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.