The goblin's DPR is 2.75 vs the monk, 3.025 vs. the barbarian...except the barbarian is raging, so that gets cut in half and then round DOWN to the nearest whole number, per the rules. So the goblin's actual DPR against the barbarian is a flat 1.
That isn't the right way to calculate the average DPR against the barbarian. Rounding after averaging is not a valid approximation. You'd want to apply the rounding
before averaging.
Recalculating:
The goblin does 1d6+2 damage, so potential outcomes are {3, 4, 5, 6, 7, 8}. Applying the damage reduction from Rage cuts those in half, and
does round down, so the outcome set is now {1, 2, 2, 3, 3, 4}. Average damage per hit is thus 2.5.
A hit lands on a 10 or better (+4 to hit vs AC 14), so you'd multiply the 2.5 by 55% for an overall average damage done to the barbarian of 1.375. Without Rage, the average damage would be 3.025 per round.
If you want to add crits, the average crit would be 4.25 damage after Rage reduction, so the overall average damage done to the barbarian would be 1.4625. I won't worry about it in the below calculations, though.
The barbarian would then survive about 10 rounds of combat with Rage up.
And then there's the question of how long it takes to kill the goblin. Both the monk and the barbarian do about as much damage as the goblin's health each round, on average, but how this plays out is a bit more complicated. Again, assuming one round per kill doesn't quite work out.
Monk
The monk does 1d6+3 damage per hit, and has two attacks from Martial Arts. The minimum damage on a hit is 4, which means 2 hits is guaranteed to kill the goblin. Rolling a 4 or better on a single hit will also kill the goblin, so you have a 50% chance of killing the goblin in 1 hit, and a 50% chance of needing a second hit.
A +5 to hit against an AC 15 means a 55% chance to hit. That gives you a 20.25% chance of landing 0 hits, a 30.25% chance of landing 2 hits, and a 49.5% chance of landing 1 hit.
The chance of killing it in one round is thus the 30.25% chance of landing two hits (guaranteed kill) plus half of the time you land one hit (24.75%), for a total of 55%. The chance of killing it in two rounds is (20.25% * 55%)+(49.5%/2 * 79.75%) = 30.88%. The chance of killing it in 3 rounds is (20.25% * 20.25% * 55%) + (2 * 24.75% * 20.25% * 79.75%) = 10.25%. The remaining 3.87% I'll put at four rounds, for an overall average of 1.63 rounds.
The monk thus takes an average of 1.63 rounds * 2.75 damage per round = 4.5 damage per goblin. He should survive two goblins and a bit.
Note: Using a handaxe as your main weapon (1d6, Vex) would improve things a fair bit, since a lot of single hits will fail to kill the goblin. Having a better chance to land the second hit would give it a nice boost. The math is a bit complicated, though. I'll see if I can put it together.
Edit: Adding Vex reduces the average number of rounds to kill a goblin to 1.53, resulting in the average damage taken per goblin killed going down to 4.2. The average number of goblins killed increases from 2.2 to 2.4.
Barbarian
I'll assume you're giving the barbarian a 2d6 greatsword in order to get the 6.6 DPR.
The barbarian has 1 attack per round, with the same 55% chance to hit. The minimum damage done on a hit is 7 (1 die +1 die + 2 rage + 3 str), which means he is guaranteed to kill the goblin if he hits.
The chance to kill the goblin in one round is thus 55%. The chance to kill the goblin in two rounds is 45% * 55% = 24.75%. The chance to kill the goblin in three rounds is 45% * 45% * 55% = 11.14%. The remaining 9.1% I'll put at 4 rounds. The overall average number of rounds to kill the goblin is 1.74. [Note: If we include Graze on the greatsword, it's guaranteed to kill the goblin in three rounds, even if you miss every time. That would reduce the average number of rounds to 1.65.]
The barbarian would thus take 1.74 rounds * 1.375 damage per round = 2.4 damage per goblin (or 2.3 with Graze). He should manage to take out 6 goblins before being knocked out. Without Rage, the barbarian would take 5.26 damage per goblin (or 5 with Graze), defeating two, and having a good chance of taking out a third (with Graze making the third almost guaranteed).
Fighter
You mentioned a fighter or paladin, so let's check out a fighter with chain mail and a shield.
AC = 16 (chain mail) + 2 (shield) = 18. A hit lands on a 14 or better, for a 35% hit rate. That's an average of 1.925 damage taken per round.
On the attack, the fighter does 1d8 (weapon) + 3 (str) + 2 (Dueling fighting style assumed) = 9.5 damage on average, with all rolls but a 1 killing the goblin.
Average rounds to kill a goblin: 55% * 87.5% = 48.125% [1 rnd] + 45% * 55% * 87.5% + 55% * 12.5% * 55% = 25.44% [2 rnd] + 45% * 45% * 55% * 87.5% + 2 * 55% * 12.5% * 45% * 55% = 13.15% [3 rnd] + 13.29% [4 rnd] = 1.92 rounds to kill a goblin.
The fighter thus takes an average of 1.92 rounds * 1.925 damage = 3.7 damage per goblin. About halfway between the monk and the barbarian.
The fighter starts with 12 HP, but Second Wind gives an extra 6.5 HP, and the fighter has two uses of it. That gives him an average effective HP of 25, and means the fighter can kill 6.75 goblins before being knocked out.
Weapon masteries don't have a significant impact on this build because of the low chance of not killing the goblin if you hit. Sap or Vex would have small improvements in the score, but I'm not going to try to calculate them.
Net
Using your HP calculation for value generated, the monk is at about +25 HP; the barbarian is at about +33 HP without Rage, or +56 HP with Rage; and the fighter is at +72 HP.
I'm not really sure including the character HP is appropriate for this metric, though. It's pretty much already factored in due to how many goblins the character can survive long enough to kill.
If you only count the HP of the goblins killed, it comes out to +15 for the monk, +19 for the non-Raging barbarian, +42 for the Raging barbarian, and +47 for the fighter.
