The advantage of smaller missile racks

[happybjorn]

Warning: this is rather dry stuff.

Some debate over the effectiveness of larger and smaller missile racks came up in the ‘Talon’ thread. It looks like this led to some of the changes made in the 1.21 patch. These changes made larger missile racks more effective than they were, but they are still less effective than smaller missile racks.

I put together a spreadsheet for weapons in TOS. It is very similar to the one provided in the unofficial guide, but it also has a number of derived statistics, the important ones here being damage per second (dmg/s), heat per second (C/s), and damage per degree of heat (dmg/C). I am including one more stat for the LRM racks, which is damage per second divided by weight (dmg/t). This comparison is important because it shows another way in which the smaller rack is more efficient (For other rack types this comparison is equivalent to dmg/s).

Lets compare the GMH2 and GMH4 racks to begin with:
a) The GMH2 does .444 dmg/s, creates .333 C/s, and does 1.333 dmg/C.
b) The GMH4 does .64 dmg/s, creates .48 C/s, and does 1.333 dmg/C.
c) 2 GMH2 racks do .888 dmg/s, create .667 C/s, and do 1.333 dmg/C.
This shows that 2 GMH2 racks are more efficient than a GMH4 rack (by about 39%). It also shows that the larger missile rack is not more heat efficient as both weapons have the same dmg/C stat.

The unguided missile racks are a little more complicated to compare because not all missiles in a volley will hit. It seems like the best way to calculate this is to assume that an average number of missiles hit, so the damage formula I am using is [(minimum number of missiles per hit + one half of remaining missiles)*damage per missile]. For the SRM racks the comparisons are:
d) The SRM4 does .5 dmg/s, creates .417 C/s, and does 1.2 dmg/C.
e) The SRM8 does .813 dmg/s, creates .625 C/s, and does 1.3 dmg/C.
f) 2 SRM4 racks do 1.0 dmg/s, create .833 C/s, and do 1.2 dmg/C.
This shows that 2 SRM4 racks are a more efficient source of damage than a SRM8 rack (by about 23%). The SRM8 rack is more heat efficient, although by a much smaller amount (about 8%).

The LRM comparisons are:
g) The LRM6 does .533 dmg/s, creates .8 C/s, does .667 dmg/C and .097 dmg/t.
h) The LRM9 does .65 dmg/s, creates .9 C/s, does .722 dmg/C and .072 dmg/t.
i) The LRM12 does .72 dmg/s, creates .96 C/s, does .75 dmg/C and .055dmg/t.
j) 2 LRM6 racks do 1.067 dmg/s, create 1.6 C/s, do .667 dmg/C and .097 dmg/t.
This shows that 2 LRM6 racks are a more efficient source of damage than a LRM12 rack (by about 48%). The LRM12 is more heat efficient, again by a smaller amount (about 12%). Comparing the dmg/t stat shows that the LRM6 rack efficiency is greater still (by roughly 76% compared to the LRM12 rack).

For the sake of thoroughness the NM comparisons are:
k) The NM7 does .375 dmg/s, creates .5 C/s, and does .75 dmg/C.
l) The NM14 does .55 dmg/s, creates .7 C/s, and does .786 dmg/C.
m) 2 NM7 racks do .75 dmg/s, create 1.0 C/s, and do .75 dmg/C.
This shows that 2 NM7 racks are a more efficient source of damage than a NM14 rack (by about 36%). The NM14 is more heat efficient (about 5%).

When presented with the choice between taking one large missile rack or two small missile racks it seems clear that it is advantageous to take the two small racks. The 1.21 changes are an improvement (IIRC, prior to 1.21 all missiles of the same type had the same heat efficiency, which I'm representing as dmg/C, and larger racks had lower dmg/s), but I think missile racks are still not balanced. There are several stats that can be tweaked balance them, but it seems to me that the easiest one to change that would make the most difference is weight.

[Burzmali]

Try not to forget that firinig 2 weapons in sequence may force you to split the 2 attacks over a heat shift, i.e. one shot in the blue and one in yellow, lowering your expected damage. Also, impacts from missile hits are added together for knokdown, side effects aside, the damage for the fall should be added. I don't know if that will tip the scales, but it should be added.

[happybjorn]

These are both good points. Their not being included is more a matter of the method of comparison I choose than oversight though. It pretty much comes down to statistics being the third type of lie.

The problem with heat you mentioned is situational and should average out over time. This objection really doesn’t apply to the method I used. I assumed that all racks would be firing at maximum rate of fire and always scored a hit (an average hit in the case of unguided missiles). While not exactly accurate in terms of representing the game, I felt it safe because the ratios would be the same (it’s a comparison of racks of the same type). Still, the reality is that situations like this do come up and many of them favor larger missile racks.

Critical hits don’t work well in this particular analysis. For example, assume that all twelve missiles from a LRM12 rack hit a titan. The average number of missiles that hit the center torso, the most likely location to be hit, is 1.8. This will not cause more that 4 points of damage so it is not enough to cause an instability check or critical hit, at least until the exterior armor is gone (also, once the external armor is gone 2 smaller racks are more likely to cause a critical hit because of their higher dmg/s). I can't continue with the analysis even though I know that missile hits sometimes cause critical hits (actually I could put together a distribution table instead of a simple average, but its not worth it).

If I could continue calculating instability checks there are too many variables to take into account and I would have to start making a lot of assumptions (lots of assumptions makes for poor logic). The important things to know are 1) chance of causing a skill check, 2) piloting skill of target, 3) move mode of target, 4) weight of target, 5) all skill check modifiers for target. Move mode and weight of target are going to determine how much damage the titan takes when it falls, while piloting skill and skill check modifiers determine the chance of falling if a check is caused. Skill check modifiers is a huge category, including chassis type, move mode, terrain type, gyro and actuator damage, missing titan locations, heat, jock injuries, and so on. I would have to make assumptions for 2) through 5) above and, further, they relate to the target and instability checks, not the missile racks in question.

I disagree that these things should be included in the calculations. I do think they are valid objections and should be taken into consideration when evaluating which weapon to use. I prefer to consider the situational circumstances when they apply, which are mostly going to be for individual titan designs. For instance, if I have medium titan that takes 16-17 seconds to run to a new hex I would rather have a SRM8 rather than 2 SRM4s.

[Thorgrim]

Yep, I did all those calculations, including min and max potential damage for UGMs, and SRM8 with 1 and 2 ammo slots, and told Larkin that IMO it was still not enough. Maybe there will be another patch.
There's also # of slots to consider, and larger racks may use less slots.

[Thorgrim]

ORIGINAL: Burzmali

Also, impacts from missile hits are added together for knokdown, side effects aside, the damage for the fall should be added. I don't know if that will tip the scales, but it should be added.

If you fire both racks in sequence, the grouped damage should be the same, as the # of rolls is the same. The RNG doesn't care how many rolls are made "per weapon", each roll is perfectly independent of every other.
If you were comparing _one_ smaller rack with one larger one, then you could have a point. But that's not the case.

[Burzmali]

Sheesh, Thorgim, let me spell it out for you.

If you are at 49 degrees when you fire a large missile rack, the attack has no penalty.
If you are at 49 degrees and fire your first small rack, your heat spikes over 50 degrees causing your second small rack to fire at a 5% penalty.

Hence there is a MARGINAL benefit to have a larger rack IN THIS CIRCUMSTANCE.

Likewise,

If you fire a small rack at a target the odds that you land enough missiles to cause an instability check is smaller than a large rack.

[Thorgrim]

Heh. Did I quote anything about the heat issue? Nope. Are you that desperate? [;)]
About the instability, yep, I was thinking of damage spread. But with 9 locations, and racks being relatively small (the LRM12 being the largest), it's not much of an issue, since at least 3 missiles have to group on a location to have a very very small chance to cause an instability check, which in turn can result in a skill check, which can lead or not to a fall.

And BTW, there's this thing called 'wait on heat' [:'(] You don't have to fire them in sequence -> this if you want to analyze the racks beyond their stats.

[Thorgrim]

ORIGINAL: happybjorn
When presented with the choice between taking one large missile rack or two small missile racks it seems clear that it is advantageous to take the two small racks.

In terms of damage output, yes. The larger racks place less of a burden on the heat reg though. But you'll always want to go for the damage [:D]

There are several stats that can be tweaked balance them, but it seems to me that the easiest one to change that would make the most difference is weight.

That would have a huge impact on the database, and that's the reason it wasn't changed. Some stats just cannot be touched.

[LarkinVB]

Happybjorn, please add the number of slots used into your statistics too.

This will make a difference for LRM and GMH.

[Thorgrim]

Yep, double LRM6s will take at least 8 slots, whereas one LRM12 can be fitted into 6 - or 7 if you want the same long run damage potential (with more missile hits on average due to the increased min thresholds). Of course, it takes longer for the LRM12 to deliver the full damage potential, due to the higher recycle time.
Same goes for all other missile types.

[Thorgrim]

ORIGINAL: Burzmali
Try not to forget that firinig 2 weapons in sequence may force you to split the 2 attacks over a heat shift, i.e. one shot in the blue and one in yellow, lowering your expected damage.

There's also some form of reverse of this: with the larger rack, when you miss (even at high odds) you miss completely; with twin smaller racks, even if you miss with one, you might hit with the other (even with a heat penalty).

[happybjorn]

Yes, # of slots can also make a difference. I’m not certain that there is a good way of calculating this, but will try looking at in two different ways.

The first way is to take dmg/s for 2 small LRM and GMH racks and adjust it for number of slots (dmg/s*7/8). The new comparisons are:
c2) 2 GMH2 racks do .777 dmg/s.
b2) The GMH4 does .64 dmg/s.
The two smaller GMH racks are about 21% more damage efficient.
j2) 2 LRM6 racks do .934 dmg/s.
i2) The LRM12 does .72 dmg/s.
The two smaller LRM racks are about 30% more damage efficient.

The second way of looking at this is to take an example of designing a GMH assault titan. I have a 200 ton design that incorporates 4 GMH4s (two ammo slots each), one in each shoulder and arm, and have used up all free slots in these locations. In order to switch them for 8 GMH2s (one ammo slot each) I will have to change to a heavier armor or larger chassis type. I choose to switch to a larger chassis type and my titan is now 3 tons heavier. As this is too heavy I drop one of the GMH2s (in one of the shoulders) for a net gain of 3.5 tons of free weight. I will use this to increase my heat reg by one level (this will probably mean upgrading from a heat reg 5 to a heat reg 6, which is a difference of 2.5 tons) and have a little bit of extra space and weight (1 ton) to improve my systems with. The result is that I have the same dmg/s comparison shown in c2) and b2) above , but I have also managed to increase my titan chassis by one level (increasing bmt and internal armor, but will probably take a larger chassis handling penalty), improve my heat reg by one level (note: this is necessary to deal with the increased heat of the smaller racks. It is of some additional benefit when dealing with core maps and enemy titans that raise your heat), and have 1 free ton to improve one of my systems.

Using the same example with LRMs doesn’t work as well. Choosing to go with 7 LRM6s and a larger chassis frees up net 10.5 tons and a little bit of space. However, it requires three more levels of heat reg to handle the extra heat, which should take up 8.5 tons, and the 2 extra tons left should probably be spent on heavier armor (milennia). The heat created by 7 LRM6s is almost the same as the max heat reduction possible on a titan (the heat created is .08C/s higher than the heat reg can handle without taking a defense check into account). This doesn’t seem like an optimal design to me.

So, after considering both of these ways of looking at the problem, I have to agree that # of slots is a factor that favors larger missile racks. Because I failed to take this into account earlier I think that the dmg/s comparisons in my initial post are inflated. I am content with the new comparison as it still shows that 2 smaller missile racks are more efficient than one large rack.

Alas, I don’t know the best way to represent this for NM and SRM racks, but I feel that these numbers should be modified too. Since I am partial to the example given above I am modifying these as dmg/s*7/8 for 2 small racks. While this an arbitrary adjustment it seems more accurate, to me at least.
m2) 2 NM7 racks do .656 dmg/s.
l2) The NM14 does .55 dmg/s.
The two smaller NM racks are about 19% more damage efficient.
f2) 2 SRM4 racks do .875 dmg/s.
e2) The SRM8 does .813 dmg/s.
The two smaller SRM racks are about 8% more damage efficient.

[Thorgrim]

ORIGINAL: happybjorn
I will use this to increase my heat reg by one level (this will probably mean upgrading from a heat reg 5 to a heat reg 6, which is a difference of 2.5 tons)

If it'd be from 6 to 7 though, that'd mean 2 additional slots, one in each arm.

The result is that I have the same dmg/s comparison shown in c2) and b2) above ,

Except that you've just dropped one small rack, so you've reduced your firepower by 1/8.

but I have also managed to increase my titan chassis by one level (increasing bmt

Not that BMT is that important for supports [;)]

improve my heat reg by one level (note: this is necessary to deal with the increased heat of the smaller racks. It is of some additional benefit when dealing with core maps and enemy titans that raise your heat),

It also makes the reg more vulnerable to crits/mesons/EMPs/lost limbs if it requires more slots.

Using the same example with LRMs doesn’t work as well. Choosing to go with 7 LRM6s and a larger chassis frees up net 10.5 tons and a little bit of space. However, it requires three more levels of heat reg to handle the extra heat, which should take up 8.5 tons, and the 2 extra tons left should probably be spent on heavier armor (milennia).

And 2 or 4 more slots for the reg.

Alas, I don’t know the best way to represent this for NM and SRM racks, but I feel that these numbers should be modified too.

Notice that for SRMs, for the same max damage potential (SRM8 with 2 ammo slots), # of slots is the same. So no mod should be applied. For NMs it should be 5/6, but the difference is not that big.

[happybjorn]

Hmm, probably should have explained my second way of looking at the problem a little better. It is an attempt at giving a practical example of taking smaller missile racks to increase your raw dmg/s while also taking into account the increased heat reg you would need to compensate for the increased heat the smaller racks produced. It hardly seemed like it would be a fair comparison to get the extra space and weight by sacrificing systems or armor so I got them by dropping a small rack and increasing chassis size.

ORIGINAL: Thorgrim
If it'd be from 6 to 7 though, that'd mean 2 additional slots, one in each arm.

It wouldn't be. Heat 6 should provide somewhere between -3.15C/s and -3.45C/s depending on what armor you use. That is more than enough for 9 GMH2 racks. If you added a shield to this (9 GMH2 racks that is) it would run a little bit hot (you would be fine if you made your defense check though).

Except that you've just dropped one small rack, so you've reduced your firepower by 1/8.

Yes, I took that into account. They may be two different examples but they conviently use the same math when comparing dmg/s with a larger rack.

And 2 or 4 more slots for the reg.

It would be 2 more slots, unless you had insufficient heat reduction to handle the LRM12s. 4 LRM12s calls for Heat 7 or better, the largest heat reg, Heat A, takes 2 more slots than that. Since the additional slots are in the LoT and CBT I wouldn't worry much about critical hits and you have bigger problems than heat if you lose one of those locations [;)]

Notice that for SRMs, for the same max damage potential (SRM8 with 2 ammo slots), # of slots is the same. So no mod should be applied. For NMs it should be 5/6, but the difference is not that big.

I applied the mod to the NM and SRM racks according the second way of looking at the problem. Unlike the LRM and GMH racks though I didn't double check them in the factory and on paper (bad me). The SRM mod seems fine. I was wrong about he NM mod, 5/6 is more accurate . So the comparison between 5 NM7s and 3 NM14s should show that the smaller racks are 14% more damage efficient (a difference of 5% from the 7/8 comparison).

[Thorgrim]

ORIGINAL: happybjorn
Hmm, probably should have explained my second way of looking at the problem a little better.

I understood it perfectly well, was just poiting out some details. I don't think a pure statistics analysis is enough to judge the effectiveness of the racks. There are other things to take into consideration, that are just not quantifiable.

It wouldn't be. Heat 6 should provide somewhere between -3.15C/s and -3.45C/s depending on what armor you use. That is more than enough for 9 GMH2 racks. If you added a shield to this (9 GMH2 racks that is) it would run a little bit hot (you would be fine if you made your defense check though).

What I meant was, IF you had to upgrade from 6 to 7, regs 7 and 8 take 2 additional slots. So that would also have to be taken into consideration IF you wanted to make a full analysis - the reg upgrade possibly requiring more slots. Notice that all this should apply for general design, not just for pure GMH/LRM designs. Take the Talon example: there's only one SRM8 rack that can be replaced with twin SRM4s.

Yes, I took that into account. They may be two different examples but they conviently use the same math when comparing dmg/s with a larger rack.

What I meant was that 7 racks don't dish out the same dmg/sec as 8. So you really can't use those numbers (2 small vs 1 large) in those examples you gave. [;)]

It would be 2 more slots, unless you had insufficient heat reduction to handle the LRM12s. 4 LRM12s calls for Heat 7 or better, the largest heat reg, Heat A, takes 2 more slots than that.

Again, 3 more levels of reg like you said could be something like 2 or 4 more slots, depending on the design. See above.

Since the additional slots are in the LoT and CBT I wouldn't worry much about critical hits and you have bigger problems than heat if you lose one of those locations [;)]

It's a vulnerability, which is never good.

[Thorgrim]

ORIGINAL: happybjorn
The SRM mod seems fine. I was wrong about he NM mod, 5/6 is more accurate . So the comparison between 5 NM7s and 3 NM14s should show that the smaller racks are 14% more damage efficient (a difference of 5% from the 7/8 comparison).

Not sure how you're doing your calculations. Your first set of results was modified by 7/8 to compensate for # of slots.
For your 2nd way of looking at the problem, they should have been further modified for the small rack that was dropped, if applicable.
So, how is the SRM mod fine? It shouldn't be modified for slots, and your example wouldn't certainly pack only 4 SRM8s, not sure if any rack would have to dropped.
NMs, the 1st mod would be 5/6 (for slots), but what about the dropped NM7? Why not a quad NM14?

[Burzmali]

Well, since large rack is not purely worst (i.e. never better in a single characteristic than two single racks), the only fair way to compare would be to do a linear regression. Unfortunately, there aren't enough data points to pull that off, so the best bet would be to pool the missiles and reduce the number of variables to equal the number of equations.

For instance,

x1 * weight + x2 * heat + x3 * volume + x4 * recharge_rate + x5 * ammo_capacity + x6 * range + x7 * heat_generated(NM) + x8 * emission_seeking(GME) + x9 * heat_seeking(GMH) = damage

and solve the set of equations. But since you can only draw meaningful data from a surplus of points, you might have to combine several of those concepts, not to mention the interactions, and the whole thing is a real pita. Regression is a hassle without enough information. If I get a chance I'll try to crunch the numbers to see since, there are 10 missile racks, the formula above can generate any meaningful results.