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I've thrown together a basic formula for working out the efficacy of Space Marine special and heavy weapons per point, below is a table of the results. I'm suprised at how high the Plasma Cannon for Tactical squads works out.

The formula is (((N*S)/A)*R)/(C)

N is number of shots (templates are assumed to have 4, blasts are assumed to have 3, rapid fire have 1.5)
S is strength of the weapon
A is the AP value
R is the range in inches
C is the cost in points including the marine holding the weapon

Obviously it's basic, I will hopefully think of ways of working in special rules like Rending and Gets Hot!! and a weighting adjuster for the LOTD special rules etc.

Comments and discussions on the value of any of this, or adjustments to the maths is welcome:

Melta weapons have "Melta". Plasma weapons have "Get's Hot!"

There isn't any way to work this in, is there?

Not to mention templates always hit.

What is represented by the Y axis?

Nightwatch wrote:Melta weapons have "Melta". Plasma weapons have "Get's Hot!"

There isn't any way to work this in, is there?

Not to mention templates always hit.

Templates and blast weapons have been designated a certain number of "shots" based on the number of models I think you will normally be able to hit with them, but it does need work.
I think for meltas I may have to do a separate formula for vehicles and try and intergrate the two together somehow, plasmas should be much easier to sort out.

Valkyrie wrote:What is represented by the Y axis?

The result from (((N*S)/A)*R)/(C) - See above

I think the result of your formula does not have any useful meaning. It doesn't tell me the efficacy of the weapon, because you don't state what the desired result is.

What the formula tells us is how well a weapon can kill well-armoured targets at long ranges. And yes, the plasma cannon can kill multiple very well-armoured targets at a long range.

There is no one number that will sum up the abilities of a weapon. Different weapons have different preferred targets.

Imo the best possible result is some formula that:
- takes into account how well the gun performs vs GEQ, MEQ, TEQ and TMC
- takes into account how well the gun performs vs armour 10, 12 and 14
- takes into account how much each of the above is played in your metagame
And even that formula is still only some kind of rough comparison because there's still stuff like range, cover, invulnerable saves, etc..

Shrubs wrote:I think the result of your formula does not have any useful meaning.

I agree. Mathhammer is only useful for vague, specific situations, but that's not how the game is played against intelligent opponents.

It's mostly for vacuum testing a unit against another. Nothing real about that.

S_P

As a huge proponent of mathhammer I have a couple big issues with your formula.

N: isn’t the number of shots, it’s the number of hits. Templates may have an average of 4 and blasts may have an average of 3, but rapid fire weapons actually have 1.667 at 12” and .667 at 24”, Assault 1’s (melta’s) actually have .667… heavy bolters would have 2, assault cannons would have 3.333.

S: strength of the weapon is in no way multiplicative by shots nor divisible by AP. S is a variable strictly relative to the toughness of the target. The vast majority of infantry models have a toughness of 3 or 4 so I’d change S to W (wounds) and treat the target as T 3.5.

W = ((S*.5) + (S* .667))/2

At least multiplying by N now fits against infantry targets but dividing by A certainly does not.

A: I’m not sure why you’d divide by AP at all. Against vehicles you either have AP or you don’t. Against infantry every AP above their save is irrelevant whether it’s 1 point above or 4 points above. AP is not inversely proportional to efficiency. I don’t even really have a suggestion for its incorporation into your formula.

R: range is multiplicative of efficiency but definitely NOT directly by a factor of inches. What’s more, an assault weapon with a 12” range technically has a range of 18” where a rapid fire weapon has a range of 24” at .666 hits and 18” at a range of 1.333 hits.

C: is fine.

Im gunna have to agree with Incarna on this one, good try but it seems to me that your equation is oversimplied to the point that the data is meaningless.

Im also going to throw this out there that you should remove range from your calculations alltogether as it doesnt have a easily measureable bearing on anything when comparing one weapon to another.

I sort of agree and can see why your dividing the sum of the number of shots and strength by the AP, its how I would have worked AP into the equation if I absolutly had to, but there are to many AP related variables in the game for it to meen much.

With that being said I would argue that you would get more information out of a chart composed of a (S*N)/C chart.

yes there is a problem.

namely that the Heavyflamer for Sternguard squads is practically zero.


i did math and a Sternguard squad with 2 flamers and 8 combi-flamers, asuming 4 hits each, will kill, not wound, KILL 20 orks. making the 2 flamers into heavy flamers netted 22 dead orks. efficiency isn't much above a regular flamer, but it is definitly worth the few pts extra, especially if the orks are 'Ard boyz.



plasma cannons are good, but not that good.

After all, plasma cannons are effected by cover saves.

yeah, flamers arn't.

Grey Templar wrote:
plasma cannons are good, but not that good.

Considering the formula completely neglects the scatter mechanic, the plasma cannon is FAR less efficient than represented.

it is interesting that all the Flamer weapons are the 4 lowest weapons, right infront of Melta guns.

Shrubs wrote:I think the result of your formula does not have any useful meaning. It doesn't tell me the efficacy of the weapon, because you don't state what the desired result is.

What the formula tells us is how well a weapon can kill well-armoured targets at long ranges. And yes, the plasma cannon can kill multiple very well-armoured targets at a long range.

There is no one number that will sum up the abilities of a weapon. Different weapons have different preferred targets.

Imo the best possible result is some formula that:
- takes into account how well the gun performs vs GEQ, MEQ, TEQ and TMC
- takes into account how well the gun performs vs armour 10, 12 and 14
- takes into account how much each of the above is played in your metagame
And even that formula is still only some kind of rough comparison because there's still stuff like range, cover, invulnerable saves, etc..

pretty much sums it up.

Sorry.

Grey Templar wrote:it is interesting that all the Flamer weapons are the 4 lowest weapons, right infront of Melta guns.

Also, the multi-melta is generally a very weak weapon on infantry unless it's deep striked. And if it's deep striked it can't fire the turn it landed... yet the multi-melta is considered stronger than practically every other choice.

Melissia wrote:

Shrubs wrote:I think the result of your formula does not have any useful meaning.

I agree. Mathhammer is only useful for vague, specific situations, but that's not how the game is played against intelligent opponents.

Vague, specific situations? How does that work?

Vague in the sense of "is this really applicable to anything that happens IRL?" Vague probably wasn't the right word, but eh.

Specific in the sense of "no cover, no other units, assume X range, assume standard deviation on random dice rolls"

yes, when i do mathhammer i always assume the actual results will be worse, but i play like the odds are average.

yes my dreadnought hits on a 2+, yes i get a reroll, but i always assume that i will roll 2 1s in a row. and it happens more often then probable.

And I roll sixes on number of shots on my Exorcists far more often than I probably should, as well. Which means my Exorcists are often dead after the first turn, to the exclusion of all of the rest of my army (which of coruse is part of hte point of taking Exorcists to begin with).

Here's a suggestion for how you might set up a better comparison...

Calculate the chance of unsaved wounds for every weapon versus Toughness 3 through 6 in cover and not cover and with versus different armor saves.

Then divide the chance for each thing by the points cost of the weapons.

Depict it in a series of tables, one for each toughness value with rows for values and columns for armor save (or columns for toughness and armor save for multi-chart.)

Then look for any weapons that really stand out against certain classes of target and against multiple classes of target.

If you want to do this quickly, use this mathammer spreadsheet I developed a while back to teach myself VBA.

Here's your formula:

=AVERAGE($I3:$R3) / Points
Where I-R is the unsaved wounds caused against varying armor and cover/invulnerable saves

The formula for I-R:
=IF($C2<=6,AVERAGE($E2:$H2),AVERAGE($E2:$H2)*5/6)
Where C2 is the AP value of the weapon, E-H is the number of wounds against a model with T3-T6
When you get to the ++ saves, remove the if statement and just use AVERAGE($E2:$H2)*5/6

NOTE: The 5/6 term is actually variable and dependent on the save required. 1/6 for 2+ (as you will only get 1 in 6 wounds), 2/6 for 3+, 3/6 for 4+, and so on. The C2<=6 term is also variable, this equates to the type of save on the model, 6 for 6+, 5 for 5+, and so on.

The formula for E-H is:
=(3+($B2-3))/6*($D2/2)
Where B is the strength of your weapon and D is the number of shots.

NOTE: Number of shots is being divided by 2 to account for the average marine hitting 50% of the time. For ease of use for flamer weapons, just double the number of hits you want to arbitrarily assign to a template weapon. Blast weapons leave as the number of models under the blast, the division by two accounts for scatter.

Throw that into excel, graph, win.

Only thing of yours it doesn't take into account is range, which is hard to quantify.

EDIT:
NOTE: You may not want to do a straight average, as things like a 2+ invulnerable save is given just as much weight as a 6+ armor save even though it is a LOT rarer.

EDIT 2:
What you have to do is have your strength value be B column, AP be C column, and shots be your D column. Also forgot that in the E-H formula, the term B2-3 is variable, the -3 is dependent on toughness. So -3 for T3, -4 for T4, etc.

Finally, this formula isn't perfect, as it doesn't take into account maxing at a 2+ to wound... but hey, I did this in like 10 minutes.

EDIT 3:
Blarg!! Updated E-H formula is:
=IF(($B2-3)>=3,(5/6)*($D2/2),(3+($B2-3))/6*($D2/2))
That fixes the not maxing on a 2+ to wound...

If want to go really nuts, you could weight the strength and toughness values by how common they are in each army. But that is rapidly getting into the realm of neat math that has almost no applicability to the actual tabletop.