Enhancement Bonus vs Damage Dice

[Baptor]

Simple question, for which many different answers may spring.

Which is better, +1 hit and damage, or +1d6 damage.

In 3.5, the answer was "equal," or at least that's how the crafting rules put it. A +1 enchancement and a +1d6 damage were both (+1) equivilents.

I am wondering, is the same true in 5e? Does bounded accuracy make +1 hit inherently much better?

Thoughts?

[Human Paragon 3]

Simple question, for which many different answers may spring.

Which is better, +1 hit and damage, or +1d6 damage.

In 3.5, the answer was "equal," or at least that's how the crafting rules put it. A +1 enchancement and a +1d6 damage were both (+1) equivilents.

I am wondering, is the same true in 5e? Does bounded accuracy make +1 hit inherently much better?

Thoughts?

I believe a d6 is better. Bounded accuracy depends on limited bonuses to work, but that doesn't mean that a +1 is that much stronger than it was in 3.5. In general, more blows will land (whether or not you have an enhancement bonus). More hits means more rolls of the damage dice. So more damage dice wins IMO.

Now, if you're talking a +5 bonus vs. a +5d6, I would think the bonus would be better because something like that which totally breaks bounded accuracy means near 100% hit rate. Therefore I believe the comparison is more like a curve than a direct ratio.

I'd rather have a d6 than a +1. a +2 vs +2d6 is about even. +3 may pull ahead of +3d6, and past there, it's the bonus all the way.

[Demonicattorney]

The enhancement bonus was better in 3.5 because of power attack. These days 1d6 is almost always better than the +1.

[Demonic Spoon]

It varies based on how much damage you do per hit and what you need to roll to hit.

If you normally hit only on an 19+, a +1 bonus means you do 50% more damage. If you normally hit on a 3+, then you only do ~6% more damage. You can fairly easily make a spreadsheet to figure out how much damage a +1 bonus is "worth" (I have one I could send along if you need, though it would have to be later)

[Xetheral]

It varies based on how much damage you do per hit and what you need to roll to hit.

If you normally hit only on an 19+, a +1 bonus means you do 50% more damage. If you normally hit on a 3+, then you only do ~6% more damage. You can fairly easily make a spreadsheet to figure out how much damage a +1 bonus is "worth" (I have one I could send along if you need, though it would have to be later)

While this is true, there is the added caveat that when figuring out the "worth" of a +1, a percentage-based damage analysis isn't necessarily sufficient. For example, a 50% increase in damage sounds huge, but if the other members of the party are hitting on 15+, your total applied damage is likely to be so low in comparison that a 50% increase might still be negligible to the course of the battle.

It's therefore also worthwhile to consider the additive increase in damage represented by a +1 to hit, which is always 1/20 of one's average damage against hittable opponents.

Alternatively, one could analyze "worth" in terms of "frequency the bonus matters". In that case there is a (slightly greater than) 50% chance that a +1 will change at least one hit to a miss over the course of 14 attack rolls. To have a similar chance of affecting at least two attack rolls, one needs to roll 34 times (54 times for an even chance at affecting at least 3 attacks rolls, and 74 times for an even chance at affecting at least 4 attack rolls).

Advantage and disadvantage of course further complicate the analysis. None of these analysis methods are inherently better than the others, but when considering what a +1 to hit is "worth", it helps to keep in mind that there is more than one way to measure.

[Demonic Spoon]

While this is true, there is the added caveat that when figuring out the "worth" of a +1, a percentage-based damage analysis isn't necessarily sufficient. For example, a 50% increase in damage sounds huge, but if the other members of the party are hitting on 15+, your total applied damage is likely to be so low in comparison that a 50% increase might still be negligible to the course of the battle.


yup, which is why I also mentioned that it depends on how much damage you do on a hit.

[Baptor]

So far the consensus is roughly tied between "the 1d6 is better" and "it depends."

That's not what I expected, honestly.

Let's consider the following senarios:

Attack bonus +11 vs AC 20: which is better, +1 hit and dam or +1d6 dam?

Also, would something like a fighter who gets 4 attacks and a paladin who gets 2 attacks make any difference? Would one be better for one but not the other?

[Xetheral]

So far the consensus is roughly tied between "the 1d6 is better" and "it depends."

That's not what I expected, honestly.

Let's consider the following senarios:

Attack bonus +11 vs AC 20: which is better, +1 hit and dam or +1d6 dam?

Also, would something like a fighter who gets 4 attacks and a paladin who gets 2 attacks make any difference? Would one be better for one but not the other?

Straight Damage-Per-Attack Boost
Enhancement: + AvgDamage/20 + .65
Damage Dice: + 2.1
So Damage dice wins unless your average base damage is over 29

Percentage Damage-Per-Attack Increase
Enhancement: ((.65)(AvgDam+1))/((.60)(AvgDam))
Damage Dice: (AvgDam+3.5)/(AvgDam)
So Damage dice wins unless your average base damage is over 29 (interesting coincidence, they won't always be equal)

Frequency of Benefit over 14 attack rolls
Enhancement: 9.1 extra average damage, plus a 36% chance of an extra AvgDam+1, a 12% chance of an extra 2*AvgDam+2, and a 2% chance of an extra 3*AvgDam+3
Damage Dice: 29.4 extra average damage

Edit: The +1d6 is multiplied on a crit, and the +1 damage isn't, so that tilts the question even more in the favor of extra damage dice. On the other hand, users of GWM and Sharpshooter sometimes get more effective bonus damage out of an increase in hit chance.

As for Fighter vs Paladin, so long as they have the same base average damage per hit (which they won't, given smite) then the number of attacks is irrelevant.

[Totema]

I dunno, being able to break through the bounded accuracy ceiling is a pretty big deal. I'm inclined to say that the enhancement bonus is better.

[Xetheral]

I dunno, being able to break through the bounded accuracy ceiling is a pretty big deal.

I'm not sure I follow... could you elaborate?

[Baptor]

I'm not sure I follow... could you elaborate?

I don't want to put words in his mouth, but I think I understand where he's coming from.

In 5e, bounded accuracy balances combat by restricting the ranges of attack bonus vs AC to a much narrower field than in previous editions so that any character is relevant at any level in regards to attack vs AC.

By contrast, hit points are like candy, and WotC has admitted that while AC wasn't intended to be the determining factor in difficulty, hit points would be.

Some of us have drawn an assumption from this philosophy that anything that stretches the boundaries of bounded accuracy skew the game heavily in favor of the one who has the bonus to hit, where as bonus damage is not as important.

I am not good at math, but I've run the numbers myself and my results seem to indicate my assumption that +hit was the be-all-end-all was not accurate. Hence I made this thread so that I could ask people who really did know math. It seems the consensus is growing towards either (damage is better) or (damage is better except where damage is already very high).

[SharkForce]

it sort of depends. the more damage you do per hit, the more important it is that each hit lands :P

that said, i prefer bonus to hit, personally. i don't know if it's more powerful or not, but to me missing feels so frustrating.

and certainly, there's something to be said for being able to hit reliably when you know that you just need to hit at all to make a huge difference.

[Baptor]

it sort of depends. the more damage you do per hit, the more important it is that each hit lands :P

that said, i prefer bonus to hit, personally. i don't know if it's more powerful or not, but to me missing feels so frustrating.

and certainly, there's something to be said for being able to hit reliably when you know that you just need to hit at all to make a huge difference.

I hear you. I still feel that +hit is just better overall, but numbers don't lie, and as a DM I've got to go with the math, not the emotion.

[Demonic Spoon]

Here's the spreadsheet (https://docs.google.com/spreadsheets/d/1jGRrI8WL4Yg0jN-njsNU_w-ZedIBCZd_ibLM9efDBvo/edit?usp=sharing) I was referring to. It's fairly simple and doesn't properly deal with crits but can help figuring out when +attack helps more than +damage.

[SharkForce]

I hear you. I still feel that +hit is just better overall, but numbers don't lie, and as a DM I've got to go with the math, not the emotion.

well sure, but i'd rather be marginally less effective, and have more fun :P

[Oscredwin]

Falling off the edge of the d20 is a big deal, and that was a (relatively easily) achievable goal in 3.X. Since you can't do that, the additional to-hit is less of a big deal. It's an area of increasing marginal returns, a little is ok, a lot is amazing.

[Xetheral]

Interestingly, I was wrong earlier... the percentage method and the fixed method produce exactly the same average damage breakpoints no matter what the chance to hit is.

Here's a list of the breakpoints. If your average damage is greater than the listed amount, then a +1 to hit and damage will do more extra damage on average than +1d6 damage will.

Edit: Thanks to SharkForce for catching an error. The table has been updated to the correct values.

http://i264.photobucket.com/albums/ii192/Xetheral/1vs1d6corrected.jpg

[SharkForce]

shouldn't the 2 row be never in all cases? it can't make you hit on a 1...

[Slipperychicken]

Simple question, for which many different answers may spring.

Which is better, +1 hit and damage, or +1d6 damage.


You'd want to calculate your character's DPR after each option. So you'd get the "+1 to hit and damage" DPR value (i.e. DPR when your attack and damage are 1 higher), and the "+1d6 damage" DPR value (when your damage is 3.5 higher). Then you just pick the bigger number.

It's not an exciting answer, I know, but that's just how you evaluate alternatives: Take the expected outcomes of each, and pick the better one.

[burninatortrog]

It seems to me that if combat lasts for a short time and/or the opponent has a high AC then the +1 to hit and +1 to damage will be more desirable, while if combat lasts for a long time and/or the opponent has a low AC then the +1d6 to damage will be more desirable.

[Totema]

I don't want to put words in his mouth, but I think I understand where he's coming from.

In 5e, bounded accuracy balances combat by restricting the ranges of attack bonus vs AC to a much narrower field than in previous editions so that any character is relevant at any level in regards to attack vs AC.

By contrast, hit points are like candy, and WotC has admitted that while AC wasn't intended to be the determining factor in difficulty, hit points would be.

Some of us have drawn an assumption from this philosophy that anything that stretches the boundaries of bounded accuracy skew the game heavily in favor of the one who has the bonus to hit, where as bonus damage is not as important.

You pretty much captured everything I meant to say with that. :smallsmile:

[GoodbyeSoberDay]

The general case, assuming BA holds and there's no Advantage or Disadvantage or Champion Fighter:

Base damage = b
Base hit chance = c

Base damage per attack = bc
Base with +1/+1 = (b+1)(c+0.05)
Base with +1d6 = (b+3.5)c + 0.05*3.5, the last bit coming from crit damage

Compare the increase in damage from +1d6: 3.5(c+0.05) and from +1/+1: c+0.05b+0.05
0.175 + 2.5c >? 0.05b
If b < 2.5 + 50c
then +1d6 damage is superior to +1/+1

So if your chance to hit is 50%, your base damage needs to be 27.5 or higher to compete. If your chance to hit is only 10%, however, your base damage merely needs to be 7.5 or higher for the bonus to hit to compensate.

The maths are a bit messier, but in general advantage will skew the result in favor of +1/+1 for a low chance to hit and +1d6 for a high chance to hit, and disadvantage will do the opposite.

EDIT: There are significant differences between 3.5 and 5e outside this basic math, however. For one, magic weapons were pretty much an assumed part of the game in 3.5, so DR/magic was all but pointless. Second, flat resistances meant that +1d6 elemental damage was completely worthless half the time, but a +1 to regular damage had its full effect unless you did no damage at all. Whereas in 5e resistance just halves the damage, no matter how small.

[Xetheral]

shouldn't the 2 row be never in all cases? it can't make you hit on a 1...

Good catch, thanks! Actually, when looking into it I found another mistake. I'll update the posted table shortly.

Edit: Updated table posted. The Adv/DisAdv numbers were all wrong too--thanks again for pointing out the error!

[Baptor]

First, thanks to everyone for doing the math! (I stink at math)


EDIT: There are significant differences between 3.5 and 5e outside this basic math, however. For one, magic weapons were pretty much an assumed part of the game in 3.5, so DR/magic was all but pointless. Second, flat resistances meant that +1d6 elemental damage was completely worthless half the time, but a +1 to regular damage had its full effect unless you did no damage at all. Whereas in 5e resistance just halves the damage, no matter how small.

This, I think, was what was skewing my understanding. In 3.5 +1d6 was not all that great, because so many things had elemental resistance and thus the die came into play maybe half the time at high levels, whereas the +1/+1 was always relevant. I remember this also being a reason most folks went for the Holy enchantment, because 75-85% of all monsters you fought were evil aligned.

In this game, +1d6 means +1d6 most of the time.

[Eslin]

Please note that the +1d6 is usually a resistable element, and that this is only taking damage into account. +hit scales much better with on-hit utility - if you're a monk or fighter who can trip with every hit, for example, +hit makes that more likely to work. Things like wolf attunement, shapeshifting into a creature with on hit effects, maneuvers, open hand technique, repelling blast and sentinel are all improved by +hit in a way that they aren't by +1d6 damage.

[Baptor]

Please note that the +1d6 is usually a resistable element, and that this is only taking damage into account. +hit scales much better with on-hit utility - if you're a monk or fighter who can trip with every hit, for example, +hit makes that more likely to work. Things like wolf attunement, shapeshifting into a creature with on hit effects, maneuvers, open hand technique, repelling blast and sentinel are all improved by +hit in a way that they aren't by +1d6 damage.

This is true, I'd have to believe that classes which have procs on their normal attacks like stun, etc, would really want the +1 hit.