Stonethrowers always deviate - some further thoughts

A while back I started thinking about why having stone throwers always deviate made them so ineffective. It occurred to me that both the problem and the answer lie in the 2d6 bell curve.

Using my model (with a 20-strong unit arranged in two ranks of 10) the unit was hit only in the shaded part of the curve: always on a 2 (2d6 - 2 remember in the "always deviates" model, so no deviation) and a 3 (1" deviation of a 1" template, not covering the maximum models but still hitting some); and less likely on a 4, 5 or 6 (4 inches of deviation, so a roll of 6, only hit the unit when the deviation is along the axis of the unit, i.e. 2 times out of 12).

By increasing the modifier, and so moving the hits into the taller part of the bell curve, the stone thrower becomes progressively more effective.

And it turns out that at 2d6 - 3, it's similar in effectiveness to the 50-50 "dodge" save:

This gives a median of three casualties and a mean of four, although with the mode at zero. So fairly close to the dodge option, and to a bolt thrower.

The only down-side to this is that the maximum deviation is now 9 inches, so the likelihood of the truly comical mis-fire is reduced.

My hope though is that this gives stone throwers a distinct niche without the worry of them being over-powered. They will be highly variable, and very effective when they don't deviate by much (and hence might seem over-powered in individual games) but in the long run not reliably good. So quite good orc-y weapons, and seemingly worth trying in a game or two!