The SimChamber Arts of War: Mathematics

[Freyia]

As you can see, this section talks about the calculations involved when resolving your attack power or defence strategies. Since doing different calculations in different orders yield different results, we have a standard order in processing calculations.

By the way, please triple check your calculations when you post your phases. I'm sure that the mods have their own tutors available for private lessons...

[Freyia]

1. Resolving Attack Strength[/b]

Occasionally you will have pilot abilities or items which boost your attack strength. The question is: In which order do you process them in?
The stages in resolving your initial attack strength are as follows:


1. Resolve Seishin effects
2. Resolve Pilot Ability
3. Resolve Inherent Ability
4. Resolve System Ability
5. Resolve Item Ability
6. Resolve Terrain Effects

- Seishin effects refers to the spells Hot Blood and Spirit which boost the damage dealt
- Pilot Ability refers to your Pilot Class, such as Getter Pilot, Personal Trooper Pilot (which have damage modification abilities). Ki-Ai also occurs during this phase, and is resolved before Dairyoku. Pilot Abilities also include abilities like the bonuses given by Anima Spiritia songs, or Ally Synchro
- Inherent Ability refers to any non-system damage modifier that is originally existant in the mech, such as Bestial Fury, Analyze, etc. This also includes any bonuses or penalities given by the terrain.
- System Ability refers to any Installed Systems, inherent to the mech or equipped, which modifies your damage, such as EXAM System or Zero System.
- Item Ability refers to individual items, excluding systems which can add damage to your weapons, such as V-Up (W), Shuffle Union Badge, etc. Items which boost damage by a multiplier or a percent (ie +25% or *2) apply their effects before items which give a fixed value bonus (ie +10).
- Terrain Effects refers to any effects that the current fight terrain may give that increases weapon damage (such as Element/Affinity or Scorched Earth).

Please note that you do rounding only at the END of all calculations.

At the end are examples showing how your final values are calculated.

[Freyia]

2. Resolving Defence Damage[/b]

This is the biggie. When you receive an attack, lots of factors kick in, such as Armor, Blocking, Barriers, etc. As with Attack Strength, if you do different things the outcome will be different. Again, we have a specific flow to resolve our damage. Please memorize it. They are listed as follows, assuming you do NOT dodge the attack:

1. Receive Attack
2. Resolve Terrain Effects
3. Resolve Blocking
4. Resolve Seishin Effects
5. Resolve Pilot Ability
6. Resolve Shields
7. Resolve Barriers
8. Resolve Armor
9. Resolve Systems/Items[/b]

- Terrain Effects refer to any effects that the current fight terrain gives that reduces damage received (such as Element/Affinity or Deep Water).
- When you Block, ALL damage received this turn is automatically halved, at the expense of your attack phase.
- Seishin Effects refers to spells such as Resist and Iron Wall which effect the amount of damage taken.
- Pilot Ability refers to your Pilot Class, such as Mazin Pilot (which can decrease damage received). Ki-Ai also occurs in this phase, and is resolved before Dairyoku. This also includes abilities such as the effects from Anima Spiritia songs.
- Shields are only usable if the unit has the Shield inherent ability (from normal Shield to special shields like Beam Shield) or if equipped with Installable Shield and halves damage when used for a single received attack. Watch your shield uses, for you can only do it a certain number of times, modified by rank, class, or mech/item abilities. Shields which also nullify certain amounts of damage (such as Beam Shield) apply their affects after the halving.
- Barriers are whose which can decrease damage when activated, such as I-Field, Gravity Wall, or Distortion Field. You pay the resources required for the barrier, and apply it's effects to a single incoming attack, unless the barrier states otherwise. The mech needs an installed Barrier to use this phase, either inherent to the mech or installed.
- Armor is comprised of inherent damage reduction (ie: Damage Received -25%) and any installed Armor-class items or abilities (ie: Chogokin Nu-Z (Armor): Damage received -40%). The damage reduced in this phase stacks, so if you have a unit with an inherent Damage Reduction -25% ability and you equip Chogokin Nu-Z, your reduction during this phase is now 65%. Take note that you cannot get more then 75% damage reduction during this phase (no equipping Space Gren Alloy on that Baron Schnell and having 110% DR for you!). Phase Shift Armor is not affected by the reduction cap, since it is a fixed-value reduction. Any sort of damage reduction which does not fall into any other category stacks here. This includes any inherent ability reduction (such as Element or Bullet Endure).
- Systems and items refers to any installed systems or items which can reduce damage, either through a percent or a fixed value, which is not Armor or Barrier-class. Examples are Zero System and Brave Hero Crest. The reduction during this phase does not stack, all reduction is applied seperately.

Please note that you do rounding only at the END of all calculations.

The minimum damage you can take through percent and multiplicative means is 1. Fixed value reductions may reduce the damage to 0.

At the end are examples showing how your final values are calculated.

[Freyia]

3. Resolving Dodge Cost[/b]

What happens when you've been targetted by someone when they have some special modifier that affects your dodge cost? What happens when you also have something similar? These are some situations you will need to think about, but the concept is easy. There are several exceptional situations you need to thing about, though.

A: When you're in a battleship[/b]
- Your dodge cost is locked at the value given by the Mothership Class inherent. If you decide to dodge, you pay that value each time, no matter what effects are applied to the attack.

B: When you have a Green Haro or Yellow Haro
- With Green Haro, your initial Dodge Cost, before all modifiers, becomes 5. Any modifiers are then applied to it to determine your final Dodge Cost
- With Yellow Haro, your dodge cost is LOCKED at 5. So no matter what modifiers are applied to the attack, you only pay 5 PCs to dodge it.

C: When you're in a battleship AND have a Green/Yellow Haro[/b]
- Battleships, believe it or not, are not crazy dodgers. The Mothership Class inherent ability overrides the effects of the Haros, so it's kinda pointless to install either of them, other then getting the extra Seishin pool.

D: All other times
- Just take the Net (final) amount of the dodge cost modifiers. But like Attack and Defence, there is an order in which these are applied. The order is as follows:

1. Resolve Opponent's Multiplicative Modifiers
2. Resolve Opponent's Fixed Modifiers
3. Resolve Own Multiplicative Modifiers
4. Resolve Own Fixed Modifiers

- Multiplicative modifiers are effects that multiply your Dodge Cost, such as Self Destruct, which has a x2 Dodge Cost modifier.
- Fixed Modifiers are effects that modify your Dodge Cost by a fixed value, such as Tesla Drive, which gives a -5 Dodge Cost modifier.

- Once the net modification is determined, apply that to your starting Dodge Cost to determine your final DC.
- Note that the minimum DC you can obtain is specified as one of your class abilities. You cannot dodge for any less then this, no matter what modifiers, unless otherwise stated.

[Shuu]

4. Resolving Chip Effects[/b]

So, you've gone and earned yourself some chips, eh? I bet you're wondering how their effects apply now. Especially if this isn't your first, and you really like this one unit. Like with all other aspects of Sim Chamber math, Chip effects follow a simple rule of multiplication, then addition. Follow this simple series of steps.

1. Add all multiplicative bonuses
2. Apply bonuses to base unit
3. Add all additive bonuses
4. Apply bonuses to base unit
5. Round HP and EN to closest multiple of 5

Let's break this down, now, for easy understanding.

Let's say that I own an Ice Chip (+25% HP, EN, and weapon damage), a Silmaril Chip (+50% HP/EN), an Assault Booster chip (+25% weapon damage), and 2 Output Booster chips (+10 EN each). I want to put all 5 on the following unit.


Musha Victory

Stats:
HP: 45, EN: 30, IS: 3, Move: G, Size: SS

Weapons:
Ressenmaru (BM)- 16 damage
Mega Beam Rifle (B)- 16 damage, 10 rounds. Tenrai Hengen only.
Mega Beam Buster (BS)- 30 damage, 1 EN/shot. Tenrai Hengen only.
Hien Gaeshi- 50 damage, 2 EN/attack
Beam Wing (S)- 70 damage, 5 EN/attack
Hien Tatsumaki Gaeshi (SV)- 12 damage/EN

Inherent Abilities
1) Usable by Ensigns or higher
2) Shield: Tenrai Hengen Only
3) Countercut
4) Tenrai Hengen: Pay 10% of your PC limit to activate. Dodge Cost -10, Damage Received -20% and gain Move: F. Unit's Affinity is Multi. Enable Mega Beam Rifle and Mega Beam Buster. HP -1 every other turn. Can be deactivated at any turn.

Purchasing Cost: 500 PCs


First step, #1, is to add up all multiplicative bonuses. In this case, we have +25% HP/EN from Ice and +50% HP/EN from Silmaril, and +25% weapon damage from both Ice and Assault. This means a +75% bonus to HP/EN, and a +50% bonus to weapon damage. Now we apply these bonuses.


Musha Victory

Stats:
HP: 78.75, EN: 52.5, IS: 4, Move: G, Size: SS

Weapons:
Ressenmaru (BM)- 24 damage
Mega Beam Rifle (B)- 26 damage, 10 rounds. Tenrai Hengen only.
Mega Beam Buster (BS)- 45 damage, 1 EN/shot. Tenrai Hengen only.
Hien Gaeshi- 75 damage, 2 EN/attack
Beam Wing (S)- 105 damage, 5 EN/attack
Hien Tatsumaki Gaeshi (SV)- 18 damage/EN

Inherent Abilities
1) Usable by Ensigns or higher
2) Shield: Tenrai Hengen Only
3) Countercut
4) Tenrai Hengen: Pay 10% of your PC limit to activate. Dodge Cost -10, Damage Received -20% and gain Move: F. Unit's Affinity is Multi. Enable Mega Beam Rifle and Mega Beam Buster. HP -1 every other turn. Can be deactivated at any turn.

Purchasing Cost: 500 PCs


After this, we now add up the additive bonuses. In this case, it's 2 +10 EN chips. This gives us +20 EN, so our new stats are:


Musha Victory

Stats:
HP: 78.75, EN: 72.5, IS: 4, Move: G, Size: SS

Weapons:
Ressenmaru (BM)- 24 damage
Mega Beam Rifle (B)- 26 damage, 10 rounds. Tenrai Hengen only.
Mega Beam Buster (BS)- 45 damage, 1 EN/shot. Tenrai Hengen only.
Hien Gaeshi- 75 damage, 2 EN/attack
Beam Wing (S)- 105 damage, 5 EN/attack
Hien Tatsumaki Gaeshi (SV)- 18 damage/EN

Inherent Abilities
1) Usable by Ensigns or higher
2) Shield: Tenrai Hengen Only
3) Countercut
4) Tenrai Hengen: Pay 10% of your PC limit to activate. Dodge Cost -10, Damage Received -20% and gain Move: F. Unit's Affinity is Multi. Enable Mega Beam Rifle and Mega Beam Buster. HP -1 every other turn. Can be deactivated at any turn.

Purchasing Cost: 500 PCs


Lastly, we now round HP and EN to the nearest multiple of 5. This means that values from 0 to 2.49999... and 5 to 7.49999... round down, while the other values round up. This means that the final stats for our test unit is:


Musha Victory

Stats:
HP: 80, EN: 75, IS: 4, Move: G, Size: SS

Weapons:
Ressenmaru (BM)- 24 damage
Mega Beam Rifle (B)- 26 damage, 10 rounds. Tenrai Hengen only.
Mega Beam Buster (BS)- 45 damage, 1 EN/shot. Tenrai Hengen only.
Hien Gaeshi- 75 damage, 2 EN/attack
Beam Wing (S)- 105 damage, 5 EN/attack
Hien Tatsumaki Gaeshi (SV)- 18 damage/EN

Inherent Abilities
1) Usable by Ensigns or higher
2) Shield: Tenrai Hengen Only
3) Countercut
4) Tenrai Hengen: Pay 10% of your PC limit to activate. Dodge Cost -10, Damage Received -20% and gain Move: F. Unit's Affinity is Multi. Enable Mega Beam Rifle and Mega Beam Buster. HP -1 every other turn. Can be deactivated at any turn.

Purchasing Cost: 500 PCs


Impressive, eh? Chips can make units very powerful, or can help to shore up weaknesses.

One final note, though. Remember that all chip effects apply on only the base unit. Should you have any ability that improves any affected stat (such as Orbital Frame, Beam Crystal Phoenix Fan, or Zero System), these abilities apply after the chip rounding occurs.

[Shuu]

Now, I'll introduce a few case studies to give you a better idea of how the above phases work in the SimChamber.

Case Study 1: GEAR Fighter Dendoh vs. Knight Gear Ogre

Knight Ogre attacks the GEAR Fighter with the following weapon:

Kumogami - Minatsuchi (V)- 25 damage/EN

For 12 EN worth, making 300 damage. Of course, the GEAR Fighter doesn't dodge, and thus accepts the attack. This seems like it'd be instant death, but the GEAR Fighter is currently in UD mode and installed Chogokin Nu-Z armor. Let's see what we end up with:

DEFENSE PHASE:

Attacking Weapon #1: Kumogami - Minatsuchi
Action Taken: Block, Iron Wall, Fire Wall
Damage Taken: 11 (!?!)
[/color]

300 damage reduced to only 6? Impossible? Maybe not. Let's see how it was done.

1. Receive Attack
Kumogami - Minatsuchi- 300 damage

2. Resolve Blocking
Blocking reduced all incoming damage by half, so:
300/2 = 150
Now the damage is down to 150.

3. Resolve Seishin Effects
Hokuto thankfully had the Iron Wall spell in his collection, which reduces damage by another /4.
150/4 = 37.5
Already brought it down to 37.5.

4. Resolve Pilot Ability
Unfortunately, Hokuto and Ginga are just normal children (at least, as normal as you can get piloting a super robot), and so have nothing during this phase.

5. Resolve Barriers
Dendoh UD has an inherent barrier called Fire Wall, which reduces all damage by 20, therefore:
37.5 - 20 = 17.5
Brought down to a mere 17.5.

6. Resolve Shields
GEAR Fighters don't come with these, so nothing is applied here.

7. Resolve Armor
The Chogokin Nu-Z armor installed reduces damage by 40%, so:
17.5 x .6 = 10.5
In other words, take 100, subtract it by the % reduction (in this case, 40), then divide by 100 to find the value to multiply the damage by.

8. Resolve Systems/Items
None here.

9. Round
.5 is closer to 1 then 0, so 10.5 rounds to 11.

So, to recap, the total damage Dendoh takes is a mere 11. A 96% reduction in power from the original attack.

Powerful weapons can be very intimidating at first. Before you chuck the match out of the window, make sure that you do ALL of your calculations correctly during your defence phase. You may discover that your odds of survival are not as low as you may thing.

[Shuu]

The unstoppable bullet against the immovable wall. Which will win? That's what we'll examine in this next case study, which pits Ryouma (Getter Pilot class) in a Shin Getter against Tetsuya (Mazinger Pilot class) in Mazinkaiser.

It's been a long, hard battle, and both pilots have reached the critical point in the fight at least once; meaning that both pilots' Dairyoku effects have been activated. Now, with it being Ryouma's go, he'll try to finish things off with a Stoner Sunshine.

Remember, Getter Pilot's Dairyoku multiplies all attacks' damage by 4, so the attack changes from:

6) Stoner Sunshine- 250 damage, 25 EN/shot. Requires Getter Pilot Class to execute.

To:

6) Stoner Sunshine- 1000 damage, 25 EN/shot. Requires Getter Pilot Class to execute.

Yikes, nasty. But let's see what happens:

DEFENSE PHASE:

Attacking Weapon #1: Stoner Sunshine
Action Taken: Take
Damage Taken: 63 (?!)
[/color]

Wowzers. Let's see how he managed to do it.

1. Receive Attack
1 Stoner Sunshine, 1000 damage to go, please.

2. Resolve Blocking
Tetsuya's a real man. One who wants his attack phase, so he did not block. No effects here.

3. Resolve Seishin Effects
Tetsuya's saving his SP for Greater Perseverence, so nothing here.

4. Resolve Pilot Ability
Tetsuya has his Dairyoku active as well, which reduces damage by a factor of 4. But before that, he has also used his Ki-Ai ability earlier, for 75% of his PCs, meaning 37.5% added reduction before Dairyoku kicks in. So we have:
1000 * 0.625 = 625
625 / 4 = 156.25

5. Resolve Shields
No shields on Mazinkaiser, so we pass.

6. Resolve Barriers
No barriers, either.

7. Resolve Armor
Mazinkaiser has Chogokin Z-Alpha armour, which reduces damage by 60%. So:
156.25 * .4 = 62.5

8. Resolve Systems/Items
Nothing to do here, so the damage is then rounded to the nearest whole number, which is 63.

So, to recap, that massive Stoner Sunshin attack was brought down to only 63 damage. 6.3% of the original damage. And people wonder why Mazin Pilots are the kings of defence.

[Shuu]

Now that we've finished looking at amazing defence, we'll take a look at how attack modifiers work. For our next study, we've kidnapped Ryouma again, and droped him in a Gundam Double Zeta. Also, this is a 200 PC match. Ryouma decided that he wants to use up 100 PCs into his Ki-Ai ability, which means a 50% boost in damage and a 25% boost in damage reduction. Let's see how this plays out:

Original stats:

Weapons:
1) Double Vulcan- 2 damage x 2, 20 rounds
2) Missile Launcher (PGSV)- 6 damage/PC
3) Beam Gun (B)- 10 damage, 8 rounds
4) Hyper Beam Saber (V)- 20 damage/EN
5) Double Beam Rifle (B)- 30 damage, 16 rounds
6) Hi-Mega Cannon (BS)- 120 damage, 10 EN/shot
7) Hi-Mega Cannon Full Power- DESTROY, 25 EN/shot. Requires NT/EH to execute.

MAP Attacks:
1) Hi-Mega Cannon (BI:3)- 90 damage, 20 EN/shot

After Ki-Ai:

Weapons:
1) Double Vulcan- 3 damage x 2, 20 rounds
2) Missile Launcher (PGSV)- 9 damage/PC
3) Beam Gun (B)- 15 damage, 8 rounds
4) Hyper Beam Saber (V)- 30 damage/EN
5) Double Beam Rifle (B)- 45 damage, 16 rounds
6) Hi-Mega Cannon (BS)- 180 damage, 10 EN/shot
7) Hi-Mega Cannon Full Power- DESTROY, 25 EN/shot. Requires NT/EH to execute.

MAP Attacks:
1) Hi-Mega Cannon (BI:3)- 135 damage, 20 EN/shot

The attack power of each weapon was increased by 50% (multiply by 1.5). Should the value of any damage end up in a decimal value, it gets rounded to the nearest whole number at the end of multiplication. Thankfully, there isn't any worry about that here.

Now, during the match, the ZZ takes enough damage to throw Ryouma into Dairyoku, meaning that all damage is now multiplied by 4. Let's see the new stats.

After Dairyoku and Ki-Ai:

Weapons:
1) Double Vulcan- 12 damage x 2, 20 rounds
2) Missile Launcher (PGSV)- 36 damage/PC
3) Beam Gun (B)- 60 damage, 8 rounds
4) Hyper Beam Saber (V)- 120 damage/EN
5) Double Beam Rifle (B)- 180 damage, 16 rounds
6) Hi-Mega Cannon (BS)- 720 damage, 10 EN/shot
7) Hi-Mega Cannon Full Power- DESTROY, 25 EN/shot. Requires NT/EH to execute.

MAP Attacks:
1) Hi-Mega Cannon (BI:3)- 540 damage, 20 EN/shot

Those are some mighty Vulcans. But as you can see, the ZZ has an effective boost of x6 damage (4 from Dairyoku x 1.5 from Ki-Ai). Enough to put fear into the hearts of most men, women, AI, aliens, and other types of foes.

[Shuu]

Our next attack boost study will concentrate more on items. To assist us, we have Loran Cehack and his Turn A Gundam. Let's take a look at his starting stats:

Original Stats:

Weapons:
1) Missile (PG)- 7 damage, 8 rounds
2) Hand Knife (M)- 9 damage
3) Beam Saber (M)- 12 damage x 2
4) Beam Rifle (B)- 16 damage, 10 rounds
5) Beam Drive Unit (BSV)- 10 damage/EN
6) Gundam Hammer (S)- 65 damage, 8 rounds
7) Moonlight Butterfly- DESTROY, EN Damage, 10 EN/shot

MAP Attacks:
1) Moonlight Butterfly (I:8)- DESTROY, EN Damage, 15 EN/shot

Now, the Crossdresser class has no special abilities, so Loran is reliant on items to get the effects he needs. For this study, he's decided to equip a Shuffle Union Badge and a V-Up (W). Let's see how this works.

Firstly, items which give a multiplicative bonus apply their effects first. This means that the Shuffle Union Badge, giving a bonus of x2 to all of Loran's attacks applies first. So, we get:

After Shuffle Union Badge:

Weapons:
1) Missile (PG)- 14 damage, 8 rounds
2) Hand Knife (M)- 18 damage
3) Beam Saber (M)- 24 damage x 2
4) Beam Rifle (B)- 32 damage, 10 rounds
5) Beam Drive Unit (BSV)- 20 damage/EN
6) Gundam Hammer (S)- 130 damage, 8 rounds
7) Moonlight Butterfly- DESTROY, EN Damage, 10 EN/shot

MAP Attacks:
1) Moonlight Butterfly (I:8)- DESTROY, EN Damage, 15 EN/shot

Now we apply the V-Up, since it gives a fixed damage boost.

After Shuffle Badge and V-Up (W):

Weapons:
1) Missile (PG)- 24 damage, 8 rounds
2) Hand Knife (M)- 28 damage
3) Beam Saber (M)- 34 damage x 2
4) Beam Rifle (B)- 42 damage, 10 rounds
5) Beam Drive Unit (BSV)- 30 damage/EN
6) Gundam Hammer (S)- 140 damage, 8 rounds
7) Moonlight Butterfly- DESTROY, EN Damage, 10 EN/shot

MAP Attacks:
1) Moonlight Butterfly (I:8)- DESTROY, EN Damage, 15 EN/shot

Nasty. So remember, items, systems, and abilities that increase attack power by a percentage take priority over those that increase them by a fixed value.#nosmileys

[Umbaglo]

In the final stop of our whirlwind tour, we'll cover dodging and DC mods. To help us, we have the ever-cheerful Hime Utsumiya and her Brain Powerd. Today, she's sparring with Jiron Amos in his Xabungle (Full Equipment). We're also out in space! Better bring your duct tape.

Now, this round, Hime is calling on help from Yuu Isami, inorder to use the Chakra Extension attack. Jiron has better things to do then get beat around, so he's going to dodge (or try, at least). Let's see how this plays out.

First, let's collect all of the modifiers Hime has.

1. Pilot Ability
The Antibody class has an inherent +5 DC mod to their attacks when in a unit with Slit Wafer, like Hime Brain is. Hime also cast Concentrate, for a further +5 DC.

2. Items
Hime is packing a Hi-Performance Targeter, which increases her target's DC by another +5.

3. Attack
Chakra Extension has an inherent +5 DC mod on it, as well.

Thustly, Hime has a total of +20 DC worth of penalities on her attack. Yikes. What's Jiron got in response?

1. Pilot Class
Walker Machine pilots don't dodge well (or at all), so he starts with a base 20 DC.

2. Items
But lo and behold! Jiron equipped a Green Haro and a Dual Tesla Drive to help him. Green sets his DC to 5, and Dual Tesla gives him a -10 DC modifier.

3. Mech Abilities
Unfortunately, though, Xabungle (Full Equipment) is cumbersome, incuring a +5 DC penality. Also, it's not designed for space at all (not many things with open cockpits and running on diesel are), giving it an extra +5 DC penality because of all the duct tape needed to hold things together. This means that Jiron has a +10 DC penality, nullifying the -10 DC penality Dual Tesla gave him.

So, Jiron's final DC is (5 + 20 - 0), or 25. Ow. Sorry, Jiron.

There's also a special DC case. This is the LOCKED case. A unit with a LOCKED DC cannot have it's DC changed by any means. They will ALWAYS dodge for that much, no matter what. Mothership Class is an example of a LOCKED DC, as is the effects of Yellow Haro.

This concludes the case studies. Remember these, and good luck in your battles.