Keen or another +1 ? Math Help Please...

[Tatsukun]

Hi all, quick question for the math folks…

I have a PC with an attack bonus of +12 / +7 Melee with a +1 Holy bastard sword that he sometimes uses one handed and sometimes two handed. His STR is 19, making the damage 1D10 + (1 Handed +5) (2 Handed +7) +2D6 holy is they are evil.

I have the opportunity to improve the weapon by “+1”, so here’s the question…

Which will end up doing more damage on average; a +2 Holy sword, or a +1 Holy Keen sword?

Let’s assume; the AC’s of the bad guys are about 20-24 or so, they are all evil, and they are all vulnerable to critical hits.

Can someone help me? I’m an English teacher, not a math teacher!

-Tatsu

P.S> The first person with a good answer is my new Personal Pagan God of Math ! !

 

[MacMathan]

I know there are better number crunchers around here than me but I will give it a shot:

Let's assume AC 22 as the average of your range.

Average damage one handed versus evil opponents: 17.5 two-handed 19.5 assuming no crits

Current chance to hit with first attack 55% with second 30%
Current chance to crit and confirm 8.5%
therefor current damage output= ~16.14 used 1H and 17.98 used 2H

Adding +1 increases average damage to 18.5 and 20.5 respectively
and the hit chances increase to 60% and 35%
Chance to crit and confirm 9.5%
therefore the damage output= ~19.24 used 1H and 21.33 used 2H

Adding Keen the chance to hit and average damage with no crits stays the same.
Chance to crit and confirm 17%
therefore the damage output= ~17.40 used 1H and 19.40 used 2H

I think the above is correct but others should double check it.

 

[Geoff Watson]

+2 Holy is much better than +1 Keen Holy.

'Keen' works on 10% of hits, for an extra 1d10+5/+7 damage, for an
average of 1.05 or 1.25 extra points of damage per hit.

+2 gives an extra +1 damage per hit, AND gives you more hits, increasing the chance to hit by 11-20%.

Geoff.

 

[Darmanicus]

Sod the math, 'Keen' just sounds better and there are feats that are related to crits.

Go with 'Keen'.

 

[Rkhet]

+2 is better... in theory. In practice you'll have to take into account what buffs you'll have available.

What spells are your wizard/cleric friends willing to spend to buff you up? Can any of them cast Greater Magic Weapon, for example? Or Keen Edge?

If both are available, go with Keen. Keen Edge only lasts 10min/level.

 

[Thanee]

+1 to hit increases your average damage per attack by 5% x your average damage per hit (unless you hit with a roll of 2+ or need to roll higher than 20 (in theory) to hit).
+1 damage increases your average damage per attack by 1 x your chance to hit.

Keen increases your average damage per attack by 10% x your chance to hit x your average damage without bonus dice per hit (if you hit with a roll of 17+).

Your chance to hit is (attack bonus + 21 - AC) x 5% (min 5%, max 95%).
Your average damage per hit is 17.5 (1H) or 19.5 (2H).
Your average damage without bonus dice per hit is 10.5 (1H) or 12.5 (2H).

Bye
Thanee

 

[Feldspar]

The numbers favor the +1. This makes sense as a fair chunk of your damage is coming from a non-crit multiplied source, the holy 2d6 damage.

h/r is hits per round, c/r is crits per round, d/r is damage per round.

+2 Holy Bastard Sword one-handed       ab=14 1d10+7 + 2d6 19x2
   ac=27  h/r=0.55 c/r=0.0550 d/r=11.41
   ac=26  h/r=0.65 c/r=0.0650 d/r=13.49
   ac=25  h/r=0.75 c/r=0.0750 d/r=15.56
   ac=24  h/r=0.85 c/r=0.0850 d/r=17.64
   ac=23  h/r=0.95 c/r=0.0950 d/r=19.71
   ac=22  h/r=1.05 c/r=0.1050 d/r=21.79
   ac=21  h/r=1.15 c/r=0.1150 d/r=23.86
   ac=20  h/r=1.25 c/r=0.1250 d/r=25.94
   ac=19  h/r=1.35 c/r=0.1350 d/r=28.01
   ac=18  h/r=1.45 c/r=0.1450 d/r=30.09

+1 Keen Holy Bastard Sword one-handed  ab=13 1d10+6 + 2d6 17x2
   ac=27  h/r=0.45 c/r=0.0800 d/r= 9.24
   ac=26  h/r=0.55 c/r=0.1025 d/r=11.35
   ac=25  h/r=0.65 c/r=0.1300 d/r=13.52
   ac=24  h/r=0.75 c/r=0.1500 d/r=15.60
   ac=23  h/r=0.85 c/r=0.1700 d/r=17.68
   ac=22  h/r=0.95 c/r=0.1900 d/r=19.76
   ac=21  h/r=1.05 c/r=0.2100 d/r=21.84
   ac=20  h/r=1.15 c/r=0.2300 d/r=23.92
   ac=19  h/r=1.25 c/r=0.2500 d/r=26.00
   ac=18  h/r=1.35 c/r=0.2700 d/r=28.08

+2 Holy Bastard Sword two-handed       ab=14 1d10+9 + 2d6 19x2 2hands
   ac=27  h/r=0.55 c/r=0.0550 d/r=12.62
   ac=26  h/r=0.65 c/r=0.0650 d/r=14.92
   ac=25  h/r=0.75 c/r=0.0750 d/r=17.21
   ac=24  h/r=0.85 c/r=0.0850 d/r=19.51
   ac=23  h/r=0.95 c/r=0.0950 d/r=21.80
   ac=22  h/r=1.05 c/r=0.1050 d/r=24.10
   ac=21  h/r=1.15 c/r=0.1150 d/r=26.39
   ac=20  h/r=1.25 c/r=0.1250 d/r=28.69
   ac=19  h/r=1.35 c/r=0.1350 d/r=30.98
   ac=18  h/r=1.45 c/r=0.1450 d/r=33.28

+1 Keen Holy Bastard Sword two-handed  ab=13 1d10+8 + 2d6 17x2 2hands
   ac=27  h/r=0.45 c/r=0.0800 d/r=10.31
   ac=26  h/r=0.55 c/r=0.1025 d/r=12.66
   ac=25  h/r=0.65 c/r=0.1300 d/r=15.08
   ac=24  h/r=0.75 c/r=0.1500 d/r=17.40
   ac=23  h/r=0.85 c/r=0.1700 d/r=19.72
   ac=22  h/r=0.95 c/r=0.1900 d/r=22.04
   ac=21  h/r=1.05 c/r=0.2100 d/r=24.36
   ac=20  h/r=1.15 c/r=0.2300 d/r=26.68
   ac=19  h/r=1.25 c/r=0.2500 d/r=29.00
   ac=18  h/r=1.35 c/r=0.2700 d/r=31.32

 

[Infiniti2000]

The numbers have already been presented, so let me just throw my support into getting the +1 enhancement bonus, not keen. If the numbers don't sway you, you certainly don't want your +4 equivalent weapon sundered easily. The higher enhancement bonus greatly helps in that regard (+2 hardness, +10 hp), possibly saving your weapon from total destruction.

 

[Tatsukun]

OK thanks guys, that was actually my gut feeling, but I couldn't trust myself.

Again the crew at Enworld save the day!

For the record, there is no cleric in the group, there is a favored soul, but he doesn't buff people (grumpy Dwarf).

The long term goals of our group involve traveling to an Evil Outer Plane, so I'll go with +2 Holy, then next time I imporve it, it'll be +2 Holy Evil Outsider bane

Thanks again !

-Tatsu

 

[Thanee]

Magebane would probably be a good choice, if you often fight evil outsiders.

Bye
Thanee