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TL;DR: as a Great Weapon Master, half-orc Barbarian, is it worth it to take 3-4 (or more?) levels of Fighter, in order to deal more damage?

I'm going to play a half-orc Barbarian in a soon-to-begin D&D 5E pure PHB campaign, starting from level 1. I've decided I'm going to use the Great Weapon Master feat, weilding a greataxe (d12). I start with 18 Strength (+4), so we can assume I'll hit 20 at the first ASI available.

A half-orc Barbarian can be a critical hit powerhouse, thanks to Savage Attacks coupled with Brutal Critical. However, other than the advantage on attack rolls granted by Reckless Attack, there's no way to raise the chance above ~10%. I find this a bit unsatisfying.

I've thought of picking up a few levels of the Fighter class, maybe after reaching level 5 with the Barbarian, in order to gain Extra Attack first. With three levels, by picking the Great Weapon Fighter fighting style and the Champion archetype, I can increase both the average damage output and the critical chance (the latter by around +5%, as far as I understand math), while also getting Action Surge.

This looks great but, of course, slows down the path towards more Brutal Critical dices and more rage uses and damage. Also, presuming I will reach level 20 (17 Barbarian/3 Fighter) in the campaign, I won't get the last Barbarian ASI (at level 19) and Primal Champion, which means, at least, I won't earn +2 to attack and damage rolls granted by reaching 24 Strength. I might take another level of Fighter (16/4) to compensate for the ASI, but that would also mean one less Brutal Critical dice (since the Barbarian earns that last one at level 17), which is kind of against the purpose of such a critical hit-oriented build.

I can't decide whether to follow this path or to only go for the Barbarian. Perhaps I didn't even correctly estimate the increase in average damage output and critical chance, as I don't really know the math.

Which choice will result in a greater damage output: going pure Barbarian, or picking some levels of Fighter by multiclassing?

Take into account the following premises, as asked in the comments.

  • I'm a half-orc and I start with 18 Strength (+4) and Great Weapon Master, as the DM allowed to choose a starting feat.
  • Barbarian should be the main class, so please consider at maximum 9 or maybe 10 levels to be multiclassed into Fighter.
  • The Fighter multiclass can follow any path that's best for damage.
  • Any other feat can be later acquired instead of an ASI, if it's best for damage, but I'd like to keep Great Weapon Master.
  • Regardless, I am going to pick the Totem Warrior subclass of the Barbarian, so exclude Frenzy of the Berserker path.
  • For the purpose of this analysis, the focus is the best total average DPR against average AC monsters. Rage can be included in the calculations.
  • Hence, Armor Class and HP pool concerns can be ignored.
  • DMG Magic Items can be expected to appear sooner or later in the campaign.
  • As remarked at the beginning, the environment is pure PHB only ("vanilla", so to speak), therefore please refrain from suggesting anything outside of the manual.

If you have a different suggestion for the class option to be multiclassed with the Barbarian, in order to increase damage (e.g., I don't know, Rogue), please point it out briefly, as it's worth a different question.

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  • \$\begingroup\$ For what it's worth, the critical hit chance with advantage for your barbarian is 9.75%, not 10% (since you have to subtract one of the outcomes for when both dice roll a 20 which is only 1 discrete crit rather than 2). Also, picking up the Champion archetype increases the critical hit chance by 9.25% to 19% (with advantage). \$\endgroup\$ – David Coffron Aug 8 at 20:32
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    \$\begingroup\$ Not a duplicate, but related: When is it optimal to dip two levels of Barbarian into this human variant fighter build? \$\endgroup\$ – MikeQ Aug 8 at 20:44
  • \$\begingroup\$ @NautArch Yes, exactly. Thanks DavidCoffron for correcting my math. \$\endgroup\$ – StackLloyd Aug 8 at 20:46
  • \$\begingroup\$ @Medix2 Well that's the burden of any "should I pick some multiclass levels" question, isn't it? But I don't think that they are all too broad and impossible to answer. I don't necessarily need to know specifically when to pick each level, a general idea is enough. If no one mentions anything, I'd probably just go for 5B - 3F - 12B to 20. Analyses like the ones below are fairly complete and pretty much what I was looking for, I'll just wait if anyone wishes to add a bit more details. \$\endgroup\$ – StackLloyd Aug 10 at 19:18
  • \$\begingroup\$ Related/Helpful on when to use GWM based on expected damage (the second answer): rpg.stackexchange.com/questions/76631 \$\endgroup\$ – Medix2 Aug 10 at 22:33
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Setup

  • Half-orc
  • You start with a +4 Strength modifier at level 1
  • Your Constitution modifier is assumed to be +3 at level 1
  • ASIs go towards raising Strength to 20, the Sentinel Feat, the Savage Attacker Feat, and raising Constitution, in that order
  • all attacks are made with Reckless Attack, -5/+10, and receive the rage damage bonus
  • The enemies' AC is 16 for the level 12 comparison and 18 for the level 20 comparison
  • Primal Path is Totem Warrior
  • No magical items
  • we optimize for Damage Per Round (DPR)

In the question's body you note that GWM, Savage Attacks, and Brutal Critical all profit greatly from critical hits, so we aim to incorporate the Champion's (Fighter) Improved Critical. The first comparison is at level 12, as that is the earliest you can have Brutal Critical and Improved Critical. The second comparison is at level 20, to determine which is the desired final state.

The other PHB Fighter subclasses offer no tangible synergy (Battlemaster) or are objectively worse than pure Barbarian (Eldritch Knight; you can't cast spells while raging).

The next Fighter Feature after Improved Critical that could produce a high DPR build is probably Extra Attack 2, but that comes as late as level 11, which you specified as too late.

The question of when to use -5/+10 has been answered many times already so I won't elaborate on it, but under the given preconditions (attack modifier, enemies' AC, average damage) it is worth it. Of course, in actual play you'll have to judge situations separately. Don't forget to include the damage increase of the Great Weapon Fighting Style, which is 0.833 per d12.

Sentinel offers simply more opportunities for Attacks of Opportunity and therefore more DPR. Note that Reckless Attack gives you advantage "until the start of your next turn", so if you used it during your turn, you'll still have advantage on Attacks of Opportunity. Savage Attacker provides a bonus of ~2 to a roll of 1d12+mod, and ~5 to a roll of 6d12+mod (with Savage Attacks and Brutal Critical 3 a Great Axe crit will do 6d12). This is a very minuscule bonus considering it only applies once per turn. Nevertheless, it is a damage bonus, although I personally would prioritize survivability over this Feat. Both feats are not included in the concrete calculations, but are mentioned in the analysis.

Although you specify that survivability can be ignored while optimizing DPR, you mention in the body that you considered Barbarian 16 Fighter 4 to get that fifth ASI back, which offers no real improvement to your offense, given that you start out with 18 Strength and GWM at level 1. Therefore I will still try to mention at least your Constitution and max HP when comparing builds. The static hp-increase-per-level will be used to calculate expected max HP (7 instead of 1d12 for barbarians). Also, don't forget that a living Barbarian deals more damage than an unconscious one, which puts a real DPR gain on better survivability, albeit hard to quantify.

Barbarian 12 vs. Barbarian 9 Fighter 3

If you go full Barbarian, you get your third ASI right at level 12, which gives you a +5 Strength modifier and two more ASIs for Savage Attacker and Sentinel.

If you dip three levels into Fighter, you get only two ASIs, resulting in a +5 Strength modifier as well, but no Savage Attacker. You also have the opportunity to pick up the Great Weapon Fighting Style, which more than makes up for it.

Damage wise, B9F3 comes out ahead by a hefty margin of +14 average damage per round (59.98 over 46.14). Sentinel can't change this in favor of B12, as the average damage per attack is also higher for B9F3 and the Feat simply gives more opportunities for an extra attack.

Barbarian 20 vs. Barbarian 17 Fighter 3 vs. Barbarian 16 Fighter 4

B20 gets you another two ASIs you could invest into Constitution, getting a score of up to 24 in both Strength and Constitution. Constitution would be your best choice for survivability, raising both your AC and your HP - which scale fantastically due to the damage resistance granted by your Rage. Indomitable Might is crazy good for stuff like grappling and shoving and Primal Champion is arguably the coolest capstone of all classes. Expected max HP: 285 (12 + 19x7 + 20x7)

B17F3 also gets you two additional ASIs, or four in total, giving you only one ASI for Constitution, getting a score of 18. But you get all Brutal Criticals (dealing 6d12 + mod on a crit) and Improved Critical, resulting in a phenomenal damage potential. Expected Max HP: 222 (12 + 16x7 + 3x6 + 20x4)

B16F4 costs you one Brutal Critical, but gets you that fifth ASI back, which we're promptly putting into Constitution, getting a score of 20. Expected Max HP: 241 (12 + 15x7 + 4x6 + 20x5)

And now what we've all been waiting for. The winner is:

  1. B17F3 with an average 72.33 DPR
  2. B16F4 with an average 67.03 DPR
  3. B20 with an average 61.33 DPR

Magic items

If you found an item that raised your strength to, say, 24 (or higher, but we're using 24 to prove a point) , B20 would gain nothing and B17F3 would gain another immense boost, making that option even more attractive.

If you found a +1/+2/+3 Magic Weapon, both options would still gain a lot, but B17F3 would even more than B20, making it, again, more attractive.

If you found an item that raised your constitution to 20 or higher, all options would gain some, as there's still Dexterity to improve, which would raise your AC. This would be hard to quantify, however, so I'm not gonna try.

My Recommendation

The jump from 61 to 72 DPR is about a 20% increase, costing you 63 Max HP (or about 22%). If you compromise for 67 DPR you lose out on half your damage increase, gaining back merely 19 max HP, which makes this a suboptimal choice in my eyes.

If you want to be unkillable, walk the Path of the Totem Warrior, (choosing the Bear at level 3) all the way to level 20 and you'll have an insane amount of HP and still deal absolutely respectable damage.

If you enjoy the satisfaction of a build well executed and reaaaally want to regularly deal those 6d12 damage (about once every two turns, opposed to once every 5 turns), go B17F3.

Level progression

One of the largest damage increases you'll feel is Extra Attack at level 5. In order not to feel left behind I suggest - should you decide to multiclass - you go 5 Barbarian, 3 Fighter, 12 Barbarian. Action Surge, the Great Weapon Fighting Style, and Improved Critical all improve your DPR substantially, providing most of your biggest DPR increases as early as possible.

(source)


"My other recommendation"

I stood before this same dilemma a while ago and solved it as follows: I asked my DM for a specific magic item and received:

Gorehowl

Greataxe, req. att.

+2 weapon. Rolls of 19 or 20 count as critical hits. Disadvantage on Stealth.

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  • \$\begingroup\$ Comments are not for extended discussion; this conversation has been moved to chat. \$\endgroup\$ – V2Blast Aug 11 at 2:52
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    \$\begingroup\$ Definetely a great and complete analysis. You answered quite all of my doubts. If I see my party is struggling with damage, I'll definetely choose the 17B/3F path you suggested. Otherwise, I'll just go full Bearbarian and become the unkillable tank they need. \$\endgroup\$ – StackLloyd Aug 11 at 19:21
  • \$\begingroup\$ "getting a score of up to 24 in both Strength and Constitution" ASI can't raise a score higher than 20, so that's not gonna work. \$\endgroup\$ – Darth Pseudonym Aug 12 at 12:02
  • \$\begingroup\$ @ammut Okay, the way you phrased that made it sound like the ASI was giving you the 24. If you meant the ASI could get your CON to 20 so that it would go to 24 at capstone, then fine, I was just not following that. \$\endgroup\$ – Darth Pseudonym Aug 12 at 14:01
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This depends on the level, whether you're raging or not, whether you're using berserker's frenzy, have advantage etc.

Since all combinations are a bit hard to consider, I'll make some assumptions:

  • Level 1 a STR score of 16 or 17 (+3) is assumed
  • The first ASI is used to buy Great Weapon Master, further ASIs are used to increase the STR to 20 asap
  • Great Weapon Master is always used to decrease the attack bonus/increase the damage
  • The char is raging, if possible
  • The only feats considered are rage, brutal crit, improved/superior crit and Great Weapon Master
  • The opponent has the AC of a monster with a CR equal to the character level (taken from Monster statistics by challenge rating, DMG p. 274)
  • No resistances or abilities preventing hits apply
  • No magic weapon is used
  • No bonus action attacks

The following 2 tables show the expected damage per round. The first column contains the character level, the first row the fighter level.

No (dis)advantage

$$ \begin{array}{r|r|r|r|r|r|r|r} &0&1&2&3&4&11&20\\\hline 1&8.1250&7.4500\\\hline 2&8.1250&8.7500&7.4500\\\hline 3&8.1250&8.7500&8.7500&8.1833\\\hline 4&8.1750&8.1333&8.1333&8.8667&8.5833\\\hline 5&16.3500&8.5500&8.1333&8.8667&9.2833\\\hline 6&16.3500&17.1000&8.5500&8.8667&9.2833\\\hline 7&16.3500&17.1000&17.1000&9.2833&9.2833\\\hline 8&17.0500&14.8667&14.8667&16.3333&9.6333\\\hline 9&20.7500&20.1333&17.1000&18.5667&21.6000\\\hline 10&18.4000&19.2333&17.8000&16.3333&19.2667\\\hline 11&18.4000&19.2333&19.2333&19.2667&19.2667&31.2000\\\hline 12&21.5500&19.2333&19.2333&21.4333&22.4000&33.6000\\\hline 13&22.2000&22.4667&19.2333&21.4333&24.6667&33.6000\\\hline 14&22.2000&23.2000&22.4667&21.4333&24.6667&33.6000\\\hline 15&22.2000&23.2000&23.2000&24.6667&24.6667&33.6000\\\hline 16&23.0000&23.2000&23.2000&26.1333&24.6667&33.6000\\\hline 17&23.6500&24.0000&23.2000&26.1333&26.1333&33.6000\\\hline 18&23.6500&24.7333&24.0000&26.1333&26.1333&33.6000\\\hline 19&23.6500&24.7333&24.7333&26.9333&26.1333&33.6000\\\hline 20&30.7500&24.7333&24.7333&28.4000&26.9333&37.0000&44.5333 \end{array} $$

Advantage

$$ \begin{array}{r|r|r|r|r|r|r|r} &0&1&2&3&4&11&20\\\hline 1&11.3588&10.4975\\\hline 2&11.3588&12.2525&10.4975\\\hline 3&11.3588&12.2525&12.2525&11.8542\\\hline 4&13.6837&11.7900&11.7900&13.1467&14.5292\\\hline 5&27.3675&14.3275&11.7900&13.1467&15.6842\\\hline 6&27.3675&28.6550&14.3275&13.1467&15.6842\\\hline 7&27.3675&28.6550&28.6550&15.6842&15.6842\\\hline 8&28.5225&25.6400&25.6400&28.3533&16.2617\\\hline 9&33.8825&32.7267&28.6550&31.3683&35.4400\\\hline 10&30.9450&32.3950&29.8100&28.3533&32.5233\\\hline 11&30.9450&32.3950&32.3950&32.5233&32.5233&51.2400\\\hline 12&35.1625&32.3950&32.3950&36.4650&36.7200&55.0800\\\hline 13&36.4300&36.7167&32.3950&36.4650&40.7867&55.0800\\\hline 14&36.4300&38.1467&36.7167&36.4650&40.7867&55.0800\\\hline 15&36.4300&38.1467&38.1467&40.7867&40.7867&55.0800\\\hline 16&37.7100&38.1467&38.1467&43.5733&40.7867&55.0800\\\hline 17&38.9775&39.4267&38.1467&43.5733&43.5733&55.0800\\\hline 18&38.9775&40.8567&39.4267&43.5733&43.5733&55.0800\\\hline 19&38.9775&40.8567&40.8567&44.8533&43.5733&55.0800\\\hline 20&47.5875&40.8567&40.8567&47.6400&44.8533&61.1800&73.4533 \end{array} $$

(results determined programmatically)

Conclusion

  • Extra Attack is the most significant factor
  • Only at levels 5, 6, 9 and 10 do 4 levels of fighter result in a better DPR than 3 fighter levels
  • Taking 11 levels of fighter drastically increases the DPR, since you get Extra Attack(2), going full fighter further increases the DPR because of Extra Attack(3), but comparing the difference between taking 4 or 11 and taking 11 or 20 levels of fighter the difference is less significant; taking into account that Reckless Attack makes it easier to gain advantage, taking some levels of barbarian can benefit your damage output.

Depending on how "barbaric" you want your char to be, aim for barbarian 17/fighter 3 or barbarian 9/fighter 11. Getting to Barbarian 5 to get the Extra Attack immediately, but if you're planing to get to fighter level 11, results in a delayed boost of the damage, but drastically increases the DPR when reaching level 12(Barbarian 1/Fighter 11).

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  • \$\begingroup\$ Looks interesting, but I don't understand if you considered Great Weapon Master and critical hits. \$\endgroup\$ – StackLloyd Aug 9 at 22:18
  • \$\begingroup\$ Just edited Great Weapon Master in... \$\endgroup\$ – fabian Aug 9 at 22:45

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