Forum adverts like this one are shown to any user who is not logged in. Join us by filling out a tiny 3 field form and you will get your own, free, dakka user account which gives a good range of benefits to you: No adverts like this in the forums anymore. Times and dates in your local timezone. Full tracking of what you have read so you can skip to your first unread post, easily see what has changed since you last logged in, and easily see what is new at a glance. Email notifications for threads you want to watch closely. Being a part of the oldest wargaming community on the net. If you are already a member then feel free to login now.

I keep hearing people say that 3 dark lances and 2 void lances are "mathematically equivalent." I guess that means they have the same average(mean) result.

Which has the higher variance?

I might have the wrong term. What I really want to know is, which gets results more consistently?

Anyone feel like figuring it out?

Lol, they are not mathematically equivalent.
Against av 12, a dark lance pens on a 5+
Against av 12, a void lance pens on a 4+

This is what people are thinking:
So it's a 3 shots with a 1/3 chance of pen
vs.
2 shots with a 1/2 chance of pen.

People think they are equivalent because they are doing the failmath I posted about in the wraithlord and mathhammer threads.

Don't be a failmath.

Against AV 12-14

the 2x void lances average .167 glances and .5 penetrating hits.
The 3x Dark lances average .25 glances and .5 penetrating hits.


Against AV 11

VL: .167 Glancing, .667 Penetrating
DL: .25 Glancing, .75 penetrating


Against AV 10

VL: .167 glancing, .833 Penetrating
DL: .25 Glancing, 1 penetrating


The Dark Lances win, but only by a few glances against AV12-14, For the rest the Dark Lances win by more.

@scuddman The values you posted show both getting an equal amount of penetrating hits, which is true.

Let me try my hand at it real quick
Immobilized/Destroyed are desired results

Against Av 12 through 14
2 Void Lances = 2*(2/3)*((1/6)*(1/6)+(1/2)(1/2)) = .3703% chance of getting a desired result

3 Dark Lances = 3*(2/3)*((1/6)*(1/6)+(1/3)(1/2)) = .3888 % chance of getting a desired result

Av 11
2 Void Lances = 2*(2/3)*((1/6)*(1/6)+(2/3)(1/2)) = .4814% chance of getting a desired result

3 Dark Lances = 3*(2/3)*((1/6)*(1/6)+(1/2)(1/2)) = .5555 % chance of getting a desired result

Av 10
2 Void Lances = 2*(2/3)*((1/6)*(1/6)+(5/6)(1/2)) = .5926% chance of getting a desired result

3 Dark Lances = 3*(2/3)*((1/6)*(1/6)+(2/3)(1/2)) = .7222 % chance of getting a desired result

Setup is (Number of Shots)*(Chance to hit)*((Chance to Glance)*(Chance to do something)+(Chance to penetrate)*(Chance to do something))

So yes, Ravager is better. Not by excessive amounts when shooting at main targets, but better nonetheless.
Time will tell whether the void mine and missiles will prove worth it.

People think they are equivalent because they are doing the failmath I posted about in the wraithlord and mathhammer threads.

Don't be a failmath.

Ok, lets do math then for those that might not know how to make accurate calcs.

If you have a unit with several weapons and want to figure out its effectiveness to destroy a vehicle, it is better to avoid calculating average results. Reason being is that probability is weighted with the chance of multiple destroyed results, and you can only destroy a tank once.What you want is calculations of at least 1 destroyed result (and maybe more but against a single vehicle multiple results are meaningless). How do you do this? Easiest way is to figure out the chance of the unit NOT destroying its target, that then gives us an easy way to figure out that chance that it does destroy its target.

So with a ravager with 3 dark lances shooting AV12 what is the chance of 1 of its DL destroying the vehicle?

2/3 chance to hit X 1/3 chance to pen X 1/3 chance to destroy = 2/27.
We can easily see that a dark lance will fail to destroy the tank 25 out of 27 times, or another way to think of it is 1-(2/27).

Now what is the chance that all three DLs on a ravager will NOT destroy the AV12 tank?
(25/27) X (25/27) X (25/27) = (25/27)^3 = ~79.4% that it will NOT destroy it.
As done a step back, we can now easily find the chance of actually destroying the tank, as it is simply 1- the above result = 20.6%

You can combine what I did above into a simple fomula, one that is even easier to deal with on a spreadsheet like excel or open office

1-((1-P)^S) Where P is probability of one shoot succesuflly accomplishing the goal (destroyed, at least shaking, etc etc, on excel you'd just reference a cell that had this calculated out) and S is the number of shots the unit has with that probability.

So are 2 void lances equivilent to 3 dark lances, as far as anti-tank? Is one better? Lets look at the void lance and its two shots as far as at least 1 destroyed result
Void lance vs AV12
2/3 X 1/2 X 1/3 = 2/18 = 1/9.
2 shots so
1-((1-P)^S) = 1-((1-1/9)^2)= ~21.0%

Void bomber is just a hair better (~0.37%) at destroying AV12.

What was noted already is that the ravager is better at atleast damaging AV12
P of DL at least shaking = 2/3 hit X 1/2 glance/pen = 1/3
P of VL at least shaking = 2/3 hit X 2/3 glance/pen = 4/9

Ravager at least shaking = 1-((1-1/3)^3) = ~70.37%
Void Bomber at least shaking = 1-((1-4/9)^2) = ~69.14%
This time its the ravager that is a hair better, but a bit more significantly so.

All in all though, they are pretty equivilent in the scheme of things as far as AV12-AV14. Of course lower AV will change things (normally this favors more shots, feel free to try this on your own). Also consider things that ignore lance like monoliths or black templar (and who knows, perhaps grey knights and future codexes will include more weapons that ignore lance).

Thanks, guys. I know its "failmath" to say they're equivalent. That's why I asked.

The results were pretty much what I predicted (in my head): Ravager has more shots and is already pretty effective, so it's more likely to do something. Good to know they're so close as far as chance to destroy.

Irdiumstern wrote:@scuddman The values you posted show both getting an equal amount of penetrating hits, which is true.

Someone didn't read my reference to the other posts about the binomial theorem. The values I posted are what people naturally calculate, not realizing that math is wrong.