[4e HouseRule] Reduce the gap between multiattack and single attack power

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Hello, a lot of people are claiming that multiattack (or non standard action extra attack) are way more powerfull (damagewise) than single attack, even if the number of damage dice is a lot more for single attack. This is supposed to be more and more pronounce the higher the level, due to increasingly high static modifier

To mitigate this I've been thinking about this house rule : make the enhancement bonus part of a damage dice.

For instance a power that deals 7[W] +Str damage used with a +5 magic longsword would actually deal : 7d10 + 7*5 + Str damage (plus other non enhancement static modifier as usual)
An implement power that deals 3d8 + Cha damage used with a +2 magic rod would actually deal :  3d8 + 3*2 + Cha damage (plus other non enhancement static modifier as usual)

This would probably not completely kill the superiority of multiattack power, but would be a step in the right direction maybe ?
As a side effect it will make the PC more powerfull by increasing their damage output (especially at high level where enhancement bonus and number of damage dice per power is high). This might actually be a benefit as it would help shorten combat length (you may have to compensate by upping a bit encounter level, or monster damage)

This is purely theoritical for the moment and hasn't been tested. Before trying it in my game, any impact that I would have completely miss ?
Make an Excel-sheet and track the differences. You could actually be onto something here, but it's purely a mathematical thing that you can calculate rather easily. I'm curious to see the results, report them back when you have them!
My only concern to this would be it's difficulty in mathing at the table.

For multi-target effects, I think static bonuses should only be applicable once per target. Then agian, I think multi-target powers could be handled easier: If you have a 4d6+Str power, you could pslit it up against 2 targets (2d6+Str against each), 4 targets (1d6+str each), or mix it up. But that would take a whole nother variation to the system. 

Poe's Law is alive and well.

Yep, would be possible to check with a few sample power.
I would need to make asumption on the average static bonus. I would go for 10 per tier (including enhancement ? is it reasonable for a moderately optimized characater ? 
Also something like 50 % hit rate.

Concerning the math difficulties, shouldn't be a problem as we are using a Virtual Table Top (roll20, which is quite good by the way) which can take care of all the math.

Other possiblity as Xeviat-DM suggest would be to go the other way around, and reduce power level of multi attack instead of upping the one of single attack. .. 
I'd do it this way:

Assume a hypothetical power that gains 1[W] every 5 levels (so 1[W]+stat at level 1-5, 2[W]+stat at level 6-10, and so on until [6]W+stat at level 26-30).

Compare that to a double-attack power (so two attacks, each dealing 1[W]+stat damage) during levels 1-10, a triple-attack during levels 11-20, and a quad-attack during levels 21-30.

Those are decent representatives of what different high-W strikers (like the Barbarian) and multi-attack strikers (like the Ranger) are capable of at each tier of play.

The hit-rate could be put at 70%, which means both classes hit on a 7, which is reasonable at every level.

The double-attacks are made with a Longsword, the high-W attacks with a Fullblade.
Assume an 18 in the attack stat, which increases by 1 at every opportunity. So damage bonuses are: L1:+4/L8:+5/L14:+6/L21:+7/L28:+8.
The enhancement bonus starts at 1, and increases by 1 every 5 levels.
Both classes use Iron Armbands of Power (+2/4/6 damage bonus at levels 6/16/26).
Both classes use frostcheese (Frost Weapon, Gloves of Ice, Siberys, Shard of Merciless Cold, and Icy Heart for a +8/+13 damage bonus at levels 11/21).
The multiattacker also uses Lasting Frost for another +5 damage bonus on every attack after the first.

So the damage would be like this:
(the first number after the W-damage is the enhancement bonus to damage)

High-W
Level 1-5: 1d12+1+4
Level 6-7: 2d12+4+6
Level 8-10: 2d12+4+7
Level 11-13: 3d12+9+15
Level 14-15: 3d12+9+16
Level 16-20: 4d12+16+18
Level 21-25: 5d12+25+24
Level 26-27: 6d12+36+26
Level 28-30: 6d12+36+27

Multi-attacker
Level 1-5: 2*(1d8+1+4)
Level 6-7: 2*(1d8+2+6)
Level 8-10: 2*(1d8+2+7)
Level 11-13: (1d8+3+15) + 2*(1d8+3+20)
Level 14-15: (1d8+3+16) + 2*(1d8+3+21)
Level 16-20: (1d8+4+18) + 2*(1d8+4+23)
Level 21-25: (1d8+5+24) + 3*(1d8+5+29)
Level 26-27: (1d8+6+26) + 3*(1d8+6+31)
Level 28-30: (1d8+6+27) + 3*(1d8+6+32)

The damage for multi-attacker assumes you always hit with the first attack so you activate Lasting Frost.

Multiply this by the to-hit rate, factor in critical hits, and you're done.

Eyeballing the numbers, I'd guess the multi-attacker still outperforms the high-W attacker, but it's a lot more close now. And the high-W has the advantage of using only 1 power, which means he can attack for comparable numbers again next round. Multi-attackers use more powers, so they run out of steam more quickly.
I did some more calculations, and it turns out the damage difference is still too large at paragon and epic tier.

To give you an idea, this is roughly the damage difference between rules as written and the proposed houserule for big W powers:

Show
Level 1-5: none
Level 6-10: ~1.5
Level 11-15: ~4
Level 16-20: ~9
Level 21-25: ~14
Level 26-30: ~20

So about what you would expect: the enhancement bonus, squared, multiplied by 0.7 (the hit chance).

This is roughly the damage difference between the proposed houserule and multi-attack powers:

Show
Level 1-5: ~5
Level 6-10: ~2
Level 11-15: ~24
Level 16-20: ~20
Level 21-25: ~38
Level 26-30: ~33

The damage difference is still significant enough that, when given the choice, a striker should always aim for multi-attacks instead of more W.

But!

You can overcome the difference by also adding the stat bonus to every W. So a 3[W]+Str attack with a +3 Fullblade, made by a Barbarian with 22 Strength, would deal:

3d12 + 3*3 (enhancement) + 3*6 (Strength) + other bonuses.

Then the rough damage difference between the proposed houserule and multi-attack powers becomes:

Show
Level 1-5: ~5
Level 6-10: ~ minus 1.5
Level 11-15: ~15
Level 16-20: ~8
Level 21-25: ~23
Level 26-30: ~7

Still quite a difference at the first 5 levels of every tier, but during the second 5 levels the exponentiality really adds up. Multi-attacks still win by a small margin, but that's compensated by the fact that big W attackers have more powers in their arsenal, and don't just blow through them in the first round.
Thanks for the work. Iwas not expecting to fully close the gap, but just reduce it. I think I'm happy with the result, and will try to propose that to my DM, so that we can try it. (we are currently still level 1, so no urgency)
No problem, I'm actually quite satisfied with the result, it's quite elegant.

Alternatively, and I like this even better, you just add all typed damage bonuses (power, feat, enhancement, item, racial) to every damage dice. Then add stat bonus and untyped bonuses to that. Makes big W attackers a little stronger if built properly, but it's even more intuitive.
Yep, quite a lof of flexibility depending on how much you want to reinforce the big W powers. The reason I chose enhancement in the first place was because it is really part of the weapon, not something independant added on top of it. But I can understand adding other type of bonus as well in the calculation.
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