Please let me know if I screwed up my math somewhere. I'm happy to correct it. Let's Mathhammer!!
In melee the soulreach grasp causes a save 52% of the time with unholy vigour.
(p(Hit) + p(roll 1)*p(Hit)) * p(Wound)
= (4/6 + 1/6 * 4/6) * 4/6 = .518518...
In the best scenario (no save, unholy vigour), this gives an average wounds per round of
p(cause save) * average damage per hit
= .518* 2 = 1.036 wounds.
In shooting, the grasp doesn't get rerolls. It also happens about half the time.
p(hit)*p(wound) * average damage / 2 = .4444
Total wounds = 1.036 + .44 = 1.476
Additionally you lose it's benefit of versitility in combat as you can only shoot what is in melee with you.
The attacks get worse against ignore rend or many low save models. They get better with more attacks (from KoS command ability).
On the other hand we have the Reaper Scythe
(p(hit) - p(rolling 6)) = p(normal hit)
= 3/6 - 1/6 = 2/6
p(normal hit) + p(roll 1)*p(normal hit) = p(normal hit with rerolls)
= 2/6 + 1/6 * 2/6 = .38889
p(normal hit with rerolls) * p(wound) = p(cause a save)
= .38889 * 4/6 * 3= .259259
Average damage by saves
p(cause a save) * p(fail save -1 rend) * # of attacks * damage per attack
2+: .2593 * 2/6 *3 *2 = .5185
3+: .2593 * 3/6 * 3 = .7778
4+: .2593 * 4/6 * 3 = 1.037
5+ .2593 * 5/6 * 3 = 1.2963
6+ .2593 * 6/6 * 3 = 1.5556
Reaping Scythe will also cause mortals on a hit of six so let's calculate that and add it in.
p(roll 6) + p(roll 1) * p(roll 6) = p(frightful touch)
= 1/6 + 1/6 * 1/6 = .1944
p(frightful touch) * # attacks * damage = average mortal wounds
= .1944 * 3 * 2 = 1.166
TL;DR
The scythe will have higher average damage against all saves thanks to mortal wounds. Since there are more attacks and static damage. The variance is going to be less -- this attack should be more reliable and higher damage.
Soulreach grasp is good against high save targets, but worse damage overall. It also benefits more from extra attack buffs. The attack is more versitile in target selection. However, some of the damage comes from shooting with doesn't happen every combat. It is also prone to common shooting debuffs. Lastly, it doesn't work when the coach runs.
I'm going to run the Scythe in most cases, since it will probably cause more damage. If you like the freedom to choose backline tagets, take the grasp.
