As a follow-up to last week’s post comparing Greatsword vs. Greataxe damage, this week we’re looking into Champion (Fighter) dips for Barbarians looking to increase their damage capacity with large weapons.

## Factors

When considering whether your Barbarian should take a dip into Champion (Fighter), there are a number of countervailing factors that can affect your damage at any given level.

- At Level 1, the Champion (Fighter) gains access to Great Weapon Fighting.
- This allows the player to re-roll 1s and 2s on damage dice.
- The Greatsword user gains 1.33 damage on average.
- The Greataxe user gains 0.83 damage on average.

- At Level 3, the Champion (Fighter) expands its critical hit range to 19-20.
- This favors the Greataxe user, who gains more damage from critical hits when accounting for the additional d12 damage dice from Brutal Critical.

- A multiclass “dip” will delay Ability Score Improvements (ASIs).
- ASIs to primary attack score favor the Greatsword over the Greataxe.
- Delaying your ASI will favor the Greataxe.

- Proficiency bonus continues to scale regardless of which class you take.
- Proficiency bonus increases favor the Greatsword over the Greataxe.

- A multiclass “dip” will prevent the character from obtaining the Barbarian’s capstone of 24 Strength, but will not infringe upon max Brutal Criticals.

## Applications

### Top Tier

What’s the best when we red-line these concepts? We’ll be comparing two Level 20 characters. The left is a pure Barbarian with the benefit of the 24 Strength capstone. The right is a Champion Barbarian with 20 Strength, plus Great Weapon Fighting and an expanded critical hit range. We’re assuming that both have the benefit of a +3 weapon, since they’re in the final tier of play.

Even with the expanded critical range, the Greatsword comes out a little bit ahead in this comparison. However, take a look at what happens when you apply advantage from Reckless Attack:

When using Reckless Attack, the Greataxe pulls into the lead. The numbers are still very close, but the Champion Barbarian experiences a higher overall damage output, except against the highest ranges of Armor Class (AC).

### Half-Orc

Let’s keep the same assumptions, except our character is a Half-Orc. As we know from last week, Half-Orcs favor the Greataxe, due to the Savage Attacks racial feature. Is that enough to make the Greataxe better when not using Reckless Attack?

The Greatsword and the Greataxe perform relatively the same. However, there is a damage variance between the classes. While the Champion Barbarian has a higher damage capacity, the pure Barbarian actually outdamages the Champion Barbarian vs. opponents with AC 17 or higher.

Finally, we see some separation when advantage from Reckless Attack is applied:

When we apply Reckless Attack, the Champion Barbarian comes out in the lead against virtually every Armor Class, especially when equipped with a Greataxe.

## Run Your Own Numbers

Since your damage scaling will depend on when you decide to take your “dip” into the Champion (Fighter) class, take some time to play with the numbers and plan out your class progression:

I’ve seen math mistakes every time I read something about a critical hit build. I can’t see the equations in the excel so I don’t know exactly were it is going wrong, but usually I see it on the reroll 1s and 2s calculation and the expected damage calculation. For both it is a very common error on the definition of expectation which is the SUM(prob*value, prob*value, …). For a half orc 5 barb, 4 champ split (giving 2 ASIs to get to 20 STR) the mod to hit is +8, and the damage would be (dice + 7) while raging. With this from AC 11 to AC 18 the numbers while reckless attacking are (20.008 19.663 19.242 18.743 18.168 17.517 16.788 15.983) for the greatsword and (19.270 18.948 18.553 18.088 17.550 16.941 16.260 15.508) for the greataxe. Your posted numbers are no where close to that.

Taking just the AC 18 as a more simple example, with the +8 hit modifier there are 9 dice values (10-18) that will hit but not crit making it a 0.45 probability to occur on a single roll, and a 0.1 probability of a crit on a single roll (19 and 20). While reckless attacking these rolls have advantage which means they need to be put into a binomial distribution calculating the probability of at least one success, bringing them to 0.6975 and 0.19 respectively. Now for the dice rolls you had the correct damage increases listed above with a single d6 going to 4.1667 damage instead of 3.5 (making the delta for two at 1.33) so I will not belabor it. To get the final damage for this example it should be the SUM( [0.6975*(2*4.1667+7)] + [0.19*(5*4.1667+7)]) or SUM( [ProbHit*(hit damage)] + [ProbCrit*(crit damage)]) which gives the 15.983 listed above as apposed to the 14.5 you list on the excel sheet.

As a side note, the math mistakes being repeated so often has lead to the misconception that 1d12 is better than 2d6 for a half orc. As you can see from above, with all of the values of 2d6 (greatsword) being higher than 1d12 (greataxe), it is generally the opposite. The only times greataxes are better is with very high ACs (18+ for most builds) or with pure barbarian half-orc builds (after brutal criticals at level 9 barb giving 4d12 crits), but you get more damage dipping into fighter than getting another crit die because frankly crits are pretty rare. It happens so infrequently that it is only useful when your character has low chance to hit at all (i.e. need a 17+ die roll to hit bringing the hit probability down closer to the static low crit probability). And for reference a level 9 half orc barb with 20 STR raging only gets marginally better expected damage though the same AC11-18 range 2d6 is (17.49 17.23 16.89 16.48 15.99 15.43 14.79 14.08) and 1d12 is (17.49 17.24 16.91 16.51 16.04 15.50 14.88 14.19) making the deltas a pitiful (0.00 0.01 0.02 0.03 0.05 0.07 0.09 0.11) which very clearly shows the trend I was explaining, 1d12 is only gets better as your likelihood of missing gets worse, so if there is a cleric in the party giving bless it just gets worse. The only argument for 1d12 is with great weapon master feat, but the same rule applies, but now becomes more meaningful because of the -5 to hit bringing the hit probability down. Overall though through most of the combinations of build I’ve ran the numbers for, it is almost always better to use 2d6 for an AC at 16 or less. And how often do you run across AC 17+ mosters in middle to low levels? I thing the one ~5% reduction in damage per hit at the super high AC monsters with GWM is still worth hitting harder all the rest of the time. I would run the expected campaign damage per round but the monsters are way to varied across campaigns to do so (much less homebrew).

Anyway, I hope you find your calculation error and make some updates for your other posts if the same errors exist. Also, I hope I was able to get you thinking on the 1d12 is better for half-orcs myth.

Best,

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I can’t track what you’re saying here, but the calculator is linked in the post. I showed my work. All the formulas are on the Data tab. All the variables at the top change based on the inputs. All the formulas are in the table below with sufficient definitions that you should be able to understand what’s going on.

I do it a little differently than you, in that I do:

+ Odds of Hitting * Damage Dice (as modified by GWF)

+ Odds of Hitting * Flat Damage (as modified by ASIs/Rage)

+ Odds of Critting * Additional Crit Damage Dice (as modified by GWF/Champion)

But, the result should be the same. Your numbers look way too high. How do you get above 20 average damage on a weapon that does 7 average on the dice plus 7 from STR + Rage? There’s no way that critical hits add an extra 6 damage. Even assuming they occur 20% of the time, you’d need to deal an extra 30 average damage on a critical hit to see that kind of bump.

By all means, if there’s something in the formula, please point it out to me. I just double-checked and it all seems square.

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Rereading my post I did a terrible job explaining the excel sheet I made and I did find a flat +2 error on all the numbers when I redid them (if I could edit it i would, but the main argument of greatsword is almost always better stays), but the dice average on 2d6 is not 7 with the GWF (the reroll on 1 and 2) it is 4.16 per die which is 8.32 for 2d6. A major note that I think my be another error for your set is what you have above is not correct. Not all hits are crits, but all crits are hits. Meaning that summing across dependent probabilities gets tricky and what you have does not account for this. Your “odds of Critting” with only the additional damage will not add up correctly for that joint probability with hitting. The easiest form for the true average damage would be as stated before (Odds of Hitting * Damage on Hit + Odds of Critting * Damage on Crit). It can obviously be written differently (separating out flat damage and so on), but yours must equal what I have which it does not and the point of my long rant. As a point with the 20.0 average damage you mentioned to start this, the value is 18.008 (reckless, +8 to hit against 11AC, +5 damage, +2 rage, half orc, greatsword) and your sheet says 17.6. {odds to hit are 0.85 and 0.05 to crit on each die, with advantage brings the binomial odds of at least one in two to 0.9975 and 0.0975. With 1d6 damage being 4.16 average with GWF that gives… (0.9975*[4.16*2 + 7])+(0.0975*[4.16*5 +7]) which is 18.0 and not 17.6. the variance comes from that small amount of unaccounted crit joint probability with hitting. Hopefully this ramble makes more sense and has fewer spelling errors!

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Just realized after writing it it was GWM (the -5 to hit for +10) and the lower hit chance but higher damage at low AC. all of those numbers have that, but the new number on the comment does not

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What happens if my DM has adopted “modified crits” rule where you add the max dice value for a crit instead of rolling an additional die? This would make the Greataxe much more favorable at our table right? (an additional 12 dmg in lieu of 6?)

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Well, not really… it moves the passing point on low hit changes, but they are equal at the 30% hit and 5% crit chance. For context if the monster has an AC of 18 and you have a +4 to hit without advantage they have the same expected damage, any better hit chance (which should be the vast majority of the campaign) and the sword is still better. Like I tried to say in the big post and somewhat failed… you crit so infrequently that making normal attacks better is almost strictly better. With that said, if you’re starting at high levels, the max die may favor a small dip into barb for reckless attack and going fighter to get the increased hit range. I didn’t bother checking in that case, but fun thought.

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