Mathhammer - 1K Sons VS the lackeys of the corpse emperor

[UsernameTaken]

Come forth, brother and sisters, and let us unite our psychic might to dominate our foes with our occult mastery of algebra!

 

The goal of this topic is to enable you to benefit from and contribute to this excel sheet, in order to determine the optimal loadouts to spill the blood of those who seek to oppose us. It shows the average number of dead models after shooting at them once from a given weapon available to us.

It is far from being complete (and probably full of mistakes), that's why your help is more than welcome!

 

The exact formula is: 

mean number of shots * chance to hit * chance to wound * chance to not save * min( mean weapon's damage, target's wounds) / target's wounds

 

I preemptively apoligize for any mistakes you might encounter, and for the ugly look of it, which comes from its uploading to google sheets.

Edited February 15, 2018 by UsernameTaken

[Kite Senet]

This seems interesting.

 

Should it be "mean damage" for weapons and "mean number of attacks" respectively in the formula here in your post? Otherwise I'm not sure how you'd deal with warpflamers or multi-damage weapons.

 

I've tried to do some mathhammer stuff before, but (as a mathematician) I tended to make the models I was using excessively complicated, trying to capture everything all at once, since I haven't played the game enough to know which simplifications were reasonable and which weren't. Is the formula here a fairly reasonable approximation of the game's actual dice flow? I would've thought that things like auras would cause pretty dramatic changes in these numbers.

 

(I was also not realizing that the dice could be modeled with Bernoulli random variables, and discrete uniform was totally overkill. But that's more than enough math-speak.)

[GreaterChickenofTzeentch]

Come forth, brother and sisters, and let us unite our psychic might to dominate our foes with our occult mastery of algebra!

 

The goal of this topic is to enable you to benefit from and contribute to this excel sheet, in order to determine the optimal loadouts to spill the blood of those who seek to oppose us. It shows the average number of dead models after shooting at them once from a given weapon available to us.

It is far from being complete (and probably full of mistakes), that's why your help is more than welcome!

 

The exact formula is: 

number of shots * chance to hit * chance to wound * chance to not save * min(weapon's damage, target's wounds) / target's wounds

 

I preemptively apoligize for any mistakes you might encounter, and for the ugly look of it, which comes from its uploading to google sheets.

 

How are Inferno Bolters measured in terms of number of shots? I assume this is at Rapid Fire range?

[UsernameTaken]

@greater chicken of tzeentch

bolters were in rapid fire indeed, i added a line for non rapid fire for clarity

 

@Kite senet

Well, my model is clearly at the other side of it: overly simplistic, it only gives what should be the expected value, which indeed might not be an accurate description of the reality for some cases: for exemple, for the contemptor, the kheres and the C-beam have a similar damage output, while one (c-beam) is much less consistent: random number of shots and damage, something that is not visible here.

 

Doing it this way sure has some flaws, but 40k is too complex to easily modelled: ideally when looking at the damage you should also consider the ammount of time during the game during which the weapon can fire, which is impacted by maximum range, durability of the carrier, etc... which are hard to include in a model (at least for me), and at some point you just have to make concessions.

 

Although, i agree that improvements could easily be made, for exemple by adding 1st quartile, median and 3rd quartile, and I welcome any idea you may have. On top of it, i still didn't have a solid course on probability, which means that my abilities in this domain are still limited to basic knowledge, so once again, feel free to bring any modifications you think are necessary.

 

As for the modifiers, the two hit ones are fairly easy with how excel works: just multiply the whole line by a factor, for rerolling ones to hit, * (1+1/6) should work, but for strength modifiers, i fear you'd have to redo the whole line

 

 

Fixes: 

• remembered terminators had a 5+ invuln made the necessary corrections
• added a line for non rapid-fire bolter
• added "mean" to the formula in the first post