Energy Enhancements are too good at +1 (math)

[FreeTheSlaves]

So anyway, I think this thread is pointing to energy weapons being good but not too good. It would be interesting to see how advantageous the enhancement is for relatively low strength & 2wf characters.

Hmmm, and I have a free morning to spare...

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The first character is my 25pt buy paladin with a base 15 str because I am part-powergamer. He can aquire a +2 sword at 7th level if we assume he can only use half his wealth on one magic item. He has weapon focus & has increased his str to 16 at 4th level. The target AC will use the SR calculation of 12+CR and so his target AC will be 19, which ime is about right on average. I will calculate total iterative damage. One example is with a +2 sword (ab +13/+8), the other with a +1 flaming sword (ab +12/+7).

Layout is the following: A = P{D[1+Pc(Mc-1)] + Db}

where
A = average damage per attack
P = Probability to hit, as a fraction
D = average weapon damage plus Str, Magic, etc
Pc = Probability to Threaten, as a fraction
Mc= Critical Multiplier
Db = Bonus Damage dice that are not multiplied by a confirmed critical


+2 sword
7.8375 = 0.75{9.5[1+0.1(2-1)]}
5.225 = 0.50{9.5[1+0.1(2-1)]}
13.0625 = average full attack damage

+1 flaming sword
8.995 = 0.70{8.5[1+0.1(2-1)] + 3.5}
5.7825 = 0.45{8.5[1+0.1(2-1)] + 3.5}
14.7775 = average full attack damage


Impressive but what happens if this character meets a harder AC? I will increase the AC19 to 24.


+2 sword
5.225 = 0.50{9.5[1+0.1(2-1)]}
2.6125 = 0.25{9.5[1+0.1(2-1)]}
7.8375 = average full attack damage

+1 flaming sword
5.7825 = 0.45{8.5[1+0.1(2-1)] + 3.5}
2.57 = 0.20{8.5[1+0.1(2-1)] + 3.5}
8.3525 = average full attack damage


The difference between the average damage of the two weapons decreased as the AC got higher. In particular it can be seen that the iterative attack of the flaming sword versus the higher AC was actually lower than the +2 counterpart. Basically, the easier to hit the enemy the better the flaming weapon while the harder to hit the enemy the better the flat enhancement. Furthermore these numbers do not take into consideration Power Attack which will allow the +2 sword to close the gap somewhat between the two. I will be back to calculate this for better analysis.

 

[Nail]

...while I, half-way 'round the world, am off to supper and family-time. Have fun!

 

[FreeTheSlaves]

I will calculate Power Attack only for the AC19 because off hand I can say that it would be foolish to do so versus the higher AC. This character will aquire Power Attack anyway so I'll dismiss the opportunity cost for taking the feat, which would be too hard to work out and would be heading off in a tangent. The +2 sword option is power attacking for 1 and uses a shield.

****

Layout is the following: A = P{D[1+Pc(Mc-1)] + Db}

where
A = average damage per attack
P = Probability to hit, as a fraction
D = average weapon damage plus Str, Magic, etc
Pc = Probability to Threaten, as a fraction
Mc= Critical Multiplier
Db = Bonus Damage dice that are not multiplied by a confirmed critical


+2 sword
8.085 = 0.70{10.5[1+0.1(2-1)]}
5.1975 = 0.45{10.5[1+0.1(2-1)]}
13.2825 = average full attack damage

+1 flaming sword
14.7775 = average full attack damage


Closed the gap between the two options by about 0.2 damage, which is pretty marginal but noteworthy. Just for completeness I'll do both swords in two hands (str *1.5 & PA 2:1 ratio) versus AC19 and both Power Attacking for 1.


+2 sword
9.625 = 0.70{12.5[1+0.1(2-1)]}
6.1875 = 0.45{12.5[1+0.1(2-1)]}
15.8125 = average full attack damage

+1 flaming sword
10.4975 = 0.65{11.5[1+0.1(2-1)] + 3.5}
6.46 = 0.40{11.5[1+0.1(2-1)] + 3.5}
16.9575 = average full attack damage


Approaching borderline stupidity, I'll calculate both weapons without PA vs a mighty AC29. This'll sort the men from the boys.


+2 sword
2.6125 = 0.25{9.5[1+0.1(2-1)]}
0.49875 = 0.05{9.5[1+0.05(2-1)]}
3.11125 = average full attack damage

+1 flaming sword
2.57 = 0.20{8.5[1+0.1(2-1)] + 3.5}
0.62125 = 0.05{8.5[1+0.05(2-1)] + 3.5}
3.19125 = average full attack damage


Okay I'm sold, for my +2 weapon it is going to be an energy weapon but this is only for +2, I'll have to recalculate at +3...

 

[FreeTheSlaves]

I'll let someone else do a comparison of the 2wf - my spare morning about used up.

 

[Rystil Arden]

The reason why the energy weapon edges out is because 1 for 1 power attack is not a favourable exchange--if you trade your +1 to hit for +1 damage, then of course the energy weapon will always do more because it has +4.5 and the other one has only +3. The point is to not use extra Power Attack with the +2 sword

 

[magic_gathering2001]

TwF

VS. AC:19

+2 longsword/shortsword
21=10+.4[.5(2*10)]+.5(10)+.4[.25(2*10)]
+1 Flaming longsword/shortsword
25.65=.9(13.5)+.4[.5(2*13.5)]+.4(13.5)+.4[.25(2*13.5)]

VS. AC:24
+2 longsword/shortsword
13.5=6+.4[.5(2*10)]+.15(10)+.4[.25(2*10)]
+1 Flaming longsword/shortsword
14.45=.5(13.5)+.4[.5(2*13.5)]+.1(13.5)+.4[.25(2*13.5)]

 

[FreeTheSlaves]

The reason why the energy weapon edges out is because 1 for 1 power attack is not a favourable exchange--if you trade your +1 to hit for +1 damage, then of course the energy weapon will always do more because it has +4.5 and the other one has only +3. The point is to not use extra Power Attack with the +2 sword

But Power Attacking with the +2 sword for 1 vs AC19 increased the overall damage by 0.2. I think what this highlighted was that the extra enhancement benefit kicks in versus higher AC foes; that and PA can somewhat mitigate the loss of comparative average damage versus low AC foes, but only slightly.

 

[Elder-Basilisk]

People say that energy resistance is a big downside to the energy enchantments.. but what about damage reduction? It goes right through that, and "any kind of damage reduction" is a lot more common in my experience than one specific type of energy resistance.

It depends what level you are and what kind of foes you face. At higher levels, you face a lot of undead and outsiders who have resistance 10 to most energies. Similarly, templated foes are pretty common and most templates grant a medley of minor energy resistances.

It's also unreasonable to compare "any kind of DR" to a "specific type of energy resistance." For instance, the ability to bypass DR/magic is irrelevant to discussion of a flaming weapon because the magic weapon already bypasses DR /magic. Odd are pretty good that DR /something you can't beat doesn't crop up any more often than energy resistance (or, worse yet, energy healing--for example a shocking weapon is a poor choice against a flesh golem). Furthermore, the ability of the energy weapon to bypass DR is only relevant when the DR negates ALL the damage from the initial attack. If Joe fighter 20 with a magic sword hits the pit fiend for 20 points of damage, even if he doesn't get through its DR, he still deals 5 points of damage. And if Joe fighter 20 had a more magic sword (enhancement=X+1), he would still get the added damage from the enhancement. In this case, he hits the pit fiend for 21 points of damage and 6 gets through. And it's certainly worth noting that the kinds of creatures with DR /other than magic tend to be the kinds of creatures with energy resistance. Demons, devils, slaadi, golems (many of whom are benefitted by one energy type), etc. So, the foes who DR ignoring damage would be most useful against are the very foes least likely to be effected by energies. About the only time I see the DR penetrating aspects of energy come up is when non-fighter archers go up against greater or elder elementals' DR 10/-

I think the energy enchantments should be more like 1.5-ish or so. The 24 average damage per hit needed to equal out a +1 enhancement with it is pretty hard to attain before 14th or so level. Even a 12th level fighter with greater specialization, greatsword, and 24 strength only does 21 on average.

You're looking at that the wrong way. The fighter with the +(X+1) two handed sword will presumably have a +1 advantage in his attack bonus vis a vis the fighter with the +X flaming two handed sword. If he power attacks for one, eliminating any attack differential, he deals three extra points of damage to the flaming sword's 3.5. (This power attack analysis, by not including situations where an extra point of attack bonus is more advantageous than two points of damage is advantageous to the energy weapons, so if they don't win here, they don't win anywhere).

So, for two handed weapons, against non-resistant foes, an energy enhancement grants a very minor damage advantage in exchange for a loss of flexibility (you don't need to power attack if you'd rather hit), hardness, hit points, etc, and the activation requirement (mostly a non-issue).

For a one-handed weapon or a two-weapon fighter, energy enhancements are a much more attractive bargain.

In no cases, however, do they add up to a +2 bonus. The two handed weapon wielder power attacks for 2 and gets 6 points more damage per hit at the same attack bonus vs. 3.5 for the energy weapon user. Even a one-handed weapon user can power attack for 2 and get 4 points of damage vs. the 3.5 from the energy weapon user. (And while it might seem like that's close, both the number of energy resistance creatures and the power of other +2 equivalent enhancements (holy, wounding, etc) mean that it isn't really in the same ballpark).

So, if you ask me, that puts energy weapons at about where they should be for a +1 enhancement. They are better than an enhancement bonus in some circumstances (one handed weapon, etc) and worse in others.

(For comparison, a keen 19-20 or x3 weapon (assuming a 75% confirmation rate) will deal more damage than a +(X+1) weapon when its wielder deals 40 points of damage per hit and on an 18-20 weapon will add more damage than the +(X+1) weapon will deal more than 26.66 damage per hit. Which is to say that keen scimitars and falchions are good weapons for high level paladins when they're smiting (because, who wants to spend a feat on Imp Crit) or two handed power attacking, single class (because if they multiclassed with fighter, they wouldn't be short on feats) barbarian, but keen is a pretty bad deal for everyone else. Keen is generally considered weak (and rightly so)).

WRT the other questions:
1. d8 energy damage would not be worth the +2 enhancement. On the two handed weapon, 4.5 points of damage still isn't close to the 6 points from power attack and a higher enhancment bonus. On one handed weapons, it's not enough more than the 4 points from power attack and the higher enhancement bonus. And on either it doesn't remotely compare to wounding or holy.

2. Burst weapons are generally not worth the extra enhancement bonus and compare very poorly to other +2 enhancments. Even in a best case scenario (Paladin with imp crit and bless weapon on an 18-20 weapon against evil foes where every threat is a hit), going from energy to energy burst weapon will only add an extra .3*5.5 (2.75) to your average damage per hit. At that point, it's almost reached the 3.3 that a two handed weapon wielder power attacking for one more point would add to his damage per hit with a +(X+1) weapon. And, even with the 3.5 damage per hit from the initial energy damage (total 6.25 damage per hit), it doesn't equal the 7 points of damage per hit from holy or the (foe's HD/2) damage per hit from wounding.

And that's the BEST case scenario. Most weapons will also have to figure in crit confirmation rolls and fewer than 30% critical hits.

 

[RandomPrecision]

Just checking - am I the only one who doesn't think the gap between energy enhancements and normal + enhancements is that great? I mean, .0X isn't that great of a difference. If +'s are better at low armor classes, and energy enhancements are better at high armor, they're probably similar in the mid level range, which is the level at which they'll probably be used the most.

 

[Elder-Basilisk]

It's not... for two handed weapons and when they work. When foes are resistant, obviously, the gap is significant. For one-handed weapons and missile weapons, when foes aren't resistant, it's noticable enough to be a good deal (most of the time).

Just checking - am I the only one who doesn't think the gap between energy enhancements and normal + enhancements is that great? I mean, .0X isn't that great of a difference. If +'s are better at low armor classes, and energy enhancements are better at high armor, they're probably similar in the mid level range, which is the level at which they'll probably be used the most.