Talos Wargear - Math Hammer

Long story short, someone is trying to convince me that Heat Lances are superior to Haywire Blasters on vehicles. I am like, super duper not convinced, because when I do the math it really doesn't look that way. Was hoping someone could check my math! (Also I didn't apply any obsessions or anything here - partly because I'm going to be using Prophets of Flesh, but also because it makes the math easier)

TLDR:

Haywire Blaster:
T7 3+ = 0.833D
T8 2+ = 0.722D
T8 3+/5++ = 0.749D

Heat Lance (18"):
T7 3+ = 0.5833D
T8 2+ = 0.5833D
T8 3+/5++ = 0.3889D

Heat Lance (9"):
T7 3+ = 0.745D
T8 2+ = 0.745D
T8 3+/5++ = 0.4967D



HWB:
Against T7 3+ = 0.833D/per gun
(2)(1/2Hit)(1/3Wound)(1/2Save)(1D)=0.1666D
(2)(1/2Hit)(1/3 - 4,5)(1MW)=0.333D
(2)(1/2Hit)(1/6 - 6)(2MW)=0.333D

Against T8 2+ = 0.722D/per gun
(2)(1/2Hit)(1/6Wound)(1/3Save)(1D)=0.0555D
(2)(1/2Hit)(1/3 - 4,5)(1MW)=0.333D
(2)(1/2Hit)(1/6 - 6)(2MW)=0.333D

Against T8 3+/5++ = 0.7499/per gun
(2)(1/2Hit)(1/6Wound)(1/2Save)(1D)=0.0833D
(2)(1/2Hit)(1/3 - 4,5)(1MW)=0.333D
(2)(1/2Hit)(1/6 - 6)(2MW)=0.333D

Heatlance (18"):

Against T7 3+ =
(1)(1/2Hit)(1/3Wound)(3.5D) = 0.5833D

Against T8 2+ =
(1)(1/2Hit)(1/3Wound)(3.5D) = 0.5833D

Against T8 3+/5++ =
(1)(1/2Hit)(1/3Wound)(2/3Save)(3.5D) = 0.3889D

Heatlance (9"):
Most difficult part of this calculation is average damage on heat lance. In Melta Range you roll 2 dice and pick the highest. Here's how I did it:

Av. Damage = (Probability of Rolling N, two dice)(Damage)
Av. Damage = (1/36)(1) + (3/36)(2) + (5/36)(3) + (7/36)(4) + (9/36)(5) + (11/36)(6)
Av. Damage = 4.4722D

Against T7 3+ = 0.745D
(1)(1/2Hit)(1/3Wound)(4.4722D) = 0.745D

Against T8 2+ = 0.745D
(1)(1/2Hit)(1/3Wound)(4.4722D) = 0.745D

Against T8 3+/5++=0.4967D
(1)(1/2Hit)(1/3Wound)(2/3Save)(4.4722D) = 0.4967D

Your math looks good, but there are 2 heat lances on the talos. Your numbers are only running 1.

As for the average damage roll while in Melta range, I would just use a number like 4.5 (which you came to independently, lol).

Another factor that you may want to incorperate is the cost of the platform. In this scenario both weapon options cost the same, but generally you want to normalize the damage per 100 pts (or another similar metric).

Overall, "A" for effort. An "A+" would have required a graph with the normalized values

Thats my $0.02

fisheyes wrote:

Your math looks good, but there are 2 heat lances on the talos. Your numbers are only running 1.

As for the average damage roll while in Melta range, I would just use a number like 4.5 (which you came to independently, lol).

Another factor that you may want to incorperate is the cost of the platform. In this scenario both weapon options cost the same, but generally you want to normalize the damage per 100 pts (or another similar metric).

Overall, "A" for effort. An "A+" would have required a graph with the normalized values

Thats my $0.02

There are also two Haywire Blasters on the Talos! These numbers just run a single HWB as well (it just has higher rate of fire).

Hmmm, you've piqued my interest, I'll try figuring that out (I like math )

Part of me thinks that our codex seems to be confused between Heat Lance/HaywireBlaster/Blaster. On a unit like Reavers where the only two options are Heat Lance or Blaster, and it has the mobility to routinely get into Melta range (whether you want to do that is a different question), the pricing makes sense. On units like Scourge/Talos, that have the option for all three, I don't really see circumstances arising that would warrant the Heat Lance over the HWB or Blaster.

Thanks for checking the math

Riiiiight. D3 shots per HWB, my bad.

Thats what I get for eating lunch with one hand, and typing with the other.

Dont forget that the Blaster is 15 pts, vs 10 pts for the HWB/Heat Lance. That is why we normalize the results

Of course, the normalized values mean less once you consider a taloi costs around 105 pts, so plus/minus 10% isnt that big a deal. But if your going to nerd out, you may as well DO IT RIGHT!

fisheyes wrote:

.....
But if your going to nerd out, you may as well DO IT RIGHT!

Oh yes, this is what triggered me into going into Nerd Mode.
As I'm prepping for teaching Math in 7th and 8th grade I thought I might refresh some of my math. Even though it isn't really covered in these grades, it's a good excuse to take a good look at the math.

So first thing of is looking at any probability issue with only averages, which isn't telling the story of variance. And variance is linked to expected results and that is what we need to direct the right amount of firepower on the right targets.

So first of I'll post the graph I made on the Twinlinked Heatlance on a BS 4+ platform.



In this graph the bottom axis is Damage dealt and how likely this is to happen if we shoot the Twinlinked Heatlance at 4+ chance to hit.
First thing what we perceive is that the probability of dealing 0 damage is off the chart.
Those values are:
T5:   50,0%
T6:   62,5%
T7+: 75,0%

Which is a glaring problem: at least half of the time the shooting is ineffective. So our risk is this, the risk we wasted shooting on a target.
Of course if you could boost the to hit and/or to wound roll, these odds would improve. For a Talos, I don't know many, but I'm no expert in the current from of 40k.

What we can count on as the reward for our shooting is at least 1 damage at the following rates:
T5:   50,0%
T6:   37,5%
T7+: 25,0%

So what this tell me is the the Heatlance is not as reliable to pick off wounds on high T targets. It does have a decent chance to inflict some more wounds, so you want to use it first, to see how much more shooting needs to go in the target to take it a bracket down for example.

If we take a look at what the chance is to do at least 4 damage the values become:
T5:   31,94% at 9": 41,58%
T6:   23,96% at 9": 31,18%
T7+: 15,97% at 9": 20,79%

What we can take away from this that there is a decent chance to get up to 4 damage or higher. Getting in close range does improve the odds but not more than about 9,5% vs T5 about 8% vs T6 and only a small 5% vs T7 or tougher.

So clearly as we would expect the weapon suffers from S6 to deliver the damage but the d6 and the melta effect help to give it high roll potential.

EDIT: I didn't include the different possible saves to mitigate damage but you can clearly see that these would linearly decrease the damage taken by the target. So any target with a decent invul save of a FnP would be less likely than 50% to get hurt from a single Talos shooting at it.

In my current perspective you would at least need to take 3 Taloï to get a good chance at reliably damaging a high T and defensive target.

El_Jairo wrote:

fisheyes wrote:

.....
But if your going to nerd out, you may as well DO IT RIGHT!

So first thing of is looking at any probability issue with only averages, which isn't telling the story of variance. And variance is linked to expected results and that is what we need to direct the right amount of firepower on the right targets.

Interesting! I really like what you've done it's a good way of seeing the impact Toughness has on the effectiveness of the Heatlance. Is the likelihood of a Haywire Blaster not doing anything similar? Or does that have to do with the low BS4+ of the Talos.

You bring up the idea of variance! And then it hit me that you can calculate variance for each of the probabilities I calculated on each target too. I think to calculate variance:

Summation[(result)^2(probability)] - (mean^2):

But if I'm being completely honest, I'm not sure how to go about the math now. It gets especially confusing with the Haywire Blaster, which I've just been assuming has 2 shots. I think you get super in detail with this. But knowing the variance would be very useful - it speaks to consistency. For example, while the HWB has higher average damage output on vehicles, it could be the case that the distribution is much wider than the Heatlance. This would make the Heatlance more consistent, despite lower damage output.

I'm going to try and fiddle around with this to see if there's anyway to graph a distribution!

So yeah the variance is just a mathematical term to show how much variance there is of the mean for a certain data sample. In this case it just describes how much difference there is between a high roll and a low roll.

Typically we want predictability and thus certainty to obtain a minimal result. Which is simply done by adding up the chance of each value that we deem as a succes. This is how I determined the chance of at least dealing 4 wounds.

My math is still a little off on the Haywire Blaster but what I can say for sure is that it totally disregards toughness through it's rules for generating Mortal Wounds on a 4+ (1) and on a 6+ (d3). That together with the fact that it delivers d3 shots make the calculations a little bit more complicated.

But what I'm confident at stating is that one Talos with Two HwBlasters will constantly put two Mortal Wounds on a tank. Which is great because these negate Toughness saves and invul saves. They only suffer from FnP.

So if in this 9th edition table are smaller and vehicles will become more prevalent the 24" range weapon which is better vs vehicles seems the best pick.

BTW, the distribution is what I showed in the graph. I just did cut of the 0 damage probability because than the detail of the damage would be lost.

EDIT: BTW I didn't see that much variance on the HwBlasters because yes there is a chance for them to do 18 Mortal Wounds but the chance is that small that it's not messing up the distribution.
Rolling 6 attacks and hitting with all of them and rolling 6's for all of them is just not something you will see happen during your lifetime.