CRA / CMA Math

It occurred to me recently that I don't think I've ever seen an analysis of the math behind when it's best to take a combined ranged or melee attack versus individual attacks. It seems fairly clear which is best when you're attacking very high or very low ARM or DEF targets, but there's a middle range in which it's difficult to judge.

This in mind, I've put together the below chart. I feel like this math is most useful and clearest when you look at only armor values. This first chart is looking at a unit of ten Long Gunners with POW10 guns firing at targets of various armor values between 10 and 20. For everything up to ARM15, it's pretty clear that individual attacks are best by far. And for everything from ARM18 and higher, you really want that full CRA.

But 15 through 17 are interesting. With ARM 15, you do the same damage with ten single attacks or with five two-man attacks, so it's best to do the two-man CRA to get the extra chance to hit. With ARM 16, you do the best damage by doubling up on attacks and doing five two-man attacks. And with ARM 17, average damage is the same whether you double up, do two five-man CRAs, or do the full ten-man CRA, so why not do the big one just to ensure the hit?

The equation gets a lot more complicated when you look at hit chances and high defense values, and I'm willing to bet that there are other factors I'm not thinking about at the moment, but if you think of 12-15 as the most common defense values, the bell curve becomes visible.

You can do single attacks on any target of DEF 12 or lower and be confident about the hit, but a lot of these targets are also the ones with the highest ARM, so you're best off consulting the first chart instead. With lower ARM targets, you see that DEF 13 is the lowest value at which you'd ever consider doubling up for two-man CRAs. By the time you get to DEF 14, you certainly want the extra RAT to jump from hitting on eights to hitting on sixes, which is a pretty significant 30% leap. DEF 15 is the lowest value at which you'd ever want to consider more than a two-man CRA, but you'll only see that defense on warcasters, high-value solos, or models with magical defenses like Blur or Bullet Dodger. And of course there's always the question of armor or boxes, for which we go back to the first chart.

There's a lot going on with the math behind combined attacks. Am I missing something key here? Let me know!