Multiple damage methods in Alpha Strike

[pixelgeek]

I was curious about the impact about the optional rules for damage allocation in the AS Commander's Edition so I wrote some code to test them out

https://zacgaming.wordpress.com/2020/11/16/alpha-strike-multiple-damage/

I will definitely not be using the Multiple Damage method any longer

[Descronan]

Nice analysis! 

My regular players use 1d12 for the multiple hit method. We know it skews the probability curve, but its faster than rolling 2d6 for each point.

[Elmoth]

The point of multiple to hit rolls is a reduction in variance. You achieve the same result rolling 1000 times, but since games are much shorter (40-80 rolls most of the time) such variances are much more noticeable. This is why multiple to hit is popular, I guess. Also, because we as players hate when our Atlas does no damage at all so yeah. Great anlysis. I have never used multiple damage but it looks like it was an (unknown) good decision on my group's part! Thanks for sharing!

[Insaniac99]

Nice clean write-up. I always prefered multiple-to-hit-rolls to standard single hit, but I was surprised to see the multiple damage results in a higher damage with bad to hit numbers.

I would have guessed, without further examination, that the difference between standard and multiple damage over enough tests would be

Code: [Select]

Standard = %Hit(DMG)
Multiple damage = %Hit(DMG*0.8)
Maybe I don't understand the Multiple damage as I'm still not sure why it is higher.  If the number of chances to hit doesn't increase, then it's only a reduction on successful hits.

  For example in a million chances, 12 on a 2d6 has a 1/36 chance of occuring, this means out of a million shots, you should hit roughly 27,778 of them.  The multiple damage rolls, as I understand it, shouldn't change that fact, it is just a step after the hit where it essentially applies the 20% damage reduction you mention.  The minimum of 1 only matters on the second, half, correct?

I should probably grab my rule book and look at the exact wording later.

[nckestrel]

A single attack roll needing a 12+ will hit 2.78% of the time, for 4 damage.  4* 0.278 = .1112 damage per attack.
A single attack roll needing a 12+ will still hit 2.78% of the time, for 1 damage. 1 * 0.278 = .0278 damage per attack.  * 4 attacks = .1112 damage per four attacks.
I'm not sure where you are getting different damages from those two methods from?

The difference isn't in the average, but the distribution.  A single, 4 damage attack will do no damage 97.22% of the time, and 4 damage 2.78% of the time. It's all or nothing.
Four, 1 damage attacks will do 4 damage, 2.78% * 2.78% * 2.78% * 2.78% = .0000597% of the time.  However, it will do at least 1 damage, 2.78% + (97.22*2.78%= 2.703%) + (97.3*0.278%=2.705%) +... ~ 10% of the time.
The average is the same, but the distribution is much wider.

[Insaniac99]

A single attack roll needing a 12+ will hit 2.78% of the time, for 4 damage.  4* 0.278 = .1112 damage per attack.
A single attack roll needing a 12+ will still hit 2.78% of the time, for 1 damage. 1 * 0.278 = .0278 damage per attack.  * 4 attacks = .1112 damage per four attacks.
I'm not sure where you are getting different damages from those two methods from?

The difference isn't in the average, but the distribution.  A single, 4 damage attack will do no damage 97.22% of the time, and 4 damage 2.78% of the time. It's all or nothing.
Four, 1 damage attacks will do 4 damage, 2.78% * 2.78% * 2.78% * 2.78% = .0000597% of the time.  However, it will do at least 1 damage, 2.78% + (97.22*2.78%= 2.703%) + (97.3*0.278%=2.705%) +... ~ 10% of the time.
The average is the same, but the distribution is much wider.

I would guess the differences between standard and multiple attacks rolls is just from the relatively low test count and the variance in most basic (i.e. not cryptographically secure) random number generators combined with some rounding in Excel.

Its the multiple damage rolls I don't understand personally.

[nckestrel]

I would guess the differences between standard and multiple attacks rolls is just from the relatively low test count and the variance in most basic (i.e. not cryptographically secure) random number generators combined with some rounding in Excel.

Its the multiple damage rolls I don't understand personally.

My guess is that he added the minimum 1 to the results regardless of hit chance.  But it only has a minimum of 1 damage, if the attack hits. 
3+ means 2 chances out of 6 do no damage, .67 chance per damage roll.
Four damage rolls, with minimum 1 damage, (67% * 1) + (67% * 1) + (67% * 1) + (67% * 1) + (33%*33%*33%*33%*1) =.67 + .67 + .67 + .67 + .01 = 2.69 average   That last bit is the chance the minimum 1 comes up, if all four damage rolls were no damage.  2.69 average damage * 2.78% hit chance = .0747 damage per attack?

[pixelgeek]

Its the multiple damage rolls I don't understand personally.

I am going to go back and verify the data but there are two factors at work. The 3+ required per damage point removes damage where it is easy to hit. The minimum damage adds it back where the chance to hit it low. So the two factors work to skew the data.

My guess is that he added the minimum 1 to the results regardless of hit chance. 

It was only added when no damage was rolled for an attack. I believe  that comes into play regardless of the odds though

[pixelgeek]

And just to be clear, I am writing code the rolls virtual dice. I have no statistical knowledge so I am sure there may be a more elegant way to do this :-)

[Joel47]

Any chance we could see the code for the "multiple damage" column? That result doesn't look right to me, either.

Edit:
The average damage should work out to be the chance to hit times the expected damage. For the "standard" non-variable, the expected damage is a constant 4; for variable damage it's still a constant (albeit a fractional one) because the expected damage won't change with the to-hit number.. We are essentially rolling 4 dice; if all 4 are 1s and 2s, we deal 1 damage; otherwise we deal the rolled damage. So 4*(2/3)+(1/3)^4 = 2.68. (And if someone whose last stats class wasn't 25 years ago wants to check my work, I'd appreciate it.)

[Dissolv]

We use the Variable damage method, but without the minimum.  This has two effects:

1) On average you do a flat 1/3rd less damage, which slows the game game a bit. 
2) The damage is now coming in unpredictable lots, so accounting for the variance, as well as some guts :-) is now required to do any significant table top maneuver. 

For the article, fine work, but....
Something does look off about the numbers.  Over the long run either system should result in the same net damage, with the big question being "do you prefer big bursts of occasional lucky damage, or small consistent lots of lucky damage?"   I would suggest looking up some statistics.  The math isn't hard, and is more reliable than a sample set generated programmatically, or by gamers. 

[LegoMech]

This is a super interesting discussion and I am eagerly following it to see which method I should be using...