Stonethrowers are this overpowered in 3rd edition WFB

The balance, or lack there of, of stone throwers appears to be a perennial topic amongst Oldhammerers. Or at least Oldhammerers who've just played a game involving one.

I pondered some house rules a while ago specifically to tone down their ridiculously accurate indirect fire option, and to make them less of a character killer, but after my recent game which my stone thrower basically won for me I thought I'd take a more fundamental look.

I based this on the fact that a comparable stone thrower and bolt thrower (e.g. 3-man) have the same points cost, and very similar limitations (i.e. you can't move and fire, turning in place counts as a move, 90 degree firing arc) but very different effectiveness. And looking at the rules it's easy to see why this is -

1. Bolt throwers shoot with a ballistic skill of 3, so hit normal troops at under half range 50% of the time, over half range 33% of the time. Stone throwers will hit 40% of the time (not allowing for deviations which still hit)
2. Bolt throwers can cause a maximum number of kills equal to the depth of the unit it hits. Stone throwers can kill anything their template can cover - probably 8 or more figures
3. Bolt throwers only cause hits up to the point they fail to wound - so if your first target survives, everyone behind him is fine too. And subsequent hits are at -1 strength cumulatively (so -2 for the third target, etc.). Stone throwers attempt to wound all their targets independently, and all at full strength

Point 2 is fairly significant, but point 3 is the real clincher.

Against this stonethrowers have two drawbacks, due to the way in which they fire:

1. They have a minimum range
2. They may deviate, and so may hit your own troops as a result - although realistically they're equally if not more likely to hit another enemy unit rather than your own unit

So on the face of things stone throwers are more fearsome, but how much more? I coded up a couple of simulations to find out. Both used the same basic assumptions:

1. A 20-strong unit of humans (the "standard" WFB creature) equipped with light armour and a shield (purely for the movement factor - it won't help them if they're hit by a war machine!) march towards a war machine 30 inches away
2. The unit is deployed in a wide (10 column) formation, about the most sensible configuration for marching against a war machine
3. The attackers move first

I ran the simulation 1,000 times, and looked at the number of attackers still standing at the point they make contact with the war machine.

When attacking a bolt thrower, things don't look too bad -

The mean and median casualties are both 3, the mode is 2. For marching straight at a war machine you'd have to say they got away fairly lightly.

Not so against a stone thrower -

Here the mean casualties is 8 and the median 7, but the mode is zero. 17% of the time the unit makes contact unscathed, but far more likely is that it takes significant casualties or even is practically wiped out. The simulation doesn't allow for routing - in fact that's not even necessary for the bolt thrower scenario, as it simply can't do enough damage in a single round - but it's a fairly likely outcome against the stone thrower.

My grasp of statistics isn't strong enough to put a figure on how much more effective the stone thrower is than the bolt thrower, but for now let's say that the stone thrower is over twice as effective. So if they need toning down, what might be a good way to do that? I've heard a couple of suggestions -

1. Allow all stone thrower casualties a 50-50 "dodge" save
2. Have stone throwers always deviate (say 2d6 - 2 inches)

Allowing the dodge evens things out a lot -

The mean and median casualties are now 4, and the mode is again zero. 19% of the time the unit survives unscathed, and there's still a lot of variation but it seems to me a lot closer to the level of damage that the bolt thrower does.

Having the stone thrower always deviate seems to rather neuter it -

The mode is still to have zero casualties but the median is now to have one and the mean to have two casualties thanks to the long tail.

This makes me fairly keen on the 50-50 "dodge" save - the variability is still there, but given the comparible points value of stone and bolt throwers then this seems a lot closer to the right outcome. Personally I'd give that dodge just to those in outside ranks, but given the formation in my simulation that makes no difference. To me though if a tightly-packed unit is hit in the centre by a big stone then there's nowhere to dodge to!

In a way the "always deviate" house rule seems to make a lot of sense - the indirect fire of a stone thrower shouldn't really have a place on a skirmish-sized battlefield, it would be more suited to siege warfare or on a BOYL-style table of all the stuff. Stone throwers have a clear anti-personnel role in early versions of Warhammer though, so for me that's another reason not to go down that route.

I'll be looking to try this out in games in future, it'd be good to hear what others think!