Bonus action conflicts aside (Hex + Martial Arts), you cannot use Martial Arts unless you take the Attack Action. Greenflame Blade is Cast A Spell. So, even if you get your sneak attack somehow on a Hexed target, it's only 3d6+2d8+4=23.5 damage on a hit.
To make this concrete: against an AC 15 gargoyle, you're taking 4.75 damage per turn and inflicting 15.08 damage per turn. In the 3.44 rounds it takes you to kill it, you take 16.38 HP of damage, or 23% of your total HP. You can kill approximately 4 CR 2 Gargoyles a day. If we take Shield spells into account, each Shield spell effectively adds 6.19 HP to your total (it blocks one attack worth 5.5 HP and, 50% of the time, that happens on the first hit and therefore reduces the second hit from 2.38 DPR to 1 DPR, for an average reduction of 5.5 + 1.38/2), so six first-level slots buys you approximately eight extra rounds to kill gargoyles, yielding ((6.19 * 6)/4.75)*(15.08/52) ~= 2.26 extra gargoyles. You can kill about 6.25 CR 2 Gargoyles a day. I'm ignoring Gargoyle damage resistances here for simplicity--assume you found a +0 magic weapon.
A bog-standard Champion at this level with Str 20 and Defense + Dueling Style (longsword + plate armor + shield) fighting unimaginatively (attack, attack, attack every turn) would do 27.23 damage per turn to the same gargoyle with three longsword strikes (no point in using War Magic unless the Gargoyle tries to play movement games) while taking 2.55 damage per turn in exchange. In the 1.91 rounds it takes the Champion to kill the Gargoyle, he takes 4.87 HP of damage, or 4.87% of his 100 HP total (assuming 14 Con for simplicity). He can kill 20.54 CR 2 Gargoyles a day, without ever even accounting for Second Wind or HD healing or better tactics like grapple/prone. You're about 33% as effective as a bog-standard, unoptimized Champion who's just bashing away unimaginatively with his longsword.
(In contrast, a Warcaster Heavy Armor Master Paladin 9/Warlock 2/Sorcerer 1 using good tactics can easily kill a hundred gargoyles and still finish at max HP.)
The build is really quite bad. This is partly due to MADness and lack of ASIs, but only partly.
I'm in two minds about contradicting you, because honestly, this build wasn't
intended to be optimised - there's a clue in the thread title, even - but... I think your calculations have some issues.
Before I continue - let's agree that the pathological example is a terribly optimised character. It would be utterly trivial to optimise at least a little - different first class, different subclass options, but there's certainly going to be a limit. It's not, actually, ever going to be a great build. When I built the example at the start, I was going for fun choices that made for something interesting to test out the multiclass rules as I understood them at the time. I'm still tempted to play such a character, but I would not play this one. For a start, heavy armour is entirely resonable for this character, since they have several routes to qualifying for it (Cleric subclass is, of course, probably the easiest) and they could easily take the Defense style and concentrate on cantrip damage most of the time. However, that's not the example as I created it, so let's ignore that and take the AC as I created it - 17. I will change the spell selections slightly (After all, people have been using Hex as an example)
A CR2 Gargoyle makes two +4 attacks which each do an average of 5 damage. Against an AC of 17, they can be expected to hit 7/20ths of the time and get a crit for 10 damage once in 20. That averages out to 2.25 damage per attack against AC 17 - so, the actual damage per round is 4.5. With 71 hit points, that means 15.333 rounds of damage taken. However, that doesn't account for Shield, of course. While first level slots are available - assuming no short rests, that's five times - shield will reduce hits from 8/20 to 3/20. It's generally better to only use Shield when the first expected attack hits, so we say there are five rounds in which damage drops to 2/20 non-crit and 1/20 crit, or 1hp. That means we have 19.666 rounds of damage. But... we haven't accounted for any of the 2nd or 3rd level spell slots. let's start with Armour of Agathys cast at 3rd level, which provides an additional 15hp and does 15 cold damage per attack to enemies that hit every round it's up (without concentration, too). We'll be sensible and not cast shield while the temp hitpoints are up, so with three castings that provides us with 29.666 rounds of combat, and 12 spikes (on average, 15h will last four hits) of 15 damage each from the AoA. This isn't a complex tactical optimisation, and assumes no maneuvering (just like the Champion build). Then there are the 2nd level slots. Let's see, what's the simplest, least optimised choice for those... Let's go for False Life. An extra 33hp (average 11 * 3) brings us to 37 rounds of combat. Of course, six of those rounds involve spellcasting, so 31 rounds of doing damage, 12 of which will have a +15 bonus to damage.
Damage-wise, you had 23.5 damage, which is actually a little high I think. Assuming greenflame blade and no Hex cast, you're looking at 1d8(rapier)+2(dex)+2d8(greenflame blade)+1d6(sneak). Accounting for the Gargoyle's resistance, that's 16.5 average. Given I've assumed Shield for the 1st level slots, I'll actually take the lower figure of 19 on average. Against an AC of 15, that's 12.35 damage per turn (accounting for crits). Including the 12 instances of 15hp damage from AoA, that's a total of 562.850 damage over 31 turns, or enough to kill 10.82 gargoyles in a day.
The Champion probably has something like 85hp (assuming +2 CON), and takes 2.5 damage per round (4 hits ever 20 attacks, 3 non-crit, 1 crit, for 1.25 damage per attack). That's 34.8 rounds of combat. Let's be minimally sensible and allow the use of second wind and action surge, once each, for 37.8 rounds of combat.
The Champion in this example does
not have a magical +0 weapon; having such an item is an overwhelming advantage to the Champion, because almost all of their damage is standard physical. Assuming STR 20, the Champion does 11.5 damage per attack, which is halved to 5.75. That's a theoretical 17.25 damage per round against this target, and they will hit 75% of the time. Accounting for crits on 19 and 20, that accounts for 14.663 damage per round. Over 37.8 rounds, that's 554.243 damage, or enough to kill 10.65 gargoyles in a day.
Which makes this overcomplicated, convoluted character
just slightly better than a Champion using no clever tactics or creativity,
if and only if Pathological is happy to spend all their daily resources to do it. That sounds about right, really - you could play the Champion a lot better than this example, and you can optimise Pathological somewhat more and use better tactics, but my point stands - when you compare them fairly, even this pathological idiot of a build is not
utterly without merit. Well, unless you really don't like overcomplicated messes, of course!
If you want to bring magic items into the comparison, by the way, you need to use ones that benefit the different characters equally - and remember, 5e is not balanced around magic weapons. I think stripping them out of this comparison is the best way to see the native power. Even a +0 sword will naturally benefit a more martial character far more than a character who relies on magic and - with this much multiclassing - Pathological will always rely on spells.
(edited slightly to make my point clearer; it could be read initially that I actually believed this build could be optimised into something good...)
