Energy Enhancements are too good at +1 (math)

[The Souljourner]

So, I was reading the "Should keen exist?" thread in House Rules, and someone mentioned that keen is pretty weak when compared to the energy enchantments, and that got me to thinking that the energy enchantments are probably way too good for what they cost. Let's do some math, comparing +1 to hit and damage versus +1d6 energy damage.

+1 to hit is +5% average damage per swing, since you'll hit 5% more often (ignoring edge cases). Thus, the enhancement bonus goes up in value as your average damage per swing goes up in value. To figure out where this equalizes with the energy enchantment, we simply use a little algebra.

3.5 = (x + 1) * 5%, x = 69

(this is a little fudged, since the +1 to damage should really be multiplied times your to-hit percentage first... but it's such a small difference, it doesn't matter much)

If your average damage per swing is 69, then +1 to hit and damage is approximately equal to +3.5 damage. If your damage per swing is over 69, +1 to hit and damage is better, if it's lower, +1d6 is better.

69 is a lot. Keep in mind that this is not average per hit, it's average per swing. That means you have to take into account how often you hit. If you only hit 50% of the time, your damage per swing will be 50% of your damage per hit.

If we do the same calculation for +2 to hit and damage, things get a little more reasonable...

3.5 = (x + 2) * 10%, x = 33.

Still kinda high, but since some things are totally immune to energy damage, but nothing is immune to the enhancement bonus, it's pretty much a wash.

The long and the short of it? Energy Enchantments should be +2. The various alignment enchantments that give +2d6 should be at least +3, maybe +4 (depending on how much of a discount you give for them not affecting all your opponents equally).

7 = (x + 3) * 15% = 43 ... kinda high for average damage
7 = (x + 4) * 20% = 31 ... more reasonable

So... adding holy to your weapon should cost +4 (maybe +3, but the fact that it lets you bypass "good" damage reduction is probably a good enough balance to the fact that it won't damage neutral creatures).

-The Souljourner

 

[Thanee]

One factor, which certainly played a role in the pricing in 3.0 was damage reduction. This is, of course, not really a factor anymore.

Bye
Thanee

 

[Rystil Arden]

The math here is not correct, as per the fudge you mentioned, except it was not fudged correctly.

To prove this, I will use the nonfudged equation for every possible value of the to-hit percentage, and show how none of them is even close to your number.

The proper equation is (DAMAGE + 3.5) * (TO-HIT%) = (DAMAGE + 1) * (TO-HIT% + .05)

Here are the equivalent values of DAMAGE you need for all possible values of TO-HIT%:

.05 (in other words, only hit on a 20): DAMAGE = 1.5
.1: DAMAGE = 4
.15: DAMAGE = 6.5
.2: DAMAGE = 9
.25: DAMAGE = 11.5
.3: DAMAGE = 14
.35: DAMAGE = 16.5
.4: DAMAGE = 19
.45: DAMAGE = 21.5
.5: DAMAGE = 24
.55: DAMAGE = 26.5
.6: DAMAGE = 29
.65: DAMAGE = 31.5
.7: DAMAGE = 34
.75: DAMAGE = 36.5
.8: DAMAGE = 39
.85: DAMAGE = 41.5
.9: DAMAGE = 44
.95: They are never equal because 1 always misses

 

[magic_gathering2001]

OK you have officially confused me
Here is my take

A third level fighter could buy a +1 longsword, or a flaming one (i know you cant have a not +1 flaming weapon but this is an example) and have +3 Strength

a CR 3 wizard could have AC 12(+2 DEX)

+1: hits on a 5-18 or 65% for average 5.5 damage and crits on a 19-20 or 10 % for average 11 damage
so every round he should expect about 4.675 damage (65% of 5.5 + 10% of 11)

Flaming: hits on a 6-18 or 60% for average 7 damage and crits on a 19-20 or 10% for average 14.5 damage
so every round he should expect about 5.65 damage

but against the fighter 4 BBEG with AC 24(+1 plate +1 shield +1 Natural from amulet)

+1: hits on a 17+18 or 10% for average 5.5 damage and crits on a 19-20 or 10 % for average 11 damage
so every round he should expect about 1.6 damage (20% of 5.5)

Flaming: hits on a 18 or 5% for average 7 damage and crits on a 19-20 or 10 % for average 14.5 damage
so every round he should expect about 1.8 damage (15% of 7)

 

[Nail]

...or, simplifying the algebra in Rystil Arden's post:

Damage = 50 * TO-HIT% -1

 

[Nail]

OK you have officially confused me...

That's okay!

What the algebra is trying to get at is this:

"How much damage does your attack have to do in order for the expected damage increase be the same for both enhancements?"

Given the simplifed equation I posted (which could be wrong, I admit!):

"If you hit about 50% of the time, then if your attack without enhancement does less than 24 hp of damage, the flaming enhancement is better than the +1 enhancement."

 

[Sleeping Dragon]

There's also quite a number of creatures with energy resistance. Even energy resistance 5 makes energy enhancements nearly useless, not to mention those with higher resistances.

 

[Rystil Arden]

...or, simplifying the algebra in Rystil Arden's post:

Damage = 50 * TO-HIT% -1

Yup, Nail you've solved the formula correctly. Hopefully, it is pretty clear from this that the +1 price of the Flaming enhancement was carefully and correctly adjudicated

 

[Infiniti2000]

There's also quite a number of creatures with energy resistance. Even energy resistance 5 makes energy enhancements nearly useless, not to mention those with higher resistances.

There also the added +10 hp and +2 hardness for each +1 enhancement. That should not be dismissed out of hand like the OP did.

 

[jgsugden]

1.) Stealth is next to impossible with a weapon that deals energy damage. Try sneaking up on a foe with a flaming sword that generates light and crackles. If you attack with a sonic mace, every monster in the dungeon is going to hear you coming.

2.) Another factor is that *THESE WEAPONS MUST BE ACTIVATED BEFORE DEALING ENERGY DAMAGE*. The description of these weapons begins with 'upon command'. The activiation section under magic weapons indicates that this requires a standard action.

So, in order to deal the extra d6 of energy damage, the character must sacrifice a standard action to activate the weapon. This is a *huge* cost in some situations. It often means allowing the enemy an extra round of attacks on you before you start hurting it.