Monday, August 22, 2011

4ED: Best weapon for Crit Monster builds

One of my gamers loves Big Crits. I have done analysis on a few crit-focused weapons on his behalf, and I'll log my comparisons here. A couple notes before jumping into mathiness:
  1. As a damage-lover who loves his [W]s, Mike would laugh at a low-die weapon like a d4 or d6. He uses a d12, so I won't even bother with anything smaller. (Or anything larger.)
  2. Our current campaign is high-paragon at level 17; while I recognize the dynamic changes at lower levels I will not calculate those levels.
(For those not in the know, in 4ED when you roll a "natural 20" you score a crit; a Critical Hit. Crits are special because in addition to maximizing your normal damage, you also roll additional damage.)

Mike's choice: Vicious.
A Vicious weapon adds 1d12 per enhancement bonus instead of the standard 1d6. This raises the average damage by 3 per bonus (1d12 average roll is 6.5, versus 1d6 average roll is 3.5.)

Vicious vs. Supremely Vicious: WINNER: Vicious.
VW adds 1d12 per plus. Avg damage 6.5 per die. (domain of results is 1,2,3,4,5,6,7,8,9,10,11,12 = 12 numbers, sum 78, avg 6.5)
SVW adds 1d8 and lets you reroll once. Presumably you'd reroll 1,2,3,4. That means your domain of results is 5,6,7,8,1,2,3,4,5,6,7,8 = 12 numbers, sum 62. avg 5.1666
All other things being equal, VW > SVW. You average about 1.3 more damage per plus.

Vicious vs. Great Hunger: WINNER: Vicious.
When you score a critical hit using this weapon, the damage of the next critical hit you score with this weapon scores increases by 1[W]. This effect is cumulative until the end of the encounter.

Forgive this horrible, horrible chart, but this analysis shows the comparison at each bonus. While Great Hunger is superior at lower levels, it's harder to generate crits as reliably, so even in that case Vicious may be a better choice.
Weapon bonus Crit Number Lost d12 v d8 Added W dmg Difference Slope
1 1 2 0 -2 n/a
1 2 4 6.5 2.5 4.5
1 3 6 13 7 4.5
1 4 8 19.5 11.5 4.5
2 1 4 0 -4 n/a
2 2 8 6.5 -1.5 2.5
2 3 12 13 1 2.5
2 4 16 19.5 3.5 2.5
3 1 6 0 -6 n/a
3 2 12 6.5 -5.5 0.5
3 3 18 13 -5 0.5
3 4 24 19.5 -4.5 0.5
4 1 8 0 -8 n/a
4 2 16 6.5 -9.5 -1.5
4 3 24 13 -11 -1.5
4 4 32 19.5 -12.5 -1.5
5 1 10 0 -10 n/a
5 2 20 6.5 -13.5 -3.5
5 3 30 13 -17 -3.5
5 4 40 19.5 -20.5 -3.5
6 1 12 0 -12 n/a
6 2 24 6.5 -17.5 -5.5
6 3 36 13 -23 -5.5
6 4 48 19.5 -28.5 -5.5