Multiclassing a Rogue in 5e - Searching for Damage

Vincenzo Camuccini - The Death of Caesar. Completed in 1805, this painting shows what happens when a high level character makes enemies and then fails his perception/investigation/insight checks. 

Vincenzo Camuccini - The Death of Caesar. Completed in 1805, this painting shows what happens when a high level character makes enemies and then fails his perception/investigation/insight checks. 

I was invited to participate in a dungeon crawl campaign. It’s set up as a race, so in this instance, I want my character to be optimized-ish. I want to play a rogue (or mostly a rogue) and I want to do a lot of damage. I have no idea how to do that.

Here are the goals of my design
High damage. Whatever I do, my character need to kill more efficiently than a standard rogue.
Avoid builds that only look to level 20. I’ve never had a character level to 20. She needs to contribute to the team during her entire existence.
Street legal. No weird homebrew rules and I don't have the Sword Coast Adventurer's Guide. It's Player’s Handbook only for this test.
Long term resources. We don’t do an 8 minute battle then a long rest. Time is of the essence. She is going to be separated from civilization, and needs to avoid single use resources.

The Contenders
Here are all the builds I wanted to compare.
Avenger. Take a Rogue (arcane) chassis, add five levels of the Fighter (battlemaster), and a two drops of Paladin. You use the battlemaster’s repost ability to spam off turn sneak attack, and then back it up with smite that is fueled from the arcane trickster’s spell slots. I love smite, sneak attack, and martial dice, and I want to combine them all together. This build is melee only.
Standard Rogue. Rogue 20 (Assassin) included for comparison purposes.
Slayer. A ranged Rogue 15 (Assassin)/Fighter 5 (Champion). This multiclass ranged rogue will take advantage of the fighter's second attack, archery fighting style, and an improved critical.
GWF. A great weapon Fighter 20 (Champion). This fighter primarily uses a great weapon fighting style and a maul. For comparative purposes, this build is assumed to have the great weapon master feat starting at level one. This build also mirrors a fighter that uses a longbow, takes the archery fighting style, and sharpshooter feat

Assumptions

  • Rogues will always get sneak attack
  • Action surge will be used for combat
  • Ability score increases will be used for primary statistic (strength or dexterity) and then for feats 
  • Main stat is +3 at level 1
  • All mundane equipment is available

Damage Per Round: The Ability to Punch
Calculating to Hit. I took the average AC of a monster at the CR of the character’s level (see DMG page 274), and used that to calculate a to hit percentage. This was used to modify the total damage a character could do. As the character’s level up, monsters become harder to hit. If you don’t invest in the stat that boosts your attack modifier, your damage will go down. The formula looks something like this:

(1-(([Average Monster AC for CR X] - [Character to hit at level X])*.05))*(average damage of hit)

Resource Use. For resource based attacks (action surge, martial dice, et cetera), I made the following assumptions. In an adventuring day, there are 6 encounters consisting of 4 turns of heavy combat, and two evenly spaced short rests. For example, a 2nd level fighter would use the action surge ability 3 times and it’s assumed she would use the action granted to attack. Thus you take the damage done by the action surge divided by eight (24 daily rounds/3 daily uses) to determine the amount to add to the round total. 

For smite, I assumed all spell slots were used for that purpose and divided the total damage by 24 (the number of estimated combat rounds per adventuring day) to get what they add to the character’s damage per round. For the rogue’s assassinate bonus I assumed it would hit 2 times out of six combats or one in every 12 rounds.

Results. All the multiclass and fighter builds landed between 49 and 54 modified damage per turn at level 20 while the standard rogue was left far behind behind. Also, the combo fighter/rogues had a more linear progression. With one exception, starting at level 8 the fighter/rogue combos drastically outpace standard fighter and rogue. The fighter catches up when they get another extra attack, but then fall behind again. The most extreme example occurs at level 19 the where the Rogue/Fighter combos are doing around 48-50 damage a turn, while the fighter floats around 40. Only at level 20, does that extra attack bring them up to speed.

People Love Charts

People Love Charts

So if you want to be a rogue and do damage, take 5 levels of fighter. The Slayer (rogue/fighter) build basically matches the Avenger (rogue/fighter/paladin) but is far less complicated to play. You don’t have to be worried about wading into melee to use your reposte or smite to max your damage.

Things I learned while I was doing this comparison:
To hit is constant. Without the archery fighting style, your character’s to hit percentage on the average AC of appropriately leveled monster is basically 65%. This assumes you spend your ASIs to pump your main ability scores.
You are easier to hit as you level up. AC is generally static for most heroes. Hence, monster to hit slowly goes up by 15 to 20% over the course of a character's’ career.
5 levels of fighter make a huge difference for a rogue. If you look at the graph, the biggest leaps in ability are when 5th level of fighter is taken. For rogues, a second attack means you basically ensure your sneak hits. Furthermore, the fighting style and martial abilities (even if you just take “champion”) pump your damage.  For example, more than 45% of the damage of the Avenger at level 20 is due to the synergistic effect of those 5 levels.
Smite isn’t as cool as I thought. By level 20, the Avenger has 25 d8s that come from smite. Spread out over an adventuring day, this accounts for about 8% of her damage. You can still nova, but you are sacrificing a bit of long term viability. Remember we are sacrificing 10% of our character levels and choosing arcane trickster to pump up the number of spell slots. It might not be worth it.
Feats require Intelligence. Part of this analysis included checking if the the power attack feats (sharpshooter and the like), where you take a 5 to hit reduction for an additional 10 damage, created a large benefit for the character. In the graph below, the Sharp Slayer was assumed to always use the feat. It made minimal differences in damage output and lost efficiency as the character's damage increased. Bottom line, you gotta be smart about it and use the ability against softer targets. The feat is worth more to a lower level character who doesn’t do a lot of damage.

Conclusion:
For me, the Rogue 15/Fighter 5 looks to be the best bet. At the end of the day, you sacrifice a few points of damage per round to avoid melee combat and resource monitoring.

What do you think? Do you agree? Did I miss something? Let me know.