What does the Marauder 2R offer that the 3R doesn't?

[Doctor Machete]

So I sat down yesterday and decided to calculate some odds for some of the variants listed here. I hope you all appreciate this, I had to reteach myself statistics for you!

First off, some assumptions. Obviously this is done with Tactics 9+ Pilots and the Marauder's System intact, but a less obvious thing to take into account is that I assumed all shots hit, rather than the 95% chance to hit you'll usually get with good Gunnery and Called Shot active. Also, this doesn't take into account damage reduction from Cover, Bulwark, and so on, nor does it count underarmoured mechs like degraded ones or those few mech variants that don't go for max cockpit armour stock. It also assumes that numbers shown on the user interface for the game are accurate, that there are no partial percentages to hit, so a Marauder's 33% chance of a headshot with a Tactics 9 pilot is actually 33%, not 33.33(...)%. I also assumed Ultra Autocannons followed the SRM/MG diminishing returns model of headshot chances, rather than the LRM/LB-X/Snub cluster model, which I'm pretty sure is true but couldn't swear to. That said, here's my working:

Listed variants are:
@Marauder3D 's 6xERML, 1xUAC10++ (16 tons of gun before ammo, 144 heat alpha before cooling, assuming ++ lasers 390 damage alpha)
@Doctor Machete 's 6xERML++, 1xUAC5++ or UAC2++ designs (a mere 13 or 11 tons of gun, 136/360 or 128/340 heat/damage alphas respectively
@aburgesser 's absolutely bonkers 2xLPL++, Gauss++, 2xML+/++ (27 tons of gun, 89/275 heat/damage, assuming ML++s - note, while they said ML+s were their minimum, two of those won't do the job against a full-armour cockpit, so I assumed ++s)
@frozx 's almost equally bonkers 4xLPL++ (24! tons of gun, no ammo needed (first flashbulb on the list!), 120/260 heat damage)
And my own design that I'm very proud of, 2xLPL++, 4xML++ (16 tons of gun, just like Marauder3D's, no ammo 'cos flashbulb, 108/270 heat/damage)

For comparison, I included some calculations for non-Marauder headcapper designs. Only one specific one, but some broad archetypes.

Headshot chance = h
Given number of Shots = s
Not landing a headshot chance = m = 1 - h
Landing two headshots that together equal a headcap = c = h * h
Not landing a paired headshot = p = 1 - c
Number of diminishing returns shots = r
Landing a second headshot of a diminishing returns weapon = u = h / 2
Not landing a second headshot of a diminishing returns weapon = d = 1 - u
Landing AT LEAST ONE headshot of a given number of shots = 1 - m^s
Landing AT LEAST TWO headshots of a given number of shots = 1 - (1 - p)^(s - 1)
Landing AT LEAST TWO headshots of a given number of shots, where a portion of them are diminishing returns weapons = 1 - (1 - (p^(s - (r + 1)) * d^r) (technically the two '1 -'s could be simplified out, and the r value left a static 1 as there's only one ballistics mount, but I leave them here to make it easier to follow and more flexible- also note, this formula only accounts for Ultra weapons and SRM2s, as diminishing return weapons with only a second shot, not larger SRMs, MGs, or Cluster weapons)

All final values rounded to the sixth decimal place, because some of these were large.

Normal Headshots
---
h = 0.18
t = 0.82
c = 0.0324
p = 0.9676
u = 0.09
d = 0.81

Two independently Headcap-capable weapons (AC/10+, LPL++, Gauss Rifle, etc.) = 0.3276
Six weapons that working together any two of them can headcap (ML++, AC/5 etc.) = 0.151837
Five AC/5++s on an Annihilator, the most I could come up with to spam independently-capable headcappers = 0.629260

Marauder Headshots
---
h = 0.33
t = 0.67
c = 0.1089
p = 0.8911
u = 0.165
d = 0.835

Two independents = 0.5511
Six working together = 0.438135
Marauder3D's Marauder is calculated using: 1 - (1 - (p^6 * d^1)) = 0.469158 (again, no need for the ^1, as that makes no difference, but it makes the formula stay consistent for ease of comprehension)
Doctor Machete's UAC5 Marauder uses an identical calculation to Marauder3D's, since as far as the formula is concerned the guns are identical, as neither the UAC10 nor the UAC5 are oneshot headshot threats, and obviously comes up with an identical result, of 0.469158
Doctor Machete's UAC2 Marauder was a real pain, and the most complex calculation by far, because the UAC2 is a headcapper only if it hits after a weapon that is not itself, but I think I got it right: 1 - (1 - (p^6 * d^1) - (1 - p * d) = 0.326002 (this one loadout caused the delay from posting yesterday, as I wanted the newly-relearned statistics knowledge to have time to 'settle' so I could double-check this after some sleep - I really was not sure I did it right, but it... seems to be correct?)
aburgesser's Marauder is pretty complex too, though thankfully simpler than Doctor Machete's second design - first the chance of oneshot headcaps, plus the chance of the MLs doubling up for a headcap: (1 - t^3) + (1 - (1 - p^2)) = 0.905178(!!!)
frozx's Marauder is actually the simplest of all of these, at only: 1 - t^4 = 0.798489
And finally, my Marauder: (1 - t^2) + (1 - (1 - p^3)) = 0.843514

So you can see that as far as pure headshot potential goes, aburgesser's Marauder is a clear winner, off the back of three independently-capable headcappers supplemented by two other weapons that working together can do it. Mine comes next, from a similar system but weighted the other way, frozx's does it through the sheer number of individual weapons that can blow a cockpit off, then the statistically identical UAC10 and UAC5 6xERML designs, then the UAC2 6xERML design.

As far as non-headshot alpha potential, in descending order we have the UAC10, UAC5, and UAC2 6xERML designs, then aburgesser's, then mine, then frozx's. For alpha heat, they go in an identical order for the first half, with UAC10, 5, and 2 ERML designs first, mainly off the back of all those ERMLs, then mix it up a bit with mine, then frozx's, and finally aburgesser's dropping to the coolest because of that Gauss and less MLs than mine.

For average range mine is of course the shortest at 330m, with the UAC10 design next at 382.5m on a per-shot basis, then UAC5 at 405, then surprisingly the Gauss and 4xLPL tied at 450 (the two standard MLs really drag the Gauss design's average down), then the UAC2 design at 420 (I know, I know...) but a good portion of that incapable of headcapping, then finally with the longest range, the all-LPL design, which is something a bit odd when you consider in tabletop Inner Sphere Large Pulses are considered short-medium-range guns in most eras they exist in, but is explained both by them not having a shorter range than standard Large Lasers in HBS!Battletech and not having any short-range guns like standard Medium Lasers to drag them down.

But the one that may decide it more than previous metrics, is gun weight. Keeping in mind that all bar the two flashbulbs will need ammo as well, with the UAC10 being particularly ammo-hungry, then the UAC5, the Gauss, then finally the UAC2 needing the least tonnage spent on ammo, while only the Gauss design will come off any easier on Heat Sink needs than the flashbulbs. The design that spends the most of its 75-ton total mass and 42.5 usable tonnage, to the point that it is flatly unable to mount max armour, is the Gauss design, followed by the quad-LPL design, then the UAC10 and my double-LPL, quad-ML design, then the UAC5 and finally the UAC2 designs. However, if you count ammo and assume an absolute minimum of 16 rounds of fire, the UAC2 design and the Gauss only have to dedicate two extra tons for a total of 14 tons on offensive capability on the UAC2 and a whopping 29 on the Gauss, the UAC5 has to spend three for 16 tons, bringing it equal to the mixed flashbulb and the dry weight of the UAC10, and then there's the UAC10, that when stocked for 16 rounds of fire needs four tons of ammo, bringing it from 16 tons dry to 20 loaded spent on offense. This leaves, after 17.5 tons of armour for maximum to the whole ton after chassis weight protection, the UAC2 design with 11 tons to spend on heatsinks, jump jets, and other things, the UAC5 and mixed flashbulb with 9 tons, the UAC10 with 5, the quad-LPL with 1, and the Gauss with -4 tons. Luckily the two designs with the least tonnage to spare are also the two coolest-running, but neither of them can mount a full jumpjet fit, the Gauss is going to have to thin out its armour substantially just to fit all its guns, and the quad-LPL is still going to be left with 60 heat after an alpha unless that one ton is spent on a heatsink, an instant-shutdown if a rookie pilot is in it and no heatbank - granted, frozx said they spent their one ton on a heatbank, but that only gets them a maximum of 45 spare heat budget before overheat, assuming a ++ heatbank and high-Guts pilot, which isn't enough for another Alpha.

Now, apart from frozx's design I don't know enough about any of the designs from other people to say for sure what their heat situation looks like, but I know what I did. So, my MAD-2R has four jumpjets and five DHS mounted, which takes up all its spare tonnage. I also have some 0-weight things on, but they're not relevant to heat. This means I have 90 cooling for my 108 alpha for an 18 heat delta (alternatively for maximum confustion, an 18 heat alpha delta - try saying that to someone with only either Battletech or maths knowledge, and watch the confusion), allowing me to, with a rookie pilot, have 3.33(...) alphas in a neutral-cooling biome, or with a high-Guts one 5 full alphas, each at a ~84% chance of a headcap. Assuming I jump max distance on top of alphaing, I still have enough heat from fully cooled for 1.40 alphas with a rookie or 2.09 with a Gutsy veteran. If I need to cool, the best options to preserve headcap chance are first to ditch 1-2 MLs, then a LPL while preserving all four MLs, then 3-4 MLs while keeping both LPLs, then everything but an LPL, with ditching both LPLs being the worst option no matter how many MLs I keep - obviously this is in decreasing chance of headcap, not increasing value of cooling. On top of that, every other design has either higher cooling needs, more tonnage spent, or both, with only the UAC2 saving enough tonnage on guns to have the spare tonnage for both cooling equal to or better than the mixed-flashbulb and jumpjets or other utility weight like TTS or an EW fit. And it's by far the worst at actually headcapping, with its Ballistic mount utterly incapable of headcapping on its own to take advantage of its superior range!

So while my design gives up average range against all the others and max total damage against most of them, I feel it is in most situations you brought a Marauder for, where you want to be headcapping as many enemies as possible, the superior option, though I will admit not all situations will benefit from it compared to other designs, particularly if you need range or sheer focused damage capacity. Although if you just want near-guarantees of headcaps without jump capability or durability for those that haven't yet felt your wrath, aburgesser's design is the way to go. And who knows? Maybe it doesn't need those four tons of armour or to be able to jump, with that pilot-deletion capability.

Nice work, although I think it is not quite right. For a starter chance for the second hit is not half the chance of the first, just the bonus is, applied on the head's value in the Front facing hit table.

The multiplier would be ((18/2)-1)+1, 0.103 for regular mechs and 0.210 for the Marauder. That assumes roll correction (so 95%->97.13%) One extra bit of info, which doesn't matter here, would be that only LRMs use clustering. All other multi-hit weapons have diminishing returns, including LBX/SNPPCs.


Without getting very deep I'm not sure how do you get your results. For example, you get 0.843514 for your build but using your own numbers (33% to hit the head) I get 73%:

Spoiler

And this is quite easy to check, no need to relearn maths, just use some online binomial calculator and combine them in a spreadsheet like above. Also this works the same way for all these builds and makes it very easy to manage small number of diminishing return weapons.

So I get these results:

Spoiler

Headcapping:

CT CORE:

That shows a very different picture. But with some caveats:
- All setups are normalized to 12.5t armor, just for comparison sake.
- As said before, base chance is roll corrected and table weight is used for hit location chances.
- All of them include one TTS+++ to account for firing at near max range (penalty) at a slightly evasive target (for more consistent firing). The UAC10++ setup also includes 2xTTS+++ to account for the -30% recoil penalty (-20% with maxed stats).
- The minimum ammo I assume is: UAC2: 10, UAC10: 10 salvos (would be 8 if could 1-hit headcap at 0% DR), Gauss: 8 salvos.

Now let's analyze:

• TEST1: no doubt the single salvo performance winner, both headcap and CT core. The issue is heat. Coolant Vent nets just barely over one DHS worth of cooling per turn, not much. Damage sustainability is still very bad with CV included and on top of that you don't get MT or AP.
• TEST2: second best performance plus runs very cool, perfect for intensive use of JJs (plus firing), in such a way that IMO it will far outdamage TEST1 if pressed and in a much safer way (jumps are much more feasible to use often while firing).
• TEST3: better range than TEST2 but not with all weapons. The MLs don't help much at 0% DR but they do for 20-60% (71/42/27/04% without MLs). So what to do, going for ML range or not?. Also runs pretty hot with the MLs on and with only 1xJJ (I could not remove DHS in order to normalize armor). Low alpha makes it relatively weak for CT core and vehicle killing.
• TEST4: decent damage and consistent range and good chances at 0% DR but not among the best for the other brackets. And (again) runs very hot. Low alpha makes it weak for CT core and vehicle killing. IMO removing one LPL would make the setup better, much more mobile and dependable.
• TEST5: a lot of damage coming from medium range weapons while still not being on the top of the food chain is not super good imo, but at least has good damage sustainability. And then, are you going to spend morale for a 2xLPL++ only Precision Shot? because if you do then chances drop a LOT, and if you get into ML range then why using LPLs and not other more efficient weapon?. Also weaker for CT core / vehicles.

Also, that quintuple-AC/5++ Annihilator design is surpringly capable of headshots, like, it beats out fully half of the listed Marauder designs and is not that far behind the others, all without a Called Shot bonus! Admittedly, it's half the speed, but with that little of its usable weight (second only to the Atlas II!) spent on guns, you can easily max the armour and mount a secondary battery of Energy weapons or some utility tonnage like jumpjets or a mech mortar or an EW fit. Hell, you can have multiple of those if you really try!

I've played (soloing) with several variants of ANH, from 5xERML 5xUAC2 to 4xUAC20, 3xUAC20 and so on. And IMO higher armor doesn't replace higher mobility. A 20t armor with 650 alpha damage doesn't come close to a 10.5t armor Marauder in terms of survivability.

Thanks! And I realised this might be a follow-up question after I posted, but a theoretical three-independently-capable-headcapper-and-nothing-else build Marauder, whether pure LPLs, mixing a Gauss or an AC/10++ in, or using some ER PPC++s for that classic Marauder feel, would have a headcap chance of 0.699237. So if you want to go for 2xER PPC++, 1x Gauss, for something mostly similar to an upteched MAD-3R, it's flatly superior in pure headcapping potential to all the 6xERML designs (as well as the quintuple-AC/5++ Annihilator) and would have the longest average range by far of all variants listed. A three ER PPC++ would actually have mildly superior range to even that, as well as no ammo requirements and less tonnage spent on weapons, although it might make it up on necessary heatsinks. Also, its arms wouldn't be symmetrical, which on a Marauder for me is a no-no.

The ANH makes for a decent support mech but is not very dependable, it needs other mechs around for some backup.
Edit (rephrased to better express myself): The ANH makes for a decent support mech and it is very dependable for CT core but not very self reliant, it needs other mechs around for some backup because it's too slow if you want to maintain distance from fast approaching mechs.


Here updated the above chart with three more mechs:

Spoiler

The ERPPC setup feels very lackluster. It has very good range but what's the point if you're not going to be able to fire that often and when a lower range mech who can also has excellent survivability and much better chances to headcap?.

Then, the two ANH based ones are good for headcapping but they're not above the marauder, and I'd say much lower when you consider survivability and flexibility for choosing targets/LoS. Their thing is more about CT core with some support around them. There (CT core), the difference between the Marauder and other mechs gets reduced a lots plus the Marauder has much lower firepower.


Also a chart comparing weapon efficiency, how many tons of weight you need for achieving 80% of destroying the location:

Spoiler

The ammo caveat from the other chart applies here. All weapons have a predefined set of salvos, of note being the UAC20, with just five salvos for the whole mission. The darker the color the better.

Edit: in the "DHS / 1x MULT" it should be "DHS / 18x MULT", because it's taking the custom bonus multiplier for that but the one actually being used is the default 18x

Edit: clarified a couple points, added response to another post, added weapon efficiency chart, added clarification about mistake in the legend from the weapon efficiency chart, rephrased ANH role.

 

[Prussian Havoc]

Thanks! And I realised this might be a follow-up question after I posted, but a theoretical three-independently-capable-headcapper-and-nothing-else build Marauder, whether pure LPLs, mixing a Gauss or an AC/10++ in, or using some ER PPC++s for that classic Marauder feel, would have a headcap chance of 0.699237. So if you want to go for 2xER PPC++, 1x Gauss, for something mostly similar to an upteched MAD-3R, it's flatly superior in pure headcapping potential to all the 6xERML designs (as well as the quintuple-AC/5++ Annihilator) and would have the longest average range by far of all variants listed. A three ER PPC++ would actually have mildly superior range to even that, as well as no ammo requirements and less tonnage spent on weapons, although it might make it up on necessary heatsinks. Also, its arms wouldn't be symmetrical, which on a Marauder for me is a no-no.

Symmetry is for me not a prerequisite.

I am a firm believer in Shield Arms and where I can swing them, Shield Arms backed up by a Shield Side Torso and “Dead Leg.” I’ve managed to Tank through many a Tournament-caliber Multiplayer Match that by the end includes a Stock Centurion-A hanging together with duct tape, bailing strings, a Hope and a Prayer. : )

 

[RecklessCaution]

Symmetry is for me not a prerequisite.

I am a firm believer in Shield Arms and where I can swing them, Shield Arms backed up by a Shield Side Torso and “Dead Leg.” I’ve managed to Tank through many a Tournament-caliber Multiplayer Match that by the end includes a Stock Centurion-A hanging together with duct tape, bailing strings, a Hope and a Prayer. : )

For some designs - even many of them! I agree. Not for Marauders and some others, though. Part of their appeal to me is the partial symmetry, either in the limbs like the Marauders or the torso like Black Knights, and I'm okay with knowing I don't play the most optimally - hell, my primary campaign lance always includes at least one punchbot, most times two!

Nice work, although I think it is not quite right. For a starter chance for the second hit is not half the chance of the first, just the bonus is, applied on the head's value in the Front facing hit table.

The multiplier would be ((18/2)-1)+1, 0.103 for regular mechs and 0.210 for the Marauder. That assumes roll correction (so 95%->97.13%) One extra bit of info, which doesn't matter here, would be that only LRMs use clustering. All other multi-hit weapons have diminishing returns, including LBX/SNPPCs.


Without getting very deep I'm not sure how do you get your results. For example, you get 0.843514 for your build but using your own numbers (33% to hit the head) I get 73%:

Spoiler

And this is quite easy to check, no need to relearn maths, just use some online binomial calculator and combine them in a spreadsheet like above. Also this works the same way for all these builds and makes it very easy to manage small number of diminishing return weapons.

So I get these results:

Spoiler

Headcapping:

CT CORE:

That shows a very different picture. But with some caveats:
- All setups are normalized to 12.5t armor, just for comparison sake.
- As said before, base chance is roll corrected and table weight is used for hit location chances.
- All of them include one TTS+++ to account for firing at near max range (penalty) at a slightly evasive target (for more consistent firing). The UAC10++ setup also includes 2xTTS+++ to account for the -30% recoil penalty (-20% with maxed stats).
- The minimum ammo I assume is: UAC2: 10, UAC10: 10 salvos (would be 8 if could 1-hit headcap at 0% DR), Gauss: 8 salvos.

Now let's analyze:

• TEST1: no doubt the single salvo performance winner, both headcap and CT core. The issue is heat. Coolant Vent nets just barely over one DHS worth of cooling per turn, not much. Damage sustainability is still very bad with CV included and on top of that you don't get MT or AP.
• TEST2: second best performance plus runs very cool, perfect for intensive use of JJs (plus firing), in such a way that IMO it will far outdamage TEST1 if pressed and in a much safer way (jumps are much more feasible to use often while firing).
• TEST3: better range than TEST2 but not with all weapons. The MLs don't help much at 0% DR but they do for 20-60% (71/42/27/04% without MLs). So what to do, going for ML range or not?. Also runs pretty hot with the MLs on and with only 1xJJ (I could not remove DHS in order to normalize armor). Low alpha makes it relatively weak for CT core and vehicle killing.
• TEST4: decent damage and consistent range and good chances at 0% DR but not among the best for the other brackets. And (again) runs very hot. Low alpha makes it weak for CT core and vehicle killing. IMO removing one LPL would make the setup better, much more mobile and dependable.
• TEST5: a lot of damage coming from medium range weapons while still not being on the top of the food chain is not super good imo, but at least has good damage sustainability. And then, are you going to spend morale for a 2xLPL++ only Precision Shot? because if you do then chances drop a LOT, and if you get into ML range then why using LPLs and not other more efficient weapon?. Also weaker for CT core / vehicles.

I've played (soloing) with several variants of ANH, from 5xERML 5xUAC2 to 4xUAC20, 3xUAC20 and so on. And IMO higher armor doesn't replace higher mobility. A 20t armor with 650 alpha damage doesn't come close to a 10.5t armor Marauder in terms of survivability.


The ANH makes for a decent support mech but is not very dependable, it needs other mechs around for some backup.

Here updated the above chart with three more mechs:

Spoiler

The ERPPC setup feels very lackluster. It has very good range but what's the point if you're not going to be able to fire that often and when a lower range mech who can also has excellent survivability and much better chances to headcap?.

Then, the two ANH based ones are good for headcapping but they're not above the marauder, and I'd say much lower when you consider survivability and flexibility for choosing targets/LoS. Their thing is more about CT core with some support around them. There (CT core), the difference between the Marauder and other mechs gets reduced a lots plus the Marauder has much lower firepower.


Also a chart comparing weapon efficiency, how many tons of weight you need for achieving 80% of destroying the location:

Spoiler

The ammo caveat from the other chart applies here. All weapons have a predefined set of salvos, of note being the UAC20, with just five salvos for the whole mission. The darker the color the better.

Edit: clarified a couple points, added response to another post, added weapon efficiency chart.

I... specifically never took into account overall hit chances? That was covered in the Assumptions section. That may account for some of our discrepencies. I was only interested in chances of a hit being a headshot, rather than trying to cover extreme ranges and evasion chevrons and everything. And I don't know where to get access to the hit tables for normal, non-precision shots, I was going by the in-game UI when making a precision shot and what I've picked up from reading the forums without doing a deep dive on it. When you say only the bonus of diminishing-returns weapons halves, what do you mean? I think I understand you, but what I think you mean is what I was saying, that the chance to hit the precision shot target halves, not the chance to hit the enemy at all, so unless I'm misunderstanding you... I'm not sure why you said it?

But you're right, some of my numbers are wrong. frozx's results are correct, but I definitely stuffed up somewhere with at least the 6xERML designs, and in fact it looks like everything but frozx's. I can only assume that with the more complex formulae I screwed up in my bracketing somewhere while entering them into the calculator, since I was using my old scientific one from high school (that battery has really lasted, by the way - not much longer and it'll be old enough to legally drink in my country!) and working everything out there with one formula rather than using distribution plots, and I remember it being particularly finicky about what it considered proper bracketing, rather than anything a human would consider good practice, as soon as you started involving exponents. I know that old adage about a poor workman blames his tools, so behold, my backup excuse! ...I was and am very tired, as I have not been sleeping well, and indeed two nights ago spaced out in the shower for over an hour, almost asleep standing up. Luckily it's summer here and I wasn't using much hot water in the mix, otherwise I would have gotten a rude awakening when my small hot water system ran out! In fact, it's 2:17pm at the moment and I have not slept since I woke up yesterday. Being too tired to sleep is considered a bad thing, right? At this point I'm surprised I'm as coherent as I am.

 

[Doctor Machete]

I... specifically never took into account overall hit chances? That was covered in the Assumptions section. That may account for some of our discrepencies. I was only interested in chances of a hit being a headshot, rather than trying to cover extreme ranges and evasion chevrons and everything. And I don't know where to get access to the hit tables for normal, non-precision shots, I was going by the in-game UI when making a precision shot and what I've picked up from reading the forums without doing a deep dive on it. When you say only the bonus of diminishing-returns weapons halves, what do you mean? I think I understand you, but what I think you mean is what I was saying, that the chance to hit the precision shot target halves, not the chance to hit the enemy at all, so unless I'm misunderstanding you... I'm not sure why you said it?

In my first comment I used your 33% to hit the head (100% base to hit, no roll correction). That did result in 73% vs ~84.3% assuming the same values but with your method vs 75% with my values (~34% for the head, ~97% base to hit).

Tables are in ...BattleTech_Data\StreamingAssets\data\constants\CombatGameConstants.json, search for the key "HitMechLocationFromFront". As it is, works for single hit weapons and no PS. For maxed PS regular mech: multiply head by 18; Marauder: multiply head by 18x2.4 (43.2). For a second hit from a diminishing returns weapon the multiplier would be ((18-1)/2)+1 = x9.5 (10.3%) -> , x22.1 (21%) for the Marauder.

Note that you cannot have lower chance than a regular non-PS hit no matter how many hits the weapon has (you divide the bonus part, not the whole multiplier), you cannot get a multiplier lower than 1 (in principle, there are some exceptions). Also note than the Marauder gets a multiplier more than double the default multiplier for PS (you get x2.4 on top) yet you don't get remotely near the chance of double the CT chance of a "normal" PS, because it's using the hit tables.

I think this will make much easier to understand what's going on with the hit tables:

Spoiler

But you're right, some of my numbers are wrong. frozx's results are correct, but I definitely stuffed up somewhere with at least the 6xERML designs, and in fact it looks like everything but frozx's

Seriously, you can use my method, it's far easier. It isn't practical at all for complex setups but for simple ones like these it's good enough and easy to understand. If you google search for an online binomial calculator, in one of the top ones enter 0.33 as "Probability of success on a single trial", 4 as "Number of trials", and 0-4 as "Number of successes (x)" (you have to do it five times). Now you got the ML binomial, same for the LPLs and then combine them with very simple formulas (sum and multiplication). Well, you need to add a column for the damage too, sum damage and multiply chances.



Edit: added extra explanatory screenshot

 

[Prussian Havoc]

For some designs - even many of them! I agree. Not for Marauders and some others, though. Part of their appeal to me is the partial symmetry, either in the limbs like the Marauders or the torso like Black Knights, and I'm okay with knowing I don't play the most optimally - hell, my primary campaign lance always includes at least one punchbot, most times two!...

I can understand that and even feel my OCD rising to the visible challenge imposed by “One Armed” Catapults and Warhammers in BATTLETECH. : )

But with more than a thousand BATTLETECH Multiplayer matches to my credit... function trumps form for me just about every single time. :bow:

 

[foamyesque]

If my math is correct, three independently capable headcap weapons plus two paired ones is not 90%. The chance all three headcappers whiff is around 30% (disregarding base to-hit), and of those 30% whiffed rounds, only around 10% will be saved by the paired weapons. So that gets you a 73% (ish) overall headcap chance. Which is by no means bad, but it's not 90%.

The quadruple headcap design gets to just over 80%. A 3D design of 1 AC/10++, 2x UAC/2++, 4x ML++, is quite complex but I think beats out pretty much everything else:

Chance the headcap whiffs is 66%. Of that, chance of no hits from the secondary weapons is ~8.7% and the chance of exactly one hit is 26.3% (1st shots from the UACs considered only). The chance of the second shot from the UACs I'm not clear on, but if I understand @Doctor Machete correctly, it's 21% individually, which would mean that the chance of no hits from the second shots is ~62%, the chance of exactly one hit is 33%, and the chance of both hitting is ~4%.

So, the situation where the headcapper misses, and only one of the other weapons hits, is: 0.66 * ((0.087 * (0.62 + 0.33)) + (0.263 * 0.62)) = 0.16, or 16%. That translates to an 84% headcap chance, which is pretty solid, and it incorporates three long range weapons and one that can no-sell bulwark (via breaching shot) and Lance Command Modules both.

A triple UAC/2 layout might get better overall numbers, but losing access to Breaching Shot hurts.

 

[Doctor Machete]

If my math is correct, three independently capable headcap weapons plus two paired ones is not 90%. The chance all three headcappers whiff is around 30% (disregarding base to-hit), and of those 30% whiffed rounds, only around 10% will be saved by the paired weapons. So that gets you a 73% (ish) overall headcap chance. Which is by no means bad, but it's not 90%.

The quadruple headcap design gets to just over 80%. A 3D design of 1 AC/10++, 2x UAC/2++, 4x ML++, is quite complex but I think beats out pretty much everything else:

Chance the headcap whiffs is 66%. Of that, chance of no hits from the secondary weapons is ~8.7% and the chance of exactly one hit is 26.3% (1st shots from the UACs considered only). The chance of the second shot from the UACs I'm not clear on, but if I understand @Doctor Machete correctly, it's 21% individually, which would mean that the chance of no hits from the second shots is ~62%, the chance of exactly one hit is 33%, and the chance of both hitting is ~4%.

So, the situation where the headcapper misses, and only one of the other weapons hits, is: 0.66 * ((0.087 * (0.62 + 0.33)) + (0.263 * 0.62)) = 0.16, or 16%. That translates to an 84% headcap chance, which is pretty solid, and it incorporates three long range weapons and one that can no-sell bulwark (via breaching shot) and Lance Command Modules both.

A triple UAC/2 layout might get better overall numbers, but losing access to Breaching Shot hurts.

I'm a bit confused. Where that 90% you talk about comes from?

I haven't looked very deep into your numbers but your 84% final chance is consistent with my calculations (I get a 84/63/63/20%). The issue is not there but elsewhere. The chances of the AC10 setup are very similar to a 4xML 3xUAC2 (86/62/62/15%). The difference is with the AC10 the efficiency plummets, meaning you're going to have a LOT less armor and/or a LOT more heat.

Losing Breaching shot doesn't hurt much because you mainly benefit from it at 60% DR. And the obvious alternative (Ace Pilot) is imo way better anyway for a non single weapon setup, you gain a lot of offensive flexibility, allowing you to keep firing in many circumstances where it would be risky without AP, an in this case defensive too (more armor). It makes easier to deal double-turn consecutive salvos without taking hits in return and to get in & out from tight situations while minimizing risks.

Another setup I think is better is the 4xERML 2xUAC2 (76/72/47/18%), with considerably lower chances but much better cooling and now better range, improving survivability. But if what you want is the more power the better then a 4xERML 3xUAC2 (86/80/62/28%), a bit better cooling and/or slightly better armored but now with better headcap/core chances than the AC10 version and longer range too (ERMLs vs MLs).


Edit: grammar

 

[foamyesque]

I'm a bit confused. Where that 90% you talk about comes from?

It's @RecklessCaution's (incorrect) number for the 2x LPL, Gauss, 2x ML layout.

I haven't looked very deep into your numbers but your 84% final chance is consistent with my calculations (I get a 84/63/63/20%). The issue is not there but elsewhere. The chances of the AC10 setup are very similar to a 4xML 3xUAC2 (86/62/62/15%). The difference is with the AC10 the efficiency plummets, meaning you're going to have a LOT less armor and/or a LOT more heat.

Losing Breaching shot doesn't hurt much because you mainly benefit from it at 60% DR. And the obvious alternative (Ace Pilot) is imo way better anyway for a non single weapon setup, you gain a lot of offensive flexibility, allowing you to keep firing in many circumstances where it would be risky without AP, an in this case defensive too (more armor). It makes easier to deal double-turn consecutive salvos without taking hits in return and to get in & out from tight situations while minimizing risks.

Another setup I think is better is the 4xERML 2xUAC2 (76/72/47/18%), with considerably lower chances but much better cooling and now better range, improving survivability. But if what you want is the more power the better then a 4xERML 3xUAC2 (86/80/62/28%), a bit better cooling and/or slightly better armored but now with better headcap/core chances than the AC10 version and longer range too (ERMLs vs MLs).


Edit: grammar

Hm. Those are actually better numbers for 40% DR than I'd thought -- I hadn't checked for requiring three hits, which you require at 40%DR; I'm kind of surprised it still clocks in at 60% overall. If that's true I've been building my 'rauder and pilots wrong :v

I do have a number with Ace Pilot + Bulwark, though, which I've been using in my heavy scouts (Uparmroured Firestarter to start with, then a Grasshopper, now a SLDF BK) and which could be shifted once I match the build up. I'll have to think about it.

 

[Doctor Machete]

It's @RecklessCaution's (incorrect) number for the 2x LPL, Gauss, 2x ML layout.

IMO yes, my own results give a 75% for 0% DR instead of a 73% (pretty sure because I use ~97.12% base chance), not a 90%, as you can see in the above charts. In any case that's far from a 90%.

Also I took one of the setups and showed the methodology to calculate the chances in a fairly simple way without directly using complicated formulas. That showed a big discrepancy between my method (one of them, I also can do it by generating millions of RNG rolls) and his. Take a look to the charts above.

Hm. Those are actually better numbers for 40% DR than I'd thought -- I hadn't checked for requiring three hits, which you require at 40%DR; I'm kind of surprised it still clocks in at 60% overall. If that's true I've been building my 'rauder and pilots wrong :v

Now, for your setup, just removing the AC10 (4xML 2xUAC2) gives you a 76/47/47/06%. A 6xML (you can directly calculate it with a cumulative binomial in many online webs) has already a 66/33/33/02% and it is equivalent to the 4xML plus the two first shots of the 2xUAC2, ignoring the secondary ones. So it's going to be higher than that, and then you can add another weapon, be it one extra UAC2 or something else, but the UAC2 is the most efficient dmg/weight/heat/spread/ammo you can add in this case.

I do have a number with Ace Pilot + Bulwark, though, which I've been using in my heavy scouts (Uparmroured Firestarter to start with, then a Grasshopper, now a SLDF BK) and which could be shifted once I match the build up. I'll have to think about it.

Ace Pilot in a jumpy mech (with good enough cooling to account for the extra heat), and in a heavy or lower weight, is godly. In an assault it would compete with Master Tactician, because the extra init is very good against other assaults. But with a heavy or lower weight?.

Spoiler

And that mech only has a 22/22/22/04% with just 5xERML++. With the M2R/M3R is somewhat similar but much faster.

 

[foamyesque]

My plan for the SL PHawk actually involves a TAG; if the bonuses stack as I hope, between the jump and the TAG bonus, it should push the remaining four MPulses (Or ERML++s) over 61. ERML++s would be 63; MPulses++s 70.

This is what I drive for scouting, frontline firepower, and headcapping all three; only finished the weapons layout last night with the final small laser. Could boost the melee further with better mods, but it's not a priority:

I go back and forth on how much cooling I need. I like the fact that the main battery runs cool, but some extra tonnage in armour'd be real nice.

 

[Doctor Machete]

My plan for the SL PHawk actually involves a TAG; if the bonuses stack as I hope, between the jump and the TAG bonus, it should push the remaining four MPulses (Or ERML++s) over 61. ERML++s would be 63; MPulses++s 70.

You cannot TAG your own remaining shots from the same mech, TAG & NARC are fired after all other weapons. What are you going to to do, tag with a different mech, which requires medium range to attack a foe who may have more than 0% DR so you can finish using the PHX, and just for a 20% DR?.

This is what I drive for scouting, frontline firepower, and headcapping all three; only finished the weapons layout last night with the final small laser. Could boost the melee further with better mods, but it's not a priority:

You can shave armor from the legs, they're reinforced so you can DFA (I suppose) but otherwise they're harder to hit than the arms, the arms are harder to hit than the torsos and you have the same armor in the legs than the side torsos. I'd drop the legs armor down to the arms level to reinforce frontal and back.

Usually I don't have rear armor at all (the PHX above has just 5 in every location but if you go for a close range playstyle it may be worth to max or near max it.

I go back and forth on how much cooling I need. I like the fact that the main battery runs cool, but some extra tonnage in armour'd be real nice.

It depends, if you want to melee you don't need that much cooling but if I wanted to play safe with a BLKB (soloing) I'd do something like this:

Spoiler

This way I can keep my desired range at all times while I have quite good accuracy for fighting near maximum range and never get into close range and exploiting AP both for hit & run and hit & hit & hit... (fire -> jump away, fire jump away, fire..). You'll do less damage per salvo but you're going to be able to fire more often and from a safer position. You'd probably end doing more damage over the entire mission than with SL/ERSLs

 

[foamyesque]

<snip>

Damn. I thought TAGs fired first, as would make logical sense. Could've sworn I saw a vehicle do that, which is what gave me the idea, but I guess I was misremembering. The reason for a TAG suite was that between +20% for the jumping and the +20% from the tag, if they stack, you can push the good medium lasers into one-shot headcappers. That gives you about 50% odds of popping off someone's head each round, and it's only slightly less damage (and significantly less heat) than carrying a full five weapons.

But that was all predicated on the TAG landing first.

S'far as the legs go: The reason they are maximum armoured is because they are irreplaceable without buying an entire new frame and transferring all the weapons and stuff over. You can't cram four DHSes in each leg in your own refits, you see. The monetary cost is whatever, but it takes the 'mech offline until you can find one in a store, and then you need to burn a whole heap of MechBay time on outfitting it. An alternative would be to have a fully setup backup ready to go in case of trouble, but that cuts into your flexibility in the MB.

 

[Doctor Machete]

Damn. I thought TAGs fired first, as would make logical sense. Could've sworn I saw a vehicle do that, which is what gave me the idea, but I guess I was misremembering. The reason for a TAG suite was that between +20% for the jumping and the +20% from the tag, if they stack, you can push the good medium lasers into one-shot headcappers. That gives you about 50% odds of popping off someone's head each round, and it's only slightly less damage (and significantly less heat) than carrying a full five weapons.

But that was all predicated on the TAG landing first.

I haven't tested it for a long time since the initial HM release but the devs themselves said it explicitly in a video pre HM release. It was a very conscious decision, so I doubt it has changed.

S'far as the legs go: The reason they are maximum armoured is because they are irreplaceable without buying an entire new frame and transferring all the weapons and stuff over. You can't cram four DHSes in each leg in your own refits, you see. The monetary cost is whatever, but it takes the 'mech offline until you can find one in a store, and then you need to burn a whole heap of MechBay time on outfitting it. An alternative would be to have a fully setup backup ready to go in case of trouble, but that cuts into your flexibility in the MB.

You're counting on an exploit, as that is not a legit build but just the way they included those extra DHS. Otherwise it is much better to lose a leg than a side torso.

And if you lose a side torso the chances to be CT cored sky rocket because the damage transfer mechanic and the high base chance to damage the ghost side torso plus the arm connected to it, and now the CT is very likely already damaged.

 

[foamyesque]

@Doctor Machete:

I actually just watched a vehicle simul-fire a TAG and a laser, and the TAG landed first and upped the laser damage. Gonna confirm with my own 'mech, but it looks like it operation 40% is go :v

As far as an exploit, well, if the devs aren't going to follow the rules of 'mech construction I don't see why I should have to either. There is a legit build -- you move two of the sinks into the torsos and the exchangers into the legs, and one sink into the arms -- so I don't feel I'm breaking things too badly. :v

 

[Prussian Havoc]

@Doctor Machete:

I actually just watched a vehicle simul-fire a TAG and a laser, and the TAG landed first and upped the laser damage. Gonna confirm with my own 'mech, but it looks like it operation 40% is go :v

As far as an exploit, well, if the devs aren't going to follow the rules of 'mech construction I don't see why I should have to either. There is a legit build -- you move two of the sinks into the torsos and the exchangers into the legs, and one sink into the arms -- so I don't feel I'm breaking things too badly. :v

Are you sure that Mech was not already “tagged” from the previous turn?

A Mech can tag for itself, but it does so one into the next Turn. And if a player is savvy he can Tag early in a round with an Ace Pilot, jump to a concealed non-LoS “Hide” site, then move last in the next Turn... all the while it’s Tag Effect was in play for the bulk of two Turns, IIRC.

 

[foamyesque]

Are you sure that Mech was not already “tagged” from the previous turn?

As it was the first time that vehicle had fired, yes, and the '1' distinctly showed up ahead of the other damage stuff. What I didn't catch clearly was the damage figure for the followup shot, which is what I need to verify. The 'tag marked' status update only showed at end-of-round, though.

 

[Doctor Machete]

I actually just watched a vehicle simul-fire a TAG and a laser, and the TAG landed first and upped the laser damage. Gonna confirm with my own 'mech, but it looks like it operation 40% is go :v

Tested and doesn't work. PHX-1B has 2xLL+++ and 2xTAG++ (to be sure) against a 40% DR foe. You can see how the TAGs are fired last. Funny enough the second TAG does get the x1.2 increased damage.

LL damage is 50 x 1.2 (quirk) x 0.6 (DR) = 36 damage.
First TAG does 1 x 1.2 (quirk) x 0.6 (DR) = 0.72 dmg.
Second TAG does 1 x 1.2 (quirk) x 0.6 (DR) x 1.2 (TAG) = 0.864 dmg.

Spoiler

CombatLog.Damage [LOG] ------------------------------------------------------------- Creating an array of 1 Variance value(s) for L Laser + + + (ID 0)
CombatLog.Damage [LOG] Variance values: 0
CombatLog.Damage [LOG] ------------------------------------------------------------- Creating an array of 1 Variance value(s) for L Laser + + + (ID 1)
CombatLog.Damage [LOG] Variance values: 0
CombatLog.Damage [LOG] ------------------------------------------------------------- Creating an array of 1 Variance value(s) for Target Acquisition Gear + + (ID 2)
CombatLog.Damage [LOG] Variance values: 0
CombatLog.Damage [LOG] ------------------------------------------------------------- Creating an array of 1 Variance value(s) for Target Acquisition Gear + + (ID 3)
CombatLog.Damage [LOG] Variance values: 0
CombatLog.Damage [LOG] WEAPON: L Laser + + + (ID 0) HITLOCATION: RightArm // Damage: 36
CombatLog.Damage [LOG] Highlander takes 36 Damage to its RightArm from L Laser + + + (ID 0)
CombatLog.Damage [LOG] ==== Armor Damage: 36 / 150 || Now: 114
CombatLog.Damage [LOG] WEAPON: L Laser + + + (ID 1) HITLOCATION: RightArm // Damage: 36
CombatLog.Damage [LOG] Highlander takes 36 Damage to its RightArm from L Laser + + + (ID 1)
CombatLog.Damage [LOG] ==== Armor Damage: 36 / 114 || Now: 78
CombatLog.Damage [LOG] WEAPON: Target Acquisition Gear + + (ID 2) HITLOCATION: LeftLeg // Damage: 0.72
CombatLog.Damage [LOG] Highlander takes 0.72 Damage to its LeftLeg from Target Acquisition Gear + + (ID 2)
CombatLog.Damage [LOG] ==== Armor Damage: 0.72 / 190 || Now: 189.28
CombatLog.Damage [LOG] Actor Highlander (9e2d0fed-3d92-42ee-92d0-2cc595709f2a.0) - !!! Damage Multiplier now 1.2 from Energy
CombatLog.Damage [LOG] Actor Highlander (9e2d0fed-3d92-42ee-92d0-2cc595709f2a.0) - !!! Damage Multiplier now 1.2 from Energy
CombatLog.Damage [LOG] WEAPON: Target Acquisition Gear + + (ID 3) HITLOCATION: Head // Damage: 0.8640001
CombatLog.Damage [LOG] Highlander takes 0.8640001 Damage to its Head from Target Acquisition Gear + + (ID 3)
CombatLog.Damage [LOG] ==== Armor Damage: 0.8640001 / 45 || Now: 44.136
CombatLog.Damage [LOG] ------------------------------------------------------------- Creating an array of 1 Variance value(s) for AC/5 + + (ID 0)
CombatLog.Damage [LOG] Variance values: 0
CombatLog.Damage [LOG] Actor Highlander (9e2d0fed-3d92-42ee-92d0-2cc595709f2a.0) - !!! Damage Multiplier now 1.2 from Ballistic
CombatLog.Damage [LOG] Actor Highlander (9e2d0fed-3d92-42ee-92d0-2cc595709f2a.0) - !!! Damage Multiplier now 1.2 from Ballistic
CombatLog.Damage [LOG] WEAPON: AC/5 + + (ID 0) HITLOCATION: RightArm // Damage: 39.6
CombatLog.Damage [LOG] Highlander takes 39.6 Damage to its RightArm from AC/5 + + (ID 0)
CombatLog.Damage [LOG] ==== Armor Damage: 39.6 / 78 || Now: 38.4

As far as an exploit, well, if the devs aren't going to follow the rules of 'mech construction I don't see why I should have to either. There is a legit build -- you move two of the sinks into the torsos and the exchangers into the legs, and one sink into the arms -- so I don't feel I'm breaking things too badly. :v

They do follow the rules of mech construction but in this case is just an unresolved bug. I'm not saying that you're breaking the game, it doesn't really matter much as the game is easy to mod. But if you're going this way why not doing it for all mechs?.

 

[foamyesque]

Tested and doesn't work. PHX-1B has 2xLL+++ and 2xTAG++ (to be sure) against a 40% DR foe. You can see how the TAGs are fired last. Funny enough the second TAG does get the x1.2 increased damage.

Dangit, visually they show first. Where can I find the combat logs like that?

They do follow the rules of mech construction but in this case is just an unresolved bug. I'm not saying that you're breaking the game, it doesn't really matter much as the game is easy to mod. But if you're going this way why not doing it for all mechs?.

Because only the SLDF Black Knight does this. I suspect what happened is that they had SHS to start with, and when the SLDF one was introduced just did a pass to convert them to DHS without altering the locations at all.

 

[Doctor Machete]

Dangit, visually they show first. Where can I find the combat logs like that?

I cannot post links but you can google search for:

battletech enable combat log

OR (there are two related but different methods)

battletech enable debug mode

 

[Jade_Rook]

Originally the SLDF Black Knight only appeared in one campaign mission. There was no way to get it otherwise. That has since been relaxed. The heat sink placement is a bug, but not a major one.