D&D 5E House rule: Extra Attacks for martials at 5,11,17

[TwoSix]

This effectively makes Fighters even worse, because now everyone gets the Fighter's core special feature by default, on top of their own class-specific equivalents (e.g. Rage damage bonus, Improved Divine Smite, Sneak Attack, etc.)

True.

It also makes attack-based cantrips more powerful, because now each individual cast can crit--it's not 35% no damage, 60% hit, 5% double damage. Instead it's a much broader spectrum that can do nothing, or anything from 1dN to 8dN--essentially turning every attack-based cantrip into an equivalent of eldritch blast.

It does give every cantrip caster functionality more like Eldritch Blast, true.

The crit thing doesn't really bother me, it doesn't actually add any DPR. It would be more powerful if the character has some kind of "on crit" feature, of course.

 

[Valetudo]

If the warlock ends up getting that third melee attack makes it past the playtest martials are gonna need a big boost. Honestly I'm fine with cantrips right now. My players light cleric is a beast but not because of her cantrips and I'm fine with e.blast(maybe make its progression class based). I do think the rogue should get a second attack but not at 5th. Maybe 8th lvl or 10. Barby could get their rage damage in reased. Prof bonus maybe? Fighters need battlemaster as core and they would be as close to perfect as a martial will get in 5e. Maybe give them the mark ability from the dmg. I haven't used it but I'm thinking about it.

 

[EzekielRaiden]

It does give every cantrip caster functionality more like Eldritch Blast, true.

The crit thing doesn't really bother me, it doesn't actually add any DPR. It would be more powerful if the character has some kind of "on crit" feature, of course.

It does affect DPR though--specifically when you factor in critical hits, not just base damage Assume fire bolt, so 1d10 damage, assume 65% chance to hit.

Single-hit cantrip without crit: 0.35×0 + 0.65×22 = 14.3 DPR
Multi-hit cantrip: 0.015×0 + 0.1115×5.5 + 0.3105×11 + 0.3845×16.5 + 0.1785×22 = 14.3 DPR.

Those parts are certainly the same. Now, separately from the above, we can calculate the bonus from crits. For the single-hit, that's simple; 0.05*22 = 1.1.

It gets a lot more complicated with the multi-hit, but we can break it into cases of conditional probability.

0.1115×0.05×5.5 + 0.3105×(0.05^2×11+0.975×5.5) + 0.3845×(0.05^3×16.5+0.0071×11+0.1354×5.5) + 0.1785×0.05^4×22+0.00048125×16.5+0.0135×11+0.1715×5.5) = 2.21. I'll round that down to 2.1, simply because I didn't put in the extra effort of subtracting out the various lower probabilities (e.g. it should be 0.975-0.05^2 otherwise you're double-counting)--the probabilities are so small that it hardly matters for the end result. (Edit: Just checked. Actual result is ~2.18295, so call it 2.18, a hair under double the damage added by crits as-is.)

Changing the chance to hit obviously throws these numbers off--e.g. the easier it is to hit the target, the better multi-hit cantrips are, and conversely, the closer you get to needing a nat 20 to hit in the first place, the closer together the two will be. Now, you might say ~1 point of extra DPR isn't much, but that's around an 8% increase in damage output for classes that really don't need to be getting a damage boost --except Warlocks, who will fall into the same "now they suck relative to other similar classes because they've lost a key differentiator." There's a reason grabbing a couple levels of Warlock to get EB+AB is so tempting for Bards, Sorcerers, and Paladins, and AB is only half of the equation (a very very very nice half, but still half.)

 

[TwoSix]

It does affect DPR though--specifically when you factor in critical hits, not just base damage Assume fire bolt, so 1d10 damage, assume 65% chance to hit.

Single-hit cantrip without crit: 0.35×0 + 0.65×22 = 14.3 DPR
Multi-hit cantrip: 0.015×0 + 0.1115×5.5 + 0.3105×11 + 0.3845×16.5 + 0.1785×22 = 14.3 DPR.

Those parts are certainly the same. Now, separately from the above, we can calculate the bonus from crits. For the single-hit, that's simple; 0.05*22 = 1.1.

It gets a lot more complicated with the multi-hit, but we can break it into cases of conditional probability.

0.1115×0.05×5.5 + 0.3105×(0.05^2×11+0.975×5.5) + 0.3845×(0.05^3×16.5+0.0071×11+0.1354×5.5) + 0.1785×0.05^4×22+0.00048125×16.5+0.0135×11+0.1715×5.5) = 2.21. I'll round that down to 2.1, simply because I didn't put in the extra effort of subtracting out the various lower probabilities (e.g. it should be 0.975-0.05^2 otherwise you're double-counting)--the probabilities are so small that it hardly matters for the end result. (Edit: Just checked. Actual result is ~2.18295, so call it 2.18, a hair under double the damage added by crits as-is.)

You don't really need to break into the multi hit scenario, where the math gets really painful.

Crit rate is independent of hit rate. No matter the AC of the target, you crit 5% of the time.

So, assuming the 17th level case, the added bonus for crit is either 5% of 4dX or 5% of 1dX repeated 4 times, which sums up to the same average. The distribution is different, of course, but considering that crits and especially multi-crits are edge cases anyway, that really isn't very applicable.

Changing the chance to hit obviously throws these numbers off--e.g. the easier it is to hit the target, the better multi-hit cantrips are, and conversely, the closer you get to needing a nat 20 to hit in the first place, the closer together the two will be. Now, you might say ~1 point of extra DPR isn't much, but that's around an 8% increase in damage output for classes that really don't need to be getting a damage boost --except Warlocks, who will fall into the same "now they suck relative to other similar classes because they've lost a key differentiator." There's a reason grabbing a couple levels of Warlock to get EB+AB is so tempting for Bards, Sorcerers, and Paladins.

Until I make further changes (which I assuredly will), Warlocks still have the AB benefit. 4d10+20 is still double most classes 4d10. The main benefit of my proposed change without other changes are subclasses like Draconic Sorcerer, where their cantrip damage for their chosen element will go from 4dX+5 to 4dX+20.

 

[EzekielRaiden]

You don't really need to break into the multi hit scenario, where the math gets really painful.

Crit rate is independent of hit rate. No matter the AC of the target, you crit 5% of the time.

So, assuming the 17th level case, the added bonus for crit is either 5% of 4dX or 5% of 1dX repeated 4 times, which sums up to the same average. The distribution is different, of course, but considering that crits and especially multi-crits are edge cases anyway, that really isn't very applicable.

Yes, but you have to control for the fact that you might hit just once (and thus that attack can crit 5% of the time), or you might hit twice (and thus either or both could crit), or you might hit three times (and get 1/2/3 crits), or four (etc.)

A one-hit cantrip like standard fire bolt is all or nothing; either the whole thing crits or it doesn't. The math is very simple. A multi-hit cantrip like eldritch blast, you have to account for all the possible cases. The raw probabilities I used above (for "just treat crits as regular hits, figure out the bonus damage later") were crunched for me by a binomial distribution calculator; I used those as conditional probabilities above.

It is an average DPR bonus to be able to crit on each individual die, not just the whole kit and kaboodle. You sacrifice a "high" (5%) chance to do ~22 bonus damage, but you gain a very high chance of doing at least one crit. Consistency does, in fact, shift the center of the distribution up a little bit.

Until I make further changes (which I assuredly will), Warlocks still have the AB benefit. 4d10+20 is still double most classes 4d10. The main benefit of my proposed change without other changes are subclasses like Draconic Sorcerer, where their cantrip damage for their chosen element will go from 4dX+5 to 4dX+20.

Sure, I'm not saying AB is going away. Also, I don't actually think Dragon Sorcerer is a problem here; Elemental Affinity says "to one damage roll of that spell." If you're careful with your house-rule wording, it wouldn't apply. E.g., call it "Extended Cantrip," with text saying something like, "Starting at 5th level, when you cast a cantrip that requires an attack roll or forces a target to make a save, you may apply its effects twice instead of once for a single casting of that cantrip." The crit benefit remains, of course, but this phrasing would mean you may make two/three/four attack rolls with fire bolt, but you can only apply Elemental Affinity to one of the damage rolls triggered by hitting.

I'm just saying, there are three benefits to eldritch blast: typing, multi-hit, and Agonizing Blast. Typing is a small but nice benefit. AB is a large and nice benefit. Multi-hit is a medium and nice benefit. Warlock, as a class, is one of the ones that needs love, not being relatively nerfed by having its distinctive features weakened by comparison.

 

[TwoSix]

Yes, but you have to control for the fact that you might hit just once (and thus that attack can crit 5% of the time), or you might hit twice (and thus either or both could crit), or you might hit three times (and get 1/2/3 crits), or four (etc.)

But you don't have to control for hit rate, is the point I was trying to make. Crit is independent of hit. Now, a crit is also a hit, so you factor in rolling a 20 as part of the hit rate, but you don't adjust the crit bonus because of the hit rate.

Now, if you were doing PF2 hit + 10 causes crit, then sure, you would need to.

When you calculate the full DPR, you do one function for determining the raw hit damage, excluding crit, and then do a second function to add in crit damage.

Like this:

Firebolt (4d10) DPR = hit rate * 22 + crit rate * 22.

If I'm casting 4 firebolts, I just do this:

4 x Firebolt (1d10) DPR = 4 x (hit rate * 5.5 + crit rate * 5.5).

The firebolts are independent attacks. You don't need to do multi-hit calculations to sum up multiple independent attacks.

Sure, I'm not saying AB is going away. Also, I don't actually think Dragon Sorcerer is a problem here; Elemental Affinity says "to one damage roll of that spell." If you're careful with your house-rule wording, it wouldn't apply. E.g., call it "Extended Cantrip," with text saying something like, "Starting at 5th level, when you cast a cantrip that requires an attack roll or forces a target to make a save, you may apply its effects twice instead of once for a single casting of that cantrip." The crit benefit remains, of course, but this phrasing would mean you may make two/three/four attack rolls with fire bolt, but you can only apply Elemental Affinity to one of the damage rolls triggered by hitting.

I want Elemental Affinity to work on all the casts, so that issue won't apply here.

I'm just saying, there are three benefits to eldritch blast: typing, multi-hit, and Agonizing Blast. Typing is a small but nice benefit. AB is a large and nice benefit. Multi-hit is a medium and nice benefit. Warlock, as a class, is one of the ones that needs love, not being relatively nerfed by having its distinctive features weakened by comparison.

Multi-hit is useful primarily because Warlock has an easy source of "on every hit" proc damage in Hex, and because the structure of the Agonizing Blast invocation allows it to be applied "N beams" times, instead of just once.

As I mentioned in an earlier post, these changes are not an attempt to create balance. I'm trying to determine where the character building meta would shift IF such changes were implemented.

 

[EzekielRaiden]

But you don't have to control for hit rate, is the point I was trying to make. Crit is independent of hit. Now, a crit is also a hit, so you factor in rolling a 20 as part of the hit rate, but you don't adjust the crit bonus because of the hit rate.

But...you do. Because the lower the hit rate is, the larger a share they cut out of the overall hits. If you actually have to crit in order to hit, then the two methods generate exactly the same damage output. Crits are not independent events.

Your math is a nice simple approximation, but it is simply not correct for calculating the actual expected value. That's why I got a different result compared to doing the simple calculation you did above--because the number of crits you can potentially get depends on how many hits you already got (since you cannot crit if you missed!)

I want Elemental Affinity to work on all the casts, so that issue won't apply here.

Fair enough.

As I mentioned in an earlier post, these changes are not an attempt to create balance. I'm trying to determine where the character building meta would shift IF such changes were implemented.

Well then, the answer is "abso-friggin-lutely yes." I'm not really sure why you would need to ask this specific question. Giving every martial character a major damage bonus, one that stacks with their own existing class-based damage bonuses, is pretty obviously a major change that shifts the meta.

The only reason to play Fighter is to get 2 levels so you can Action Surge. For every other purpose, either Barbarian or Paladin is simply, straight-up superior.

Likewise, giving every caster a small but meaningful damage bonus

 

[TwoSix]

But...you do. Because the lower the hit rate is, the larger a share they cut out of the overall hits. If you actually have to crit in order to hit, then the two methods generate exactly the same damage output. Crits are not independent events.

Your math is a nice simple approximation, but it is simply not correct for calculating the actual expected value. That's why I got a different result compared to doing the simple calculation you did above--because the number of crits you can potentially get depends on how many hits you already got (since you cannot crit if you missed!)

I think we're talking past each other. When I do DPR calculations, I separate out the damage portion of the hit from the damage bonus of the crit.

Again, simple example.

Assume I cast a +11 hit bonus 4d10 firebolt against a target with a 20 AC. That means I miss 40% of the time (1-8 on the d20) and hit 60% of the time (9-20 on the 20).

My firebolt's hit damage will average 22 (mean of 4d10).

Now, on 5% of my attacks (20 on the d20), my attack will also be a crit. So on 5% of my attacks, I add another 22 (mean of 4d10).

So my DPR is 0.6 * 22 + 0.05 * 22 = 14.3.

If I cast 4 1d10 firebolts, with the same hit rate, the only thing that changes in this calculation is that I use 5.5 (mean of 1d10) instead of 22. So the DPR of one firebolt is 3.575. All of the firebolts have that DPR, so the full damage is 3.575 * 4 = 14.3.

Well then, the answer is "abso-friggin-lutely yes." I'm not really sure why you would need to ask this specific question. Giving every martial character a major damage bonus, one that stacks with their own existing class-based damage bonuses, is pretty obviously a major change that shifts the meta.

The only reason to play Fighter is to get 2 levels so you can Action Surge. For every other purpose, either Barbarian or Paladin is simply, straight-up superior.

As I mentioned in the OP, I wasn't questioning IF there's a balance change, I'm asking HOW. Specifically looking for subclass features or feats that would strongly impacted by having lots of attacks in the higher Tiers.

Paladins, Rangers, and Artificers are not changed (right now). Do you think these changes would elevate Barbarian, Monk, or Rogue to be a better choice than Paladin (the de-facto "best warrior" class)?

 

[EzekielRaiden]

As I mentioned in the OP, I wasn't questioning IF there's a balance change, I'm asking HOW. Specifically looking for subclass features or feats that would strongly impacted by having lots of attacks in the higher Tiers.

Paladins, Rangers, and Artificers are not changed (right now). Do you think these changes would elevate Barbarian, Monk, or Rogue to be a better choice than Paladin (the de-facto "best warrior" class)?

Monk probably not? Most of their damage is coming from ki stuff and martial arts, which I don't think would be radically changed by getting more extra attacks. I guess it would let you save your ki for more utility effects or something?

Barbarian...maybe. Spells are undeniable flexibility for Paladin. But Barbarian (presuming Totem, since it's quite strong) getting to tack Rage damage on twice as often might make a difference?

But if your goal is to close the gap with spellcasters, extra attacks per round is of limited utility--it requires that the party face more rounds of combat to get more benefit. Meanwhile, spells get more benefit from facing fewer rounds of combat. Thus the inherent tension: casters are always wanting to favor something closer to the 5MWD (or, I guess in 5e, the "three-hour workday," since casters usually still want to take at least one short rest per day), while non-casters are always wanting to favor the longest possible day.

If you can ensure that Paladins (and casters generally) actually HAVE to run out of spells now and then, then yes, this change would very likely push Barbarians into the same zone or even just above it. But if you can't ensure that Paladins have to run out of spells sometimes (or delay running out of spells by not spending them early on when they would have liked to--because the two are mostly equivalent), then no, I don't think the Barbarian is pushed up far enough.

 

[TwoSix]

But if your goal is to close the gap with spellcasters, extra attacks per round is of limited utility--it requires that the party face more rounds of combat to get more benefit. Meanwhile, spells get more benefit from facing fewer rounds of combat. Thus the inherent tension: casters are always wanting to favor something closer to the 5MWD (or, I guess in 5e, the "three-hour workday," since casters usually still want to take at least one short rest per day), while non-casters are always wanting to favor the longest possible day.

If you can ensure that Paladins (and casters generally) actually HAVE to run out of spells now and then, then yes, this change would very likely push Barbarians into the same zone or even just above it. But if you can't ensure that Paladins have to run out of spells sometimes (or delay running out of spells by not spending them early on when they would have liked to--because the two are mostly equivalent), then no, I don't think the Barbarian is pushed up far enough.

To be clear, none of this is with the goal of balancing anything.