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Thread: Galactic Chairmen Guide :: Battle Equations Revised

  1. #1
    Section Leader Nachteule's Avatar
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    Galactic Chairmen Guide :: Battle Equations Revised

    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

    Term Description Range Abbrevation
    ATK 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!
    Last edited by Nachteule; August 6th, 2018 at 22:02.
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  2. #2
    Galactic Chairman Pliusomiot's Avatar
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    In my experience the most important attribute out of the new ones is CR DMG RES - with so many commanders able to hit specials every round and with relatively low AntiCrit value (compared to Critical) of most recent commanders, the CR DMG RES is the only mean i can afford to avoid one hit kills in most of the cases.

    Thank you Nachteule for sorting out the questions regarding TrueDamage (and the whole new stats saga)
    Pliusomiot.s480 /World1383/Android
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  3. #3
    Section Leader Nachteule's Avatar
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    One lesson from this is: better level-up your R7 Impact (ATK/S-ATK) than your R7 Purity for Rick.
    One level of Impact gives +25 k ATK and + 25 k S-ATK.
    One level of Purity gives +120 k True Damage.

    With special modifier of 400 % (and potential Accu overcharge) one level of Impact gives > 200k more damage in special attacks where one additional level Purity gives only 120k more.
    Last edited by Nachteule; February 28th, 2018 at 16:36.
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  4. #4
    Four-Star Admiral JLeroux's Avatar
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    Thank you Nachteule, great stuff and will come in handy! :-)
    World684(iOS) - Lvl 110
    Fleet: Elena [+15], Nicholas [+15], Richard[+15], Roland (SS)[+15] and Slade (T5)[+15].

  5. #5
    Section Leader Nachteule's Avatar
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    Recents test indicate that on special attacks the S-Damage and the Damage Up and Down is considered. (And for normal attacks the Damage Up/Down, only.)
    Galactic Chairman
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    Event log: https://docs.google.com/spreadsheets...it?usp=sharing
    PVP: Raksha [+T3], Vela'rath [+15], Nicholas [+15], Slade T-IV [+15], Roland [+15]

  6. #6
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    Quote Originally Posted by Nachteule View Post
    Recents test indicate that on special attacks the S-Damage and the Damage Up and Down is considered. (And for normal attacks the Damage Up/Down, only.)
    Great info Nach!

    Hey, I do have a question about speed. Does slot location matter as much as it used to? For example. if I slot Raksha in the middle slot of the top row and the enemy slotted Raksha in the top slot of the 1st row and we both had equal speed, who fires first? Additionally, does total speed determine 1st attack or is it based on which Raksha has the highest speed or both?

  7. #7
    Section Leader Nopo's Avatar
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    Hi Alarinn, who shoots first depends on total overall fleet speed not on individual commander's speed or slot location. slot location does determine the order of which commander in your own fleet goes first when it is your turn to shoot. As to if both fleet are the same speed. that i am not sure who shoots first
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  8. #8
    Quote Originally Posted by Nopo View Post
    As to if both fleet are the same speed. that i am not sure who shoots first
    If I am not mistaken is the attacker. In situations like Pandora and CCC, no idea how they define who is the attacker and the defender, but Arena, GL and CtC are easy to evaluate.

  9. #9
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    Quote Originally Posted by Nopo View Post
    Hi Alarinn, who shoots first depends on total overall fleet speed not on individual commander's speed or slot location. slot location does determine the order of which commander in your own fleet goes first when it is your turn to shoot. As to if both fleet are the same speed. that i am not sure who shoots first
    Oh ok then I'll need to readjust my fleet. I have as much speed as I can afford right now with half my fleet with lvl 9 dual r7 and the other half at lvl 8. Takes so long to get 5+M gala energy.

  10. #10
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    Quote Originally Posted by Nightbolt View Post
    If I am not mistaken is the attacker. In situations like Pandora and CCC, no idea how they define who is the attacker and the defender, but Arena, GL and CtC are easy to evaluate.
    Yep and the attacker can beat anyone as long as he can last 18 or so rounds when Tap ends the battle and awards it to the attacker. I had a lvl 99 newbie attack me in GL and his Raksha was his beast because he had full cabin and 2 eye IIIs and I couldn't finish him off. I was completely untouched but lost the battle because Tap sides with the attacker.

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