Aethervoid Pendulum or Quicksilver Swords?

Aethervoid Pendulum or Quicksilver Swords?

Another statistical note. Which is better… the Aethervoid Pendulum or the Quicksilver Swords? Both are endless spells that cause damage after moving. Both cast on a 6, move 8" and can fly. The pendulum has a range of 8", but can only move in a straight line; the swords have a range of 6" but can move how they like.

The key rules are

After this endless spell has moved, roll a dice for each unit that has any models that it passed across, and each other unit that is within 1" of it at the end of its move. On a 2+, that unit suffers D6 mortal wounds.
After this endless spell has moved, you can pick 1 unit that has any models it passed across and roll 12 dice. For each 5+, that unit suffers 1 mortal wound. In addition, mortal wounds caused by this ability cannot be negated.

So the pendulum has a ⅚ change of doing d6 damage to a small number of units; the swords can do up to 12 damage to 1 unit - but that damage can't be negated, so no wards or bodyguard rolls

So how much damage should be expected?

The graph above shows the probability of causing at least a given number of wounds to one unit affected by each of the endless spells. These values are before wards are applied. In all cases, the swords do better - though even with the swords, the probability of causing 9 wounds or more is so small (0.003) it looks like a 0 on the graph.

Of note, the swords have about a ⅓ chance of taking out a 5 wound hero in one go, regardless of wards; and a slightly better than ⅙ chance of taking out a 6 wound hero.

The graph above shows the probabilities of doing exact amount of damage. Unsurprisingly the pendulum distribution is almost flat, the swords have a peak at 4 wounds, a maximum at 12, and are slightly right skew.

The expected damage is 4 from the swords and 2.9 from the pendulum. The pendulum though might do those expected 2.9 wounds to more than one target - the swords will only ever hit once a hero phase. However, the pendulum damage might be reduced by wards, but the sword damage will not.

So if the purpose of the spell is to target a single unit, take the swords. If you're hoping to hit multiple units, consider the pendulum.