Maths problem +2h weapons.

[DeathOfRats]

Ok Maths gurus, I have a question

Is the average damage of a Falchion better than a Greatsword if you have Improved Critical? If strength has an effect, figure it out with 24 strength and weapon specialization !

Do you apply 1 1/2 times damage bonus for high strength when using a 2h weapon?

Thanks.

 

[Altamont Ravenard]

Ok Maths gurus, I have a question

Is the average damage of a Falchion better than a Greatsword if you have Improved Critical? If strength has an effect, figure it out with 24 strength and weapon specialization !

This will largely depend on what you usually must roll in order to hit. If you're usually facing creatures that you can hit, say, on a 10, then the falchion will get more criticals, and probably be a better weapon. If you only usually hit on a 16 (for example), then the Improved Critical feat isn't that useful since some of the figures in your critical range aren't even enough to cause normal damage.

Since you apply your STR bonus and Weapon SPecialization to both attacks, they don't really matter when you compare the effectiveness of each weapon.

Lemme try to whip up a little analysis real quick...

Do you apply 1 1/2 times damage bonus for high strength when using a 2h weapon?

Yes, meaning that with a 24 STR (ie +7 damage bonus), you actually get +10 damage bonus when using a weapon two-handed.

AR

 

[Altamont Ravenard]

OK, he're my little analysis. The Greatsword seems to come out on top by an insignificant amount...

The 1st column represents the chance you have to hit. The 2nd column represents your chance of getting a critical hit. The 3rd column represents the chance of getting a normal hit (which is basically 1st column - 2nd column). The 4th column represents estimated damage output, ie (Chance to get a critical hit * average damage * 2) + (Chance to get a normal hit * average damage).

For the greatsword, with Improved critical, you need to hit on a 17 (20%) or more to get a chance of getting a critical hit. Your chance of getting a critical hit is (Chance to hit)² if your to-hit probability (1st column) is < 25%; and 20%*(Chance to hit) if your to-hit probability is > 20%.

For the falchion, with Improved critical, you need to hit on a 15 (30%) or more to get a chance of getting a critical hit. Your chance of getting a critical hit is (Chance to hit)² if your to-hit probability (1st column) is < 35%; and 30%*(Chance to hit) if your to-hit probability is > 30%.

I hope the tables are ok...

Greatsword (crit 17-20, ave dam 7+2+10 = 19, ave crit dam 38)			
%ToHit	%Crit	%Normal	Ave dam
0,0%	0,0%	0,0%	0,00
5,0%	0,3%	4,8%	1,00
10,0%	1,0%	9,0%	2,09
15,0%	2,3%	12,8%	3,28
20,0%	4,0%	16,0%	4,56
25,0%	5,0%	20,0%	5,70
30,0%	6,0%	24,0%	6,84
35,0%	7,0%	28,0%	7,98
40,0%	8,0%	32,0%	9,12
45,0%	9,0%	36,0%	10,26
50,0%	10,0%	40,0%	11,40
55,0%	11,0%	44,0%	12,54
60,0%	12,0%	48,0%	13,68
65,0%	13,0%	52,0%	14,82
70,0%	14,0%	56,0%	15,96
75,0%	15,0%	60,0%	17,10
80,0%	16,0%	64,0%	18,24
85,0%	17,0%	68,0%	19,38
90,0%	18,0%	72,0%	20,52
95,0%	19,0%	76,0%	21,66
100,0%	20,0%	80,0%	22,80

Falchion (crit 15-20, ave dam 5+2+10 = 17, ave crit dam 34)			
%ToHit	%Crit	%Normal	Ave dam
0,0%	0,0%	0,0%	0,00
5,0%	0,3%	4,8%	0,89
10,0%	1,0%	9,0%	1,87
15,0%	2,3%	12,8%	2,93
20,0%	4,0%	16,0%	4,08
25,0%	6,3%	18,8%	5,31
30,0%	9,0%	21,0%	6,63
35,0%	10,5%	24,5%	7,74
40,0%	12,0%	28,0%	8,84
45,0%	13,5%	31,5%	9,95
50,0%	15,0%	35,0%	11,05
55,0%	16,5%	38,5%	12,16
60,0%	18,0%	42,0%	13,26
65,0%	19,5%	45,5%	14,37
70,0%	21,0%	49,0%	15,47
75,0%	22,5%	52,5%	16,58
80,0%	24,0%	56,0%	17,68
85,0%	25,5%	59,5%	18,79
90,0%	27,0%	63,0%	19,89
95,0%	28,5%	66,5%	21,00
100,0%	30,0%	70,0%	22,10

Of course, any other input from other mathemagicians will be appreciated

AR

 

[DeathOfRats]

Hmmm, I was figuring with a +19 to hit at 10th level without magic bonuses that would give you a 60% chance to hit with your first attack against an adult black dragon (CR 11), which is probably one of the higher AC's at that level. Second attack comes in at 35% chance to hit.

At level 18 against a AC 42 wyrm black dragon you are at +27 to hit without magic, which is only a 25% chance of hitting with your first attack, and 0% not including natural 20 to hit on iterative attacks. That is probably one of the worst case scenario's though and you are likely to be hitting most regular things on your first attack.

Also, if you compare with say a scimitar vs dwarven waraxe which comes out better on average vs regular creatures? Does the improved threat range (with improved critical in both cases) yield much bigger average damage or does the improved multiplier balance out?

 

[Altamont Ravenard]

I've put together a little Excel sheet that will let you compare all the weapons you want

Just put the correct values in the grey boxes and compare to your heart's content...

AR

 

[DeathOfRats]

Sweet, thanks a lot !

 

[Staffan]

Falchion average damage per hit: 1.15*(5+bonuses), or 1.30*(5+bonuses) with improved critical or keen.
Greatsword average damage per hit: 1.10*(7+bonuses), or 1.20*(7+bonuses) with improved critical or keen.
The multipliers come from having a 10, 15, 20 or 30 percent chance of scoring a crit, leading to 100% increase in damage. Before you start arguing about the confirmation roll, that's kind of irrelevant. The chance of getting a crit assuming a successful hit in the first place is exactly the same as the chance that the original hit roll is a threat, because the confirmation roll has the same probability as the hit roll. In other words:
P(crit)/P(hit) = P(threat), because P(crit) = P(threat)*P(hit).
There is a corner case where the threat range is effectively lowered, and that's when the thing you're fighting is so tough that you need to roll more than the minimum threat range to hit - if you only hit on a 19, an 18 is still a miss even if you're using a falchion. But ignoring that, we then get an equation for when the falchion is superior to the greatsword, assuming similar bonuses. I'm including the crit-increasing effect here:
1.30*(5+bonuses) > 1.20*(7+bonuses)
6.5+1.3*bonuses > 8.4+1.2*bonuses
0.1*bonuses > 1.9
bonuses > 19

In other words, when your total damage bonuses exceed 19, the falchion is a better weapon against opponents that are vulnerable to crits.

 

[Altamont Ravenard]

Staffan, you seem to rule the Math World, would you mind giving my Excel sheet a look, to see if I've made any booboos? Thanks.

AR