Introduction

Usually I don't care about the damage numbers that pop-up in blue, red and yellow when I watch Galaxy Legend battles. Seeing the VICTORY notification is enough!

But recently I used my Primus fleet accidentally for Infinite Cosmos and while I was still wondering what's different this time I noticed a strange thing mechanically: The Accu recharge did not work as expected.

With 100 Accu my very weak Primus Caro (augmentation level 0) dealt 9710914 damage and with being hit once she dealt 11429318 damage next turn.

Well, I am not permanently checking all numbers I see but 11.4 M damage is so much lower then 1.25 x 9.7 M damage that it worked up my curiosity.

Old Battle Equations

Old battle equations have been figured out by pioneers of the game and published in the old forum of Galaxy Legend. You can read the complete story here: http://www.tap4fun.com/forum/viewtopic.php?f=6&t=25874

But those equations do not incorporate all recently introduced commander stats like Damage Up/Down or True Damage.

Battle Equations Terms and Abbrevations

TermDescriptionRangeAbbrevationATK Attack force > 0 ATK S-ATK Special attack force boost > 0 S-ATK E-ATK Energy attack (Destroyers) > 0 E-ATK DEF Attack defense > 0 DEF S-DEF Special attack defense > 0 S-DEF E-DEF Energy attack defense > 0 E-DEF Accum Accumulator for special attacks ≥ 100 A Spec. Mod. Special attack modifier > 0 % S True Damage Guaranteed damage, can not be prevented by DEF, S-DEF > 0 TD Damage ↑ Normal attack increase damage modifier ≥ 0 % DU Damage ↓ Normal attack reduce damage modifier ≥ 0 % DD S-Damage ↑ Special attack increase damage modifier ≥ 0 % SDU S-Damage ↓ Special attack reduce damage modifier ≥ 0 % SDD Crit ATK Critical attack increase damage modifier > 150 % CAU CR DMG RES Critical attack reduce damage modifier ≥ 0 % CAD

Observation Modeling

Given the observed numbers 9710914 and 11429318 at 100 and 125 Accu, respectively, and assuming that each unblocked hit still gives +25 Accu the most simple model has been a linear function with Accu as slope and an accu-dependent part and a constant part: Damage(Accu) = Accu-dependent x Accu + Accu-independent

Using the observed numbers and d for accu-dependent and i for independant you get:

9710914 = d * 1 + i and 11429318 = d * 1.25 + i

That equation system can be solved resulting in d = 4 * (11429318 - 9710914) = 6873616 and finally i = 9710914 - 6873616 = 2837298

So the accu-independent part of that approach was 2.8 M.

My next idea was to check what commander attributes could feed a value of 2.8M for my Caroline. True Damage came into mind but my Caro only had a True Damage value of 1238701 (from Manoinver's Cabin and a R7 Purity) and all Legendary Equipment had been remove before battle.

Close to helplessness I checked my Caro again and finally noticed a small fragment of the special description: "...and 1.5M holy damage to the target..."

Ok. 1238701 + 1500000 = 2738701. That number was very close to the accu-independent part of the damage of 2837298. But the difference had yet to be explained by an underlying rule.

Finally I just divided 2837298 by 2738701 to check the relation and got 1.03600. GOTCHA!! It turned out that 1.036 - or displayed as percent value: 3.6 % - was exactly the S-Damage ↑ value of that commander.

Revised Battle Equations

I guess that tap4fun did not change the old battle equations when they included new parameters. With that underlying assumption the new battle equations can be given as follows.

To easify things I will use the following shortcuts:

- ATK - DEF ~ NAT (normal attack term)
- (S-ATK - S-DEF) + (ATK - DEF) ~ SAT (special attack term)
- E-ATK - E-DEF ~ NET (normal energy attack term)
- S-ATK + (E-ATK - E-DEF) ~ SET (special energy attack term)

Normal attack:

[Max(NAT; 0) + TD] x [(100 + DU - DD) / 100]

Normal energy attack (Destroyer):

[Max(NET; 0) + TD] x [(100 + DU - DD) / 100]

Special attack:

Update 2018-05-15 (seems like damage up/down is used, too):

[Max(SAT; 0) x (S / 100) x (A / 100) + TD] x [(100 + SDU + DU - SDD - DD) / 100]

Special energy attack (Destroyer):

Update 2018-05-15 (seems like damage up/down is used, too):

[Max(SET; 0) x (S / 100) x (A / 100) + TD] x [(100 + SDU + DU - SDD - DD) / 100]

For critical attacks upper equations have to be multiplied by:

[(CAU - CAD) / 100]

Remarks:

- If a low level player attacks a high level player the values of DEF and S-DEF can be higher than ATK and S-ATK. In order to avoid negative damage the battle terms have to be checked for being below 0. In that case I suppose they will be set to 0.
- Percent values can be used directly in these equations. E. g. the special modifier of Rick is 400 % - just set S to 400 if using these equations for calculations.

Summary

I am pretty confident that the real imlemented battle equations are those displayed here. Due to lack of time I could not verify all assumptions. Further factors that have an impact on the final damage are Stardust shields (Raksha, Moracle) and Legendary Equipments. A good test design might be to attack Primus with and without Legendary Equipment (putting the equipment in the wrong color-slot to avoid bias). Probably I find the time to conduct those experiments in next weeks or better you guys out there perform your own tests to verify or correct those equations.

If you have any questions or doubts feel free to ask or tell, respectively. If not stay tuned for future updates on that matter!