Analysis
So it's easy for Python to perform linear regression on a set of data and spit out coefficients. So that's the answer, right? Put in the range, damage per missile, cluster size, tonnage, etc. into a computer, plug the numbers that come out in front of new ranges, damages, etc. and enjoy your new, canon-consistent missiles.
That doesn't work for a few reasons:
Negative Coefficients
It turns out that as medium range goes up, the tonnage and crit requirements for the missile drop. I'm not sure why; I think it has something to do with MRMs and Rocket Launchers having a range distribution that doesn't match the 1/2/3 pattern of most weapons.
Most coefficients for missiles per shot are positive, which means that somehow the more capable a missile is the more of them you can cram into one ton of storage space.
Those types of effects would be a problem--and they are: a super-light missile system with a 1/20/21 range bracket would be a problem. Fortunately, we're deriving tons/missile tube, crits/missile tube, heat/missile tube, and missiles/ton from our set of data. That means that if we try to min/max one stat with a 'bad' coefficient, the other stats will swing back around and cancel it out.
Name Dmg/Msl Cl Min SR MR LR Acc %Cl Tubes Tons Heat Crits Ammo AvgDmg Cluster/To-Hit Mods
CQZ 2 5 2 7 9 21 47 0 0.84 2 7.5 10 1 70 8.4 +3, +1 to hit
CQZ 3 5 2 7 9 21 47 0 0.84 3 11.5 16 1 46 12.6 +3, +1 to hit
Let's take a look at the CQZ system. It's available in two and three shot systems because 4-shot systems generate 21 heat per shot. At 7.5 and 11.5 tons and 1 crit each, they're some of the densest weapons I've ever seen.
They have a +3 bonus on their cluster hits roll, but they also have +1 difficulty to hit. Their range is 9/21/47 with a minimum range of 7.
Their damage profile is missiles which deal 5 damage each and land in 2 point groups of damage. That averages out to around 8.4 damage for the CQZ 2 and 12.6 for the CQZ 3. Does 10 to 16 points of heat really balance that? It's a weird, good scatter PPC with a ludicrous range.
It's too good, even before you remember vehicles exist, but we can easily throw out anything with a range above 38 hexes (ELRM max range) and run the math from there. Just as those competing derived qualities can balance, there can also be sweet spots where they fail to balance.
What Equipment?
When piling all those missile stats in, which equipment gets included? LRMs and SRMs certainly. What about Rocket Launchers? ELRMs? Thunderbolt missiles? one-shot LRMs? improved one-shot LRMs? How do you even add MMLs? What does and doesn't count?
I've included Thunderbolts in almost every model and when I do, they end up with insane ammo per ton when in actuality they have very limited ammo because of how powerful they are. Unitary missiles don't seem to be compatible with regular missile types. Even if we accept an SRM 1 as, essentially, a unitary missile system.
One-shot and improved one-shot systems are likewise difficult. If we're feeding a system the same LRM stats three times with slightly different outcomes for no reason (tonnage, tonnage +0.5, and tonnage -0.5), then our numbers are going to be bad. That brings us back to templating as a solution: creating a set of very basic equations and then bolting features onto them like "one-shot," "boosted," or "enhanced."
I opted to remove os, ios, and MMLs from the equations for simplicity.
Ancillary Qualities
What about how Rocket Launchers have you roll 3D6 and take the lowest result? You notice how I ended up with cluster hit percentage as a factor in the CQZ missiles? That was necessary. Also, the ammo-lessness of RL's aren't as easy to represent as simply putting 0 in their shots/ton data.
I mean, I did that, but it didn't work well (Rocket Launchers existed so far to the edge of the bell curve that only one model satisfactory recreated them).
What about the LRM ability to use Artemis IV ammo? The MRM being Apollo FCS compatible. The strictly-better Swarm LRMs? Indirect fire ability? Rocket launchers are technically primitive technology, but primitive LRMs simply have cluster and shots/ton maluses. Enhanced LRM can explode in the tube.
None of that is modeled in the base stats and it's hard to model it in numbers. "Explodability" is not factorable.
Linear and Quadratic Relationships
The only way I could find to work with a dataset this size (around 20 weapons and around 20 factors), was linear regression. I couldn't find a quadratic function that would work with a 2D array of that size. If you know one, shoot it to me.
So necessarily things are linear and that's why Rocket Launchers don't work and Thunderbolt missiles have too much ammo. Some things, even if you're using granular factors, will still fall prey to the fact that they're too far afield to get even remotely onto the single line that mostly works for everything else.
It's a current limitation. If was invested enough to pull out some old Calc and Diff. Eq. books I might be able to do it. I'm strongly tempted. I just blasted through a three day weekend running linear regressions, critiquing models, and developing test equipment. My eyes feel funny after transferring 9 significant digits of data from my code laptop to my desktop for about 50 variables.
But I don't know if there's been a more definitive examination of Battletech missiles and if not, then I kinda owe it to my fraternity to go all the way on this. I'd like what I'm doing here to last a while.
Or at least until the release of a new Inner Sphere missile system.
I might circle back to the quadratic analysis. In the meantime, I believe that the best application is the templates model. To reverse engineer LRMs and SRMs, then reverse engineer secondary systems like MRMs and RLs that were built on top of them. Then create new systems and bolt those secondary systems onto them.
Here's a peek of the results. Boosted SRMs:
Name Dmg/Msl Cl Min SR MR LR Tubes (1) (2) (3) (4) (5) (6) (7) (8) (9) Tons Heat Crits Shots/ton
BSRM 2 2 2 0 5 8 17 2 0 1 1 1 0 0 0 0 0 1 1 1 60
BSRM 4 2 2 0 5 8 17 4 0 1 1 1 0 0 0 0 0 2 3 2 30
BSRM 6 2 2 0 5 8 17 6 0 1 1 1 0 0 0 0 0 3.5 4 3 20
BSRM 8 2 2 0 5 8 17 8 0 1 1 1 0 0 0 0 0 4.5 5 3 15
(1) Unitary Warhead - A Thunderbolt missile. SRM 1's don't count.
(2) Multifire - Capable of using alternate ammo types.
(3) Guidance - Has regular guidance as opposed to unguided MRM/RLs
(4) Booster - Has a boosted range (Extended LRMs)
(5) Hotload - Reduced minimum range. Explodes in rack (Enhanced LRMs)
(6) Streak - Missiles do not fire unless they hit, and hit with all missiles.
(7) Primitive - Special flag for Rocket Launchers.
(8) OS - One-shot systems.
(9) LRM - The base missile system is LRM (as opposed to SRM)
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