So I was trying to create a little "how many hits to kill each unit with different modifiers" spreadsheet.

Mostly to help me to know when buying HP/ATK up in the research center was actually impactful.

Anyway, I was trying to figure out the actual math so my spreadsheet would work, and came across this weird bit of math the devs decided to do.

Any stat increase (Heavy Armor Specialist, Senior Attack/Defense Specialist, ATK/HP in research center, Amp Core, Firepower control system, etc.) ends up being additive with any other stat increase on the unit.

BUT, any stat DECREASE (cost control, "mass produced" units, "extended range" units) ends up being multiplicative. Specifically talking about ATK% and HP% here.

So, for instance, if you have Cost Control (-13% stats), you're using Sledgehammers, you took mass produced sledges (-30% stats), you purchased both research upgrades ( 10% ATK, 15% HP), and you applied an amplifying core to them ( 75% stats), their stats would go through the following formula:

 Base * (1   Research   Amp Core) * (1 - Cost Control) * (1 - Mass Produced)

With actual numbers:

• HP: 3,264 * (1 0.15 0.75) * (0.87) * (0.7) = 3776 HP.

• ATK: 608 * (1 0.1 0.75) * 0.87 * 0.7 = 685 ATK.

I confirmed in the practice tool that this is how it works. I don't know why, but this essentially makes stat decreases have less impact than they appear to have.

If they were additive like the increases instead, the above sledges would have 3535 HP, and 641 ATK.

Increases are likewise less impactful as additive than multiplicative. The original sledges, but multiplicative increases instead, would have 4000 HP, and 713 ATK.

The only exception to the above rules is level ups. They are multiplicative. The 3776 HP, 685 ATK sledges above go to 7553 (rounding) and 1370 ATK at level 2. Again, confirmed in the practice tool.

This is why adding a 100% ATK "Improved Firepower Control System" equipment (or any stat increase equipment, this one is just easy to understand) to a unit doesn't always increase their stats by a clean double. It ends up being additive with other increases to the unit. Meaning these cards are slightly less effective than they appear if you have other stat increases on the field (research, specialist cards, etc.).

In other words, if you had already purchased the ATK research, your units will have 10% ATK. If you apply the 100% card to them, they'll now have 110% ATK from base, not 120%. Their attack will increase by the base attack. For tanks specifically this will look like:

 608 * 110% = 669   608 = 1277.

 1277 / 669 = 191%.

If you were confused why the stat didn't double when you applied something like this, that's why.

I guess this decision was to minimize the impact of both increases and decreases, so neither got out of control. Still it's an oddity and it caused me a lot of headache. I haven't seen this discussed anywhere, including the wiki, so I figured I'd put it out there somewhere in case someone out there cares. :)

TL;DR

ATK/HP equations work like this:

 Base * (1   Increase1   Increase2   ...   Increase(n)) * Decrease1 * Decrease2 * ... * Decrease(n)