also, since this is an Open hand, if the flurries hit, I can knock prone, push up to 10 ft or remove reactions. This are similar to
three seperate manuevers for the battlemaster. So, let us assume the battlemaster used either Manuevering Attack (which allows one ally to move) Tripping attack (knock prone) or pushing attack (push 15 ft)
BM fighter Longsword+Shield and Dueling Style
Level 3 2d8+5 = 14
Level 5 4d8+10 = 28
Action Surge would make that 19 and 38. Action Surge
and a die on every attack makes 28 and 56
BM Fighter Greatsword
Level 3 2d6+1d8+3 = 16.5
Level 5 4d6+2d8+8 = 33
Action surge would make that 22 and 46. Action Surge
and a die on every attack makes 31 and 64
So, offensively, the monk using a single point of ki is better than the Sword and Board battlemaster using 1 or 2 dice. The S+B can barely catch up if they action surged instead before 5th level, and at fifth Action surge is superior
to a single ki point
The GW does better. Behind with 1 die at 3rd, ahead with 2 die at 5th (by a single point on average). Action surging is superior again.
Defensively? Just for giggles.
The monk can bonus action dodge, which is an approximate +5 to AC to any number of attacks.
The Battlemaster has nothing comparable. The closest two they have is Parry which reduces the damage of a single attack (making it inferior) or Evasive Footwork, which increases AC while moving, meaning it is intended to be used against opportunity attacks. The Monk could just spend the ki to disengage instead though, which just cancels those attacks outright.
So. Superior damage to the Battlemaster with Shield. Superior Defenses to the Battlemaster with greatsword, and comparable damage unless the fighter is using action surge. Which they can do once. Also, while the BM has 4 dice for maneuvers, which is +4d8 total. The monk has between 3 and 5 ki. Which means they can keep up on the damage and the defense for a bit longer.
So. Tell me again how Monks have worse damage and worse AC than
any BM Fighter? After all, the Sword and board drops his shield and pulls a second weapon? They lose their +2 to damage on each strike, and their superior AC, and are attacking for only d6+dex mod on their main had and d6 straight in their off-hand.
Lower hp? I'll give that to you.
Surpasssed at level 11? I'll give that to you as well.
But before level 11, the monk is not the inferior melee class.
Because the monk can not rely on the patient defense, it will be stuck with ranged weaponry (unless ready to take a risk). He will then be worst off than the melee characters, archers will have their higher damage with longbows beating what the monk can do. At higher level, the monk will be about the same as an archer. 1d10 +5, but the monk will lack magical bonuses from magic bow and arrows.
A) It isn't much of a risk, it is the same risk as the Greatsword fighter
B) Magic daggers are a thing
C) Monk matches longbow by level 11th in terms of damage dice. They would be less accurate than a dedicated ranged character, but monk at range is still better than a strength fighter or a paladin at range.
The monk will not be able to disengage freely (no Ki...). This means that moving in, attacking and moving out; will produce an OA, which can potentially be lethal to the monk if multiple enemies are in reach and if the monk is less than top HP (which is likely since the monk had no short rest).
1) Why yes, if the monk plays like an idiot and tries to move away from three or more enemies proccing multiple attacks of opportunity, they might be in trouble. Same with literally anyone.
2) Could produce an OA. There are a lot of factors there. Monk could end up killing that enemy, They could be a shadow monk (meaning they can teleport away in dim light). But, they are no worse off than the Paladin, Fighter or Ranger in this same scenario. A Greatsword fighter, low on hp, who runs back into melee is in trouble. And, likely more trouble than the monk, because their inferior movement options mean they likely can't get back out even if they kill the enemy.
Why are you presenting this like a uniquely monk problem?