Champion vs Battlemaster (damage)

[Yakk]

The BM and the Champion both have non-damage abilities. To keep things simple, I'm going to ignore them (I'd consider the BM's non-combat to be as good or better than the Champion's, but that isn't relevant as I'm ignoring them).

Looking only at damage dealing abilities, the Champion from 3-9 has 19-20 crit range. At 10-14 they have a 2nd fighting style (which can sometimes be leveraged for more damage, but usually ends up being interception or defensive or similar). And from 15+ they have 18-20 crit range.

The BM, meanwhile, has 4d8 short-rest superiority dice from 3-6, 5d8 from 7-9, 5d10 from 10-14, and 6d10 from 15-17, and 6d12 from 18+.

A very simple BM has precision strike, and at least 1 maneuver that lets them add +[SD] damage to a hit. They then use the +[SD] only on crits, and use precision strike only when they miss by 1 (guaranteed to turn a miss into a hit).

1 in 20 attacks crit, and deal +2[SD] damage. 1 in 20 attacks miss by 1, and deal +[W]+Str damage. The BM can do this up to 4+ times per short rest.

Assuming they are using a greatsword (this gives the Champion the best situation) and have GWF style, [W] average 8 and 1/3 damage.

Comparing at level 3, level 5, 11 and 17 (start of each tier, plus first level of subclass), we get:

Champion 3: +0.42 DPR
Champion 5: +0.85 DPR
Champion 11: +1.25 DPR
Champion 17: +2.5 DPR

BM 3: +1.02 DPR (up to 40 rounds between short rests)
BM 5: +2.13 DPR (up to 20 rounds between short rests)
BM 11: +3.65 DPR (up to 16 rounds between short rests)
BM 17: +3.65 DPR (up to 20 rounds between short rests)

The endurance of the BM's superiority dice in this really really conservative spending situation is more than long enough for almost every situation. And, before level 17, the amount of time it would take for the Champion to catch up even if the fights where really long is pretty crazy; 100 rounds at level 3, 50 rounds at level 5, 47 rounds at level 11, 29 rounds at level 17 (between short rests for the Champion to match this very conservative BM's damage).

BM can do better than this simple model; using Precision on attacks that miss by 2 or 3 is the easiest thing to do. And the BM is imposing saves for annoying conditions like "prone" with the above, which I utterly ignored.

What would be needed to close this gap most of the way? Well, we could just subtract.

BM-Champ 3: 0.6 DPR
BM-Champ 5: 1.3 DPR, or 0.6 per attack
BM-Champ 11: 2.4 DPR, or 0.8 per attack
BM-Champ 17: 1.2 DPR, or 0.4 per attack

You'll note that the gap closes in T4 -- the 18-20 crit range helps a lot.

If we set 10 rounds between short rests, the gap is:
L3: 6 damage per short rest
L5: 13 damage per short rest
L11: 24 damage per short rest
L17: 12 damage per short rest

I want to keep this multiclass friendly (ie, not be OP as a 3 level dip into champion). So while extending the crit range to 18-20 at level 3 is tempting, it ends up delivering more for a 3 level dip in T2/3/4 for an other class than for a pure-fighter Champion.

...

A chance to swing a 2HS is "worth" about 7-9 damage.

So

Improved Second Wind: Starting at level 3, a Champion make a weapon attack when they use their second wind. If they qualify for the two-weapon fighting bonus action, they may make it as well.

The gap per short rest then becomes:
L3: -1 damage per short rest
L5: 5 damage per short rest
L11: 15 damage per short rest
L17: 3 damage per short rest

Third Wind: Starting at level 7, a Champion can use Second Wind twice between short or long rests instead of once.

The gap per short rest then becomes:
L3: -1 damage per short rest
L5: 5 damage per short rest
L11: 6 damage per short rest
L17: -6 damage per short rest

This won't match an optimized BM, but will make the Champion feel beefier. And the extra attack on a second wind is nicely dramatic.

The complexity of this is low; you just have to remember to swing when you use your second wind. It is tied to an ability you already have to remember. It is ok for multiclassing, but not crazy; it uses up the bonus action (which many optimized builds already have a use for).

Now, one downside is that the Champion in 10 rounds competes with a BM with 20+ rounds of endurance. The BM can less efficiently just burn dice faster and outpace the Champion again.

But if I scale up the Champion's per-SR damage, it might be too much for shorter days.

Hmm. Thoughts? Maybe ... recover Second Wind on a critical? That gets crazy in T4.

[paladinn]

My champion/brute mashup adds the fighter's proficiency bonus to damage at L3. At L15, on a crit, the fighter's level is added to damage.

At L7, the fighter's prof bonus is added to all saves.

It might still be "lackluster", but it's an improvement (and still very simple).

[Yakk]

My champion/brute mashup adds the fighter's proficiency bonus to damage at L3. At L15, on a crit, the fighter's level is added to damage.

At L7, the fighter's prof bonus is added to all saves.

It might still be "lackluster", but it's an improvement (and still very simple).

At 65% accuracy, you get BM-Champ:
BM-Champ 3: -0.7 DPR
BM-Champ 5: -3.9 DPR
BM-Champ 11: -5.4 DPR
BM-Champ 17: -18.15 DPR

So your Champion does as much more damage (at level 3) than a BM did before your change.

At level 5 and 11 the Champion's gap with BM is now twice it was before your change, in the opposite direction.

At level 17, your Champion's damage gap with the BM is very, very large.

We can do the Vanilla fighter. 2 HS, GWF, no feats, no magic, 65% hit chance. Ignoring action surge (treat it as an extra around).

Vanilla
L 3: 7.8 DPR
L 5: 16.9 DPR
L 11: 26 DPR
L 17: 26 DPR

BM
L3: 8.8
L5: 19.3
L11: 29.65
L17: 29.65

Baseline Champ:
L3: 8.2
L5: 17.7
L11: 27.2
L17: 28.5

Your Champ
L3: 9.5 (8% over BM, 22% over Vanilla)
L5: 21.6 (12% over BM, 28% over Vanilla)
L11: 35.1 (18% over BM, 35% over Vanilla)
L17: 47.9 (62% over BM, 84% over Vanilla)

So your Champion outdamages this "naive" BM and Vanilla increasingly at higher levels.

Now, BM is known as a decent 3 level dip. How does your champion perform as a 3 level dip?

Suppose you already have 2 attacks, 20 strength, and after 3 levels you'll have 5 proficiency, and you already have a GWF before the dip.

Baseline Champ 3 level Dip: +0.8333333 DPR
"Simple" BM 3 level Dip: +1.1 DPR for 40 rounds/SR
Your Champ 3 level Dip: +7.3 DPR (!) (!!!!!)

I can model a more complex BM. Suppose we aim for 10 rounds/SR instead of 40. So we want to burn 0.4 dice per round on average.

Burning a die on a crit is a no-brainer (0.05 dice/round).
Miss by up to 2 (0.1 dice/attack)
Reaction attack (0.15 dice/round)

This adds 0.05 * 9 (crit) + 0.05*(7/8 + 8/8)*(8.33+5) (turn miss into a hit) + 0.15 * ( 0.7 * 8.333 + 0.65 * 5 + 4.5 * 0.7) (riposte)
= 0.45 + 1.25 + 1.834999965 = 3.54 damage per round

Still, under half the Champ 3 you designed.

So my concerns:
1. Your champ 3 is a must-do 3 level dip. It is crazy strong.
2. Your champ improves the champ more at later levels, when the Champ is relatively stronger, and less at lower levels, where the Champ needs more help.

When you have a 15% chance to crit, throwing on an extra "add fighter level" to the damage ... well, it is awesome, but I don't think it is needed. By T4 you get lots of crits, and many of them come from that range.

If you like yours, try just adding a flat +2 damage on the Champion instead of +Prof.

+2 Champ over Baseline Champ:
L 3: +1.3 DPR
L 5: +2.6 DPR
L 11: +3.9 DPR
L 20: +5.2 DPR

BM-+2 Champ 3: -0.7
BM-Champ 5: -1.3
BM-Champ 11: -0.2
BM-Champ 17: -2.7

or you could go the Brute route; give the Champ +1d4 damage. This has the benefit of doubling on crits, which is fun.

[Yakk]

Idea:

"Weapon Mastery": Whenever you hit with a weapon, if the d20 roll was odd, deal an extra set of weapon damage dice.

This replaces the Champions critical at level 3. It turns all odd d20s into "crits lite" (they don't cause other dice to double, just weapon damage dice).

With 65% hit rate (hit on an 8+) with a GWF greatsword, this adds 5/20 * 8.333 = 2.1 Damage per swing.

It is better for non-'smite' PCs (MC paladins/warlocks/rogues) than the 19-20 crit range, as pure champions are unlikely to have other piles of dice to double.

It feels great even at higher levels, but doesn't super-scale; weapon damage dice stay static. It does scale with number of attacks, but it doesn't scale quadratically.

At level 15, we could just make it "always roll weapon damage dice twice" and while it is strong, it wouldn't be crazy. (Doing it at level 3 is a bit too much).

There is some fun synergyzing it with increased crit range from, say, hexblade warlocks; crits on 19 are nasty.

It is also really good with advantage.

If you hit on an 8+, you have:
5 pips are +1[W],
1 pip is crit
7 pips are normal hits
7 pips are misses

Let's ignore the difference between +[W] and crit for now. 6 pips are +[W] 7 are not.

On 2d20 we get:
6*20 + 14*6 = 204 / 400 are +1[W]
7*7 = 49 / 400 are full misses
So 51% 2[W]+Str, 12% miss, 37% [W]+Str, or 1.39[W] + 0.88Str. At level 3 this is 14.2 damage per swing.

Without the feature, crit chance is 9.75% (call it 10%), so .98[W]+.88Str or 10.8 damage per swing; +3.4 damage per swing from this feature if you have advantage.

More importantly, I think this feature is fun. It is much larger than 19-20 crit range, and can afford to be without breaking multiclassing, as it only doubles weapon damage dice. This means it doesn't synergyze with paladin/warlock/etc smite or rogue sneak attack. The bonus is best on a character with more attacks, not with dice they can double, so it helps champions more than it helps non-champions for the most part.

[Damon_Tor]

Idea:

"Weapon Mastery": Whenever you hit with a weapon, if the d20 roll was odd, deal an extra set of weapon damage dice.

This replaces the Champions critical at level 3. It turns all odd d20s into "crits lite" (they don't cause other dice to double, just weapon damage dice).

With 65% hit rate (hit on an 8+) with a GWF greatsword, this adds 5/20 * 8.333 = 2.1 Damage per swing.

It is better for non-'smite' PCs (MC paladins/warlocks/rogues) than the 19-20 crit range, as pure champions are unlikely to have other piles of dice to double.

It feels great even at higher levels, but doesn't super-scale; weapon damage dice stay static. It does scale with number of attacks, but it doesn't scale quadratically.

At level 15, we could just make it "always roll weapon damage dice twice" and while it is strong, it wouldn't be crazy. (Doing it at level 3 is a bit too much).

There is some fun synergyzing it with increased crit range from, say, hexblade warlocks; crits on 19 are nasty.

It is also really good with advantage.

If you hit on an 8+, you have:
5 pips are +1[W],
1 pip is crit
7 pips are normal hits
7 pips are misses

Let's ignore the difference between +[W] and crit for now. 6 pips are +[W] 7 are not.

On 2d20 we get:
6*20 + 14*6 = 204 / 400 are +1[W]
7*7 = 49 / 400 are full misses
So 51% 2[W]+Str, 12% miss, 37% [W]+Str, or 1.39[W] + 0.88Str. At level 3 this is 14.2 damage per swing.

Without the feature, crit chance is 9.75% (call it 10%), so .98[W]+.88Str or 10.8 damage per swing; +3.4 damage per swing from this feature if you have advantage.

More importantly, I think this feature is fun. It is much larger than 19-20 crit range, and can afford to be without breaking multiclassing, as it only doubles weapon damage dice. This means it doesn't synergyze with paladin/warlock/etc smite or rogue sneak attack. The bonus is best on a character with more attacks, not with dice they can double, so it helps champions more than it helps non-champions for the most part.

This would interact with Elven Accuracy in a kind of funny way, and I'm not sure how I feel about it. We tend to treat EA as just "triple advantage" but that's not quite how it works, and in edge cases like this the difference in the precise mechanism is relevant.

Let's say this champion attacks an opponent with advantage, the enemy AC is 14, the champ rolls a 15 and an 18. He would then want to use Elven Accuracy to reroll the HIGHER dice of 18 so his 15 can hit and get him his extra bonus die.

[Yakk]

Sure. But really, just roll 3 dice (so long as you know the AC, or decide you can ask the DM if it hits before you do the reroll).

For a less exact model, imagine if every hit-roll had a 50-50 chance of being (crit or +1[W]).

Then with advantage, you have
MissMiss
HitMiss (50% of these have +1[W])
Mis**** (50% of these have +1[W])
HitHit (75% of these have +1[W])

This is HM + 3/4 H^2 are +1[W], and 2HM+H^2 are hits.

At 2/3 hit rate this is 5/9 +1[W] and 8/9 hit rate.

With EA, you have
MMM
MMH (50%)
MHM (50%)
HMM (50%)
MHH (75%)
HMH (75%)
HHM (75%)
HHH (7/8)

3/2 HM^2 + 9/4 H^2M + 7/8 H^3 are +[W], and hit chance is 3HM^2 + 3H^2M + H^3

At 2/3 hit rate this is
3/2 2/3 1/3^2 + 9/4 4/9 1/3 + 7/8 8/27 +1[W]
= (3/27) + (9/27) + 7/27 = 19/27 +1[W]

3 2/3 1/3^2 + 3 4/9 1/3 + 2^3/3^3
= 6/27 + 12/27 + 9/27 = 26/27 hit

So 70% +1[W] and 96% hit chance with EA at 2/3 accuracy.

Base:
33% 2[W]+Stat
33% [W]+Stat

Advantage:
55% 2[W]+Stat
33% [W]+Stat

EA:
70% 2[W]+Stat
26% [W]+Stat

Assuming 1d8 [W] and 20 dex and duelist we get:

Base: 10.8 per swing
Advantage: 12.6 per swong
EA: 14.2 pre swing

Assuming 2d6B2 and 20 strength we get:
Base: 13.3 per swing
Advantage: 16.3 per swing

Assuming 1.5 attacks at 1d6+5 dex (dual wielding model)
Base: 12.8 per 1.5 swings
Advantage: 14.1 per 1.5 swings
EA: 15.9 per 1.5 swings

So elven accuracy isn't enough to make a 2WF dex double SS match a 2HF str greatsword, but they get close; close enough that my crude "50% of hits get +1[W]" might not be good enough of a model. And EA is worth extra damage, but not absurd amounts.

The extra utility from advantage does mean that Champion 3 dip is very good for Barbarians; this (to me) is mainly because Barbarian after T1 is lackluster more than anything.

[paladinn]

I'll bail at this point. All the math is making my head hurt. And the "2[W]" reminds me too much of 4e.

[Yakk]

I'll bail at this point. All the math is making my head hurt. And the "2[W]" reminds me too much of 4e.
Oh yes, you don't use 2[W]. I just use it as shorthand in design. [W] doesn't feel 5e ish.

Weapon Master: When you hit a creature with an odd roll of a d20, roll the weapon damage twice.

The point of the math is that the benefit is not that way out of line with other 3rd level features.

[JNAProductions]

I'll bail at this point. All the math is making my head hurt. And the "2[W]" reminds me too much of 4e.

You say that like it’s a bad thing.

Towards Yakk… I dunno if I like it. It’s mathematically fine! But game feel and gameplay, I’m not sure on.