Critical stacking and feats - balanced? (Math-fu needed)

[Grayhawk]

For this comparison, lets focus on the Rapier, the Longsword and the Battleaxe. AFAIK, they deal equal amounts of damage with their different damage die and critical threat ranges/multipliers.

Now, let's say that Improved Critical and Keen only adds 1 to the threat range each, but they stack. (I know that this favors the low threat/high multiplier weapons.) Let's also introduce a new feat called Surgical Strike, that does away with the confirmation roll on a threat, but only for finessable weapons.

Will this make someone with Improved Critical and Surgical Strike wielding a Rapier (1d6, 17-20x2, no confirm needed) the equal of someone with a Battleaxe and Improved Critical (1d8, 19-20x3)?

How far will the Longsword fall behind at 1d8, 18-20x2?

What if all wield Keen weapons?

 

[CRGreathouse]

Without number crunching (yet), I have to say that I think Surgical Strike would be overly powerful. First of all, it's best when your opponent has a high AC, so it benefits you most when you need it most. Second, special critical-related abilities will be triggered more easily.

That is, even if the numbers did come out equal, Surgical Strike would be better than Improved Critical in actual gameplay.

 

[Grayhawk]

More questions come to mind:

1: Does it make a difference if a crit only multiplies the damage die?

2: Will the 'no need to confirm' be more powerful than a doubling of the threat range? Always?

Thanks for any insight you math savy guys can provide!

 

[FireLance]

I've done up a quick Excel spreadsheet to compare. I've picked two average numbers to use as a comparison. The first assumes the characters face opponents with ACs evenly distributed between 2 and 20 points above their best attack bonus. The second assumes the characters face opponents with ACs evenly distributed between 5 and 15 points above their best attack bonus. The spreadsheet does not take iterative attacks into account.

Playing around with the numbers produces some interesting results:

1. The longsword and battleaxe maintain their relative strengths regardless of damage bonus. The battleaxe is slightly (0.02%) superior over the 2-20 range and equal over the 5-15 range. Improved Critical makes it slightly better (0.18%) over the 2-20 range, but they are still equal over the 5-15 range. Adding +1 or +2 to the threat range of both weapons increases the battleaxe's advantage.

2. The rapier benefits the most from a high damage bonus. It is inferior when the damage bonus is low, but outperforms the longsword when the damage bonus is +19 or more, or +10 with Improved Critical.

3. Surgical Strike is probably too good. With Surgical Strike, a rapier starts to outperforms a longsword from a +3 damage bonus. By +10, it is outperforming a longsword by about 7.72% over the 5-15 range.

4. Extra damage which is not multiplied makes all weapons more equal to each other.

Hope this is helpful.

EDIT: Analysis changed after fixing error pointed out by CRGreathouse (below).

 

[Grayhawk]

Very cool, FireLance; thanks for taking the time to do this!

Unfortunately I don't have Excel so I can't open the file, so maybe you (or someone else) can tell me how the following examples compare:

Rapier 1d6, 17-20x2
Longsword 1d8, 18-20x2
Battleaxe 1d8, 19-20x3

Rapier 1d6, 16-20x2
Longsword 1d8, 17-20x2
Battleaxe 1d8, 18-20x3

For this comparison, assume a roll of 15 is needed to hit and that a crit only multiplies the damage die.

How balanced are they?

What if you include a damage bonus of +6 (that is multiplied on a crit)?

 

[CRGreathouse]

I've done up a quick Excel spreadsheet to compare. I've picked two average numbers to use as a comparison. The first assumes the characters face opponents with ACs evenly distributed between 2 and 20 points above their best attack bonus. The second assumes the characters face opponents with ACs evenly distributed between 5 and 15 points above their best attack bonus. The spreadsheet does not take iterative attacks into account.

Your spreadsheet counts critical damage twice: once when it hits, and once agian if it crits. This is the reason that the average damage for longsword is better than battleaxe in your spreadsheet -- actually the battleaxe should have a (tiny) lead on the longsword, since it doesn't lose any of its threat range when a 20 is needed for a hit.

 

[Pyrex]

Each point of Crit Potential (range x (multiplier-1)) adds 5% to the average damage of the weapon.

First batch:
Rapier 3.5, +20% = 4.2 average damage per strike
Longsword 4.5 + 15% = 5.175 a.d.p.s.
Battleaxe 4.5, + 20% = 5.4 a.d.p.s.

Battleaxe is the clear winner here beating the rapier by ~28% on average damage.

Second batch:
Rapier 3.5 +25% = 4.375
Longsword 4.5 + 20% = 5.4
Battleaxe 4.5 + 30% = 5.85

Battleaxe still wins, advantage increases to ~33%.

Adding a damage bonus (that is not multiplied) decreases the advantage %, but the Axe will still always be better.

Adding a damage bonus that is multiplied does not change the advantage %, but as average damage increases, the difference in a.d.p.s goes up.

 

[CRGreathouse]

Rapier 1d6, 17-20x2
Longsword 1d8, 18-20x2
Battleaxe 1d8, 19-20x3

Rapier 1d6, 16-20x2
Longsword 1d8, 17-20x2
Battleaxe 1d8, 18-20x3

For this comparison, assume a roll of 15 is needed to hit and that a crit only multiplies the damage die.

How balanced are they?

What if you include a damage bonus of +6 (that is multiplied on a crit)?

I wrote up a spreadsheet to test this. Here's the average damage:

Threat range +1: Lsword 1.55, battleaxe 1.62, rapier 1.26
Threat range +2: Lsword 1.62, battleaxe 1.76, rapier 1.31

+6 damage multiplied in:
Threat range +1: Lsword 3.62, battleaxe 3.78, rapier 3.42
Threat range +2: Lsword 3.78, battleaxe 4.10, rapier 3.56

For comparison, without changing the threat range or adding damage:
Lsword 1.49, battleaxe 1.49, rapier 1.21


All of these assume a 15 is needed to hit. I can run it for other numbers if you'd like...

 

[Grayhawk]

Very cool, guys; thanks a lot!

All of these assume a 15 is needed to hit. I can run it for other numbers if you'd like...

How about if a 5, 10 or a 20 is needed?

 

[FireLance]

Using the revised spreadsheet (CRGreathouse, thanks for pointing out the error, BTW), I get the following:

No Damage Bonus

5 to hit:
Threat range +0: Longsword 3.96, battleaxe 3.96, rapier 3.22,
Threat range +1: Longsword 4.14, battleaxe 4.32, rapier 3.36
Threat range +2: Longsword 4.32, battleaxe 4.68, rapier 3.50

10 to hit:
Threat range +0: Longsword 2.72, battleaxe 2.72, rapier 2.21
Threat range +1: Longsword 2.85, battleaxe 2.97, rapier 2.31
Threat range +2: Longsword 2.97, battleaxe 3.22, rapier 2.41

20 to hit (same average damage regardless of threat range):
Threat range +0: Longsword 0.24, battleaxe 0.25, rapier 0.18
Threat range +1: Longsword 0.24, battleaxe 0.25, rapier 0.18
Threat range +2: Longsword 0.24, battleaxe 0.25, rapier 0.18

Over 2-20 range:
Threat range +0: Longsword 2.47, battleaxe 2.48, rapier 2.01
Threat range +1: Longsword 2.59, battleaxe 2.70, rapier 2.10
Threat range +2: Longsword 2.70, battleaxe 2.92, rapier 2.18


+6 Damage Bonus

5 to hit:
Threat range +0: Longsword 9.24, battleaxe 9.24, rapier 8.74,
Threat range +1: Longsword 9.66, battleaxe 10.08, rapier 9.12
Threat range +2: Longsword 10.08, battleaxe 10.92, rapier 9.50

10 to hit:
Threat range +0: Longsword 6.35, battleaxe 6.35, rapier 6.01
Threat range +1: Longsword 6.64, battleaxe 6.93, rapier 6.27
Threat range +2: Longsword 6.93, battleaxe 7.5, rapier 6.53

20 to hit (same average damage regardless of threat range):
Threat range +0: Longsword 0.55, battleaxe 0.57, rapier 0.50
Threat range +1: Longsword 0.55, battleaxe 0.57, rapier 0.50
Threat range +2: Longsword 0.55, battleaxe 0.57, rapier 0.50

Over 2-20 range:
Threat range +0: Longsword 5.77, battleaxe 5.77, rapier 5.46
Threat range +1: Longsword 6.03, battleaxe 6.30, rapier 5.69
Threat range +2: Longsword 6.29, battleaxe 6.81, rapier 5.91