Wednesday, 29 May 2013

Warhammer Mythbusters: Daemon Prince Versus OnG Gunline

Hello Everyone, recently I was accused of being a hobby wrecker on the wargamerau forums for having the audacity to take not one but two Doom Divers as "Doom Diver's don't miss" and "2 means a priority target down turn 1." Now the thing is I don't think either of these are true and because I fancy myself a bit of a mathematician I thought I'd run the numbers with a bit of Mathhammer. I know it's not to everyone's taste, but it's handy to know the odds when you're pushing your toys around.

Are these fellas breaking Warhammer?


The Scenario: 2 Doom Divers vs. a WoC Daemon Prince (50x50 base) with a 1+/5++ and a charmed shield.

Myth #1: A Doom Diver Doesn't Miss!

Doom Divers are notoriously accurate due to their ability to veer back onto target, but at the end of the day what is the actual percentage chance to hit a Daemon Prince?

To start with you have a 1/6 chance to misfire and for the sake of simplicity I am going to assume that the DP is in a position such that it would not be hit by a Skidmarks or Out of Control result on the misfire table.

Thus the odds of hitting off of the scatter dice alone are: 1/3*5/6 = 27.8%

Hmm not too good, but of course the Doom Diver can scatter.

If it scatters 2" it is then 0.25" away from the base (a DD base is 0.75" in radius) and thus a veer result of 1, 2 or 3 will take it back on target. The odds of this occurring are: 1/6*1/2 = 8.3%

If it scatters 4" it is then 2.25" away from the base and thus a veer result of 3,4 or 5 will take it back on target. The odds of this occuring are: 1/6*1/2 = 8.3%

If it scatters 6" it is then 4.25" away from the from the base and thus a veer result of 5 or 6 will take it back on target. The odds of this occuring are 1/6*1/3=5.6%

If it scatters 8" or 10" it can't make it back onto the target.

Thus the probability of a Doom Diver comes in at: 27.8+8.3+8.3+5.6 = 50%

Hitting a Daemon Prince thus is only a 50/50 chance even for a doom diver. This is still less than a Cannon which has a 66% chance to do the same by firing 10" from the back of the base. That's just against a single 50x50mm base. If you're targetting the centre of 45 Halberdiers (why would you) the odds of a hit will get close to 83%. But we're talking priority targets and they tend to be small, and linear (knights etc.)

Verdict: Myth Busted! Doom Divers are significantly more accurate than stone-throwers, but they aren't cannons either. The odds of your general or single model copping a hit are 50/50 at worst and better if he's on a smaller base.

Myth #2: Two means Priority Target down Turn 1!

The other nasty trick Doom Divers pull is ignoring armour saves, leaving the poor Daemon Prince with just a 5++ to keep him safe. Let's see what damage two Doom Divers are likely to do given they hit.

First off we can expect to generate 7 hits on the DP (most likely rolling 2 dice). There is a 5/6 chance that one of the hits gets bounced by the charmed shield so we end up with 6.16 hits.

A Doom Diver is S5 while a DP is T5, so you can expect 3.08 wounds, already less than the DP's 4 wounds. He's got his 5++ ward so ends up taking 3.08*2/3 =  2.05 wounds inflicted!

Verdict: Myth Busted! Even if both Doom Divers hit they're only likely to do 2.05 wounds, not enough to kill the beast. You can move this up slightly by getting some BS shooting onto the guy to use his Charmed Shield. Of note is that a Rock Lobber given it hits does 1.94 wounds on average but of course they only hit 27.8% of the time (direct line of sight).

So What? WoC Generals take heart, on average an OnG gunline with double Doom Diver and Rock Lobba will only manage 2.2 wounds a turn on your DP (I haven't accounted for the misfire chart which brings this down slightly.) What does this mean? 2 turns will kill your DP the majority of the time so you need to get into combat quick. If you're there on T1 you should be fine, and by staying out of LoS of the Rock Lobbas you can buy another turn of safety. This may sound daunting, but the other 1900 points of your army is not even copping a scratch.

I hope that you enjoyed this article. I know that math-hammer isn't to everyone's liking and I agree that having an opponent working his abacus as you try to play a game is irritating. However I feel that a good knowledge of the probabilities involved in the game is key to good rational decision-making. My caveat though is it is a dice game and these are only probabilities, on the day anything can happen so don't come crying to me.

I enjoy running the numbers on these sorts of things, so if there's anything you want me to have a go at let me know and I'll do it up.

Cheers. Jeff


10 comments:

  1. I think the 66% probabilty for the cannon is too high.
    10" from the back being just hit means that 8" will just fall short if you assume a 2" base.
    A 50mm base is also just short of 2".
    So you have 6/36 misfire chance + 2,M; 2,2;, 2,4; 2,6 all misssing plus other combos up to 8.
    = 55% chance of hitting

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    1. I've used that an 8" hits (taken from Bugman's Brewery, I figured Dwarves would have Cannons down pat). If you take it that an 8" doesn't hit you're correct.

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    2. I don't know I'm a NOOB with dwarfs and haven't looked at Bugmans site.
      But, it sounds to me that they want their cake and eat it.
      If 10" hits the back, then 8" must fall just in front and miss.
      If 8" hits the front than 10" will shoot just past.

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    3. If the base is on a slight angle it will hit as the distance (in this case the width of the base)increases with the degree of angle if going in a straight line (point A to B) across an object (a square base).

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    4. I was just going to post that, as that what occurred to me driving to work and not concentrating.
      So yes most of the time 8" and 10" would hit

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    5. I imagine they've looked at it as if it were mapped onto a Cartesian plane. In that case the x coordinates would be [8,10] and thus if the bounce belongs to [8,inf) would intersect that set. Realistically, a 50mmx50mm base is not exactly that(nothing is), but I suppose it's easier to assume it is. Pardon my sloppy notation, I'm an applied maths major.

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  2. Great article. I dont understand the people who dismiss mathhammer, its a game of chance with every aspect involving math...

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