Formulas about damages

[Arada]

Hi everyone !

I made a stats guide I submitted to Special K to complete her work of gathering information but I just figured you might be interested as well.

Here's a guide about stats and how they work/are used in the game.
Hopefully, it's understandable and you guys can help me complete it (especially talking about STA here).

Before I start, just know you can find all enemy's stats on this page (http://psupedia.info/Enemies) and that there's a tool for getting character's stats and calculate attacks and magic attacks at this page (http://psutools.com/calccharstats).

This is guide is about giving the detailed formulas about damages. All of this is mathematics based and I know a lot of people aren't very found of that. But fear not, I will explain what everything implies on the way, with exemples and pics to back my results up.

Also, to be honest, I've just gathered information and tested it out. Exemples and explanations are from me, though.

Some things to note:
- "element" will represent the percentage of either armor or weapon with the give attribute. If the enemy is from the opposite element, treat this value as it is. If the enemy is of the same element, you have to treat element as a negative value. If the element is not identical nor opposite to the enemy's, treat it as 0.
- If you're using a unit affecting a stat relevant in a formula, simply add the bonus or malus to the characters stat. For exemple, when calculating an attack if you have a unit boosting your ATP by 100, the "Character ATP" in the formula will mean 'Base Character ATP + Unit bonus".
- Buffs only boost the base character stat. So treat the stat as if it was X% higher (or lower in case of debuffs).

1. Attack

It is represented by ATP in the game and is used to calculate all damages made in the game. There are a few exceptions, though, such as TECHs and TCSM damage (which are TP based). I'll cover Magic Attack later.

Attack formula:
((Character ATP + Weapon ATP) * PA modifier + ((Character ATP + Weapon ATP) * PA modifier) * (0.75 * element) - Enemy DFP) / 5

This formula doesn't represent the exact number of damage you'll but there's a last variable, that some call variance, which is used to make damages variations. Variance is different for each weapon and it would require thousands of tests to find them all. So I'll just treat this last random factor as if my result was 3 to 5% accurate. Meaning I can do 3-5% more or less damage than the calculation.
If you want to know more about variance, see this topic (http://boards2.sega.com/psu_board/viewtopic.php?t=85556). Just know that this variance can make some weapons with lower ATP actually make higher damage on average, as shown in the topic.

So, after theory comes practice.

My test subjects will be Ollaka lvl 30, Gohmon lvl 30 and Rappy Polec lvl 30. They're respectively Fire element, Ice element and Light element. They all have 112 DFP.
The character used is a Newman male lvl 140, ForteTecher lvl 20. So for this test, his ATP is 648.
The weapon used is Rikauteri with 677 ATP.
The PA is Rensei-Sou at level 29 which has a 164% ATP boost and gives my bow an element of 30% Ice.

Now, I just need to fill the values in the formula:
Ollaka: (((648 + 677) * 1.64) + ((648 + 677) * 1.64) * (0.75*0.30) - 112) / 5 = (2173 + 0.225 * 2173 - 112) /5 = 2550 / 5 = 510
Gohmon: (((648 + 677) * 1.64) - ((648 + 677) * 1.64) * (0.75*0.30) - 112) / 5 = (2173 - 0.225 * 2173 - 112) / 5 = 1572 / 5 = 314
Rappy Polec = (((648 + 677) * 1.64) - ((648 + 677) * 1.64) * (0.75*0.0) - 112) / 5 = (2173 - 112) / 5 = 2061 / 5= 412

Results:
http://img367.imageshack.us/img367/2159/psu20080919212145002vp9.png
http://img367.imageshack.us/img367/8237/psu20080919212530006hi1.png
http://img411.imageshack.us/img411/714/psu20080919212945007ui7.png

So the formula's right but what does this all mean ?

The element makes a difference. Change nothing but the element in the above exemples, the results are: 575 (+13%) on the Ollaka, 214 (-20%) on the Gohmon. Pretty good difference.

But what about differences on a character like a Beast male ?
Let's take a Beast male, lvl 140 and ForteFighter 20. Base ATP: 2204.
His weapon will be a Mugunruk (732 ATP) and we'll use Dus Majarra lvl 40 (3 combos at 185% ATP, 210%ATP and 410% ATP).
The only thing that'll change will be the element of the spear, once it'll be 30% and then 50%.

Ollaka (30%): 700 base attack, 1314 at combo 1, 1495 at combo 2, 2941 at combo 3
Ollaka (50%): 777 base attack, 1458 at combo 1, 1658 at combo 2, 3259 at combo 3
It's respectively +11%, +11%, +11% et +11%.

Does the weapon ATP really matter ?

No, not really.
Let's take a Muktrand (676 ATP, -7% compared with the Mugunruk)
With a 30% Muktrand on the Ollaka -> 686 (-2%), 1289 (-2%), 1466 (-2%), 2884 (-2%)

So a 7% difference in stat means a 2% difference in damage in the end.

The character stats are used the same way as the xeapon stats so they have the same impact. But keep in mind that these tend to grow a lot. So your character level still has a great impact.

The PA modifier has an very important role.
Let's take Dus Majarra lvl1 (+131% ATP at combo 1) which gives us a result of 906 damage at combo 1 with a Muktrand 30% Ice on an Ollaka (-30%).

So PAs probably have the biggest role here. You'll now know that someone with low PAs will be very inefficient compared to someone of lower level but with high PAs.
Also, the impact has been reduced with AotI but it keeps an important role in the damage you'll deal.

Last notes:
- Just atacks and critical hits give <result> x1.5
- Resistant enemies give <result> x0.5
- Just attacks and critical hits on resistant enemies give <result> x0.75

2. Accuracy

It is represented with ATA in the game.

Hit rate formula:
1 - (Target's EVP / ((Character ATA + Weapon ATA) * PA modifier) * 10))

So, for an exemple, I'll take an Ollaka lvl 30 with 223 EVP. My character has 432 ATA and the Rikauteri give 401 ATA. The PA ATA modifier is 72%.

So it would make:
1 - (223 / ((432 + 401) * 0.72) * 10 = 1 - 0.03 = 97% Hit rate.

What does it mean ?

Well, considering the best enemies have an EVP of around 1000, and that it would still make around 85% chances to hit, ATA isn't very relevant.
Just know that, in this case, a ATA boost of 130 would NOT change the hit rate (eventhough it would actually be very close to 97% when my first result is more arond 96.7%). The only thing really important and relevant here is the enemy EVP (and yours will be when we will see about Evasion).

3. Defense

All enemies attack the same way (for physical attacks) and the formula for their damage uses the same basis as the characters but with simplications.

But first, we'll have to find our DFP in the formula. It's quite easy:
(Character DFP + Armor DFP) + (Character DFP + Armor DFP) * element

In the exemples, my character will use a Hizeri-Senba, 29% Light which has 198 DFP. The character's DFP is 160.
My DFP will be:
Against Light enemy: (160 + 198 ) + (160 + 198 ) * 0.29 = 462
Against Dark enemy: (160 + 198 ) - (160 + 198 ) * 0.29 = 283
Against Neutral enemy: (160 + 198 ) + (160 + 198 ) * 0 = 398

The enemies attack with this formula:
(Enemy ATP + Enemy ATP * element - Character DFP) /5

Note: Enemy element is either 0 in the case of a Neutral one, 50% in the case of an enemy with an opposite element or -50% in the case of an enemy with the same element as yours.

Let's take a lvl 110 Rappy Polec for our exemple (2557 ATP):.
The damage I'll take will be:
(2557 - 2557 * 0.5 - 462) / 5 = 163

Result:
http://img142.imageshack.us/img142/1350/psu20080920110736006ih8.png

What does it imply ?

+5 DFP means one less damage taken. The higher your armor's element, the better as against the right enemies a 30% armor will turn your +5 DFP into +6 or +7 DFP.
Getting an armor with great stats is essential as the element does nothing alone but it's more a matter of balance in this case. An armor with average element and stats will do better than one with a super high DFP of super high element.
Also, with the enemy damage formula, you see that having the right element armor is absolutely essential in your survival strategy. The "ATP * element" modifier can become a bonus for you if you have the right element equiped it dramatically reduces enemy damages as on the one hand, your DFP is higher and on the other hand the enemy ATP gets a 50% malus.

4. Evasion

Evasion is represented by EVP.

It's the reverse formula from the Hit Rate:
(Character EVP + Armor EVP) / (Enemy ATA * 10)

Let's take the exemple of a level 150 Ollaka (399 ATA), my character has 1042 EVP and his armor has 262 EVP:
(1042 + 262) / (399 * 10) = 33%

So the enemy has a 33% Miss rate against me. 1/3 attacks miss. Not bad.

As said before, it's your EVP that matters the most here so the higher, the better. But as you can see, usually, armors don't grant that much a bonus so you can only really count on your character's base EVP in this case. It's a way better strategy to have a better DFP bonus than EVP bonus from your armor.

5. Magic Attacks

Magic attacks are based on TP. All TECHs use the following formula. Beware though, as it is that much more complex.

((Character TP + Weapon TP) + (Character TP + Weapon TP) * (0.75 * TECH element) + (Character TP + Weapon TP) * (Weapon element * 0.75) - Enemy MST) / 5

TECH element is found as follow: 10 + TECH level (capped at 50).
On a Rod, you also get a 20% boost represented with <result> x1.2.
Critical hits with a Rod give (<result> x1.2) x1.5
Resistant enemies with a Rod give (<result> x1.2) x0.5
Critical hits with a Rod on resistant enemies give (<result> x1.2) x0.75

So I'll give exemples.
My character has 2491 TP and uses a Psycho Wand (958 TP) and Diga lvl 40 (+290% TP). So TECH element is 10 + 40 (max: 50) = 50% (Ground)
The Rod's element is 0%.

The test target is a Badira lvl 106 with 260 MST (Fire element).
(((2491 + 958 ) * 2.9 + ((2491 + 958 ) *2.9) * (0.75 * 0.0) + ((2491 + 958 ) *2.9) * (0.75 * 0.0) - 260) / 5) x 1.2 = ((3449 * 2.9 - 260) / 5) * 1.2 = (9452 / 5) * 1.2 = 1890 * 1.2 = 2269
The test target is a Volfu lvl 100 with 463 MST (Lightning element).
(((2491 + 958 ) * 2.9 + ((2491 + 958 ) *2.9) * (0.75 * 0.5) + ((2491 + 958 ) * 2.9) * (0.75 * 0.0) - 463) / 5) x 1.2 = ((9712 + 3642 -463) /5) * 1.2 = 3094

Results:
http://img241.imageshack.us/img241/2217/psu20080921134955004kn1.png
http://img140.imageshack.us/img140/3826/psu20080921142432026xy6.png

Here, stats are close to nothing. So "level your TECHs" is the best and only advice I'll give.

6. Magic Defense

As with defense, you'll have to find your MST in the formula first.
(Character MST + Armor MST) + (Character MST + Armor MST) * element

Put the result in the enemy magic attack formula:
(Enemy TP + Enemy TP * TECH element - Character MST) / 5

TECH element, here is calculated the same way (10 + TECH level). To determine the TECH level, just catch the "look" of the TECH and you can easily determine if it's 1+, 11+, 21+, etc...
When you know that, you'll know the TECH level as it is always the first level in an evolution step.
Say you're against a Carriguine which uses 21+ looking Megid, then the level of its Megid is 21.
Darbelan throw basic 11+ Megids so their Megid is level 11.

//////////////GOTTA PUT A MAGIC DEFENSE EXEMPLE////////////////////////

7. Special Effects resistance

It's based on STA. Little is known about this stat and how to resist to Special Effects (SE).
The SE are effects like Burn, Virus, Freeze, etc... They're broken down into 5 levels (1 to 5).
SE are inflicted only if damage are dealt. If the attack misses or deals 0 damage, no SE can be dealt.
I've found no formula about this stat in the game but players, after several tests, have concluded that 22-23 gives you immunity to SE 1.
SE 5 will always apply if the attack is succesful. The enemies with imunity will be affected but players with Resist units won't.

[fayt6]

wow..i ddnt read it but...it seems comprehensive good job

[Majarra]

Very good guide. I cant really understand the formulas or the math part cause im terrible at it. But everything sounds good. in short: Congrats! This should be stickied!

[Arada]

Very good guide. I cant really understand the formulas or the math part cause im terrible at it. But everything sounds good. in short: Congrats! This should be stickied!

Thanks. For each stat, I made after the exemples a little "what does it imply" paragraph for people have difficulties with maths.

I should rework the presentation, though.

[Dhylec]

This is quite a math intensive guide. Good for those who wanna know about the mechanism behind the numbers. Though I can't verify the accuracy of those numbers, I think this is an interesting guide. I'll have it up in the sticky list for references.


I should rework the presentation, though.
That could help also.

[Hrith]

- Resistant enemies give <result> x0.5http://keffypoo.free.fr/psu/network/bullet_resistance.png

502 x 0.5 =/= 215

[Tycho]

((Character ATP + Weapon ATP) * PA modifier + ((Character ATP + Weapon ATP) * PA modifier) * (0.75 * element) - Enemy DFP) / 5

This formula doesn't represent the exact number of damage you'll but there's a last variable, that some call variance, which is used to make damages variations.

There is no 'variance' variable. There is only 'variable ATP' -- another way of saying that weapons have a minimum as well as a maximum ATP/TP value. This is set per weapon, hence easy to test. The PSU/AOTI guides listed all these minimum values by the way. I wrote them down for PSU at one point, but I dunno if there's still any lists floating around. I never got around to checking if you could easily read them using CE either.
Anyway, if you feel like testing this claim, get some 1* weapon using a maxed character, and check if the damage you're doing would change much (same circumstances etc., so no comparing the first and second hits of PAs, since they have different PA mods). There should be next to no variance left.
There shouldn't be a 0.75 modifier to the element either -- this is the only part where you're using a number that's too low, which is where you must have gotten the idea that it's possible to get above the expected value.
Also, you forgot about the monsters' elemental stat, one of the reasons why I could never figure things out exactly when I tried. Unless they changed anything lately, it's 5% for all monsters (offline SEED-Magashi used to be the only exception).
One last comment; you're making the formulas look really redundant using your notation, which is probably why it looks so confusing to most people.
My version:

Damage = 0.2 * (PA mod * (buff mod * base ATP + min~max weapon ATP) * (1.05 + att. element) - (buff mod * DFP))

.. where for 24% fire, 'att. element' is 0.24; ATP/DFP can all be substituted with TP/MST to get the magic damage formula.
I might still be off, but I never even really bothered too much with the order in which they apply so far, and I haven't done any testing in ages. Sou probably knows better.
Anyway, if there's anything that still weird in this formula it's the part in the elemental clause. Just using (1 + element) or writing the element as 1.24 from the start was needed to avoid having to copy the rest of the formula again (like you did), but for some reason this defending element makes you do 5% more damage (before extracting DFP obv)... even without using the 'right' element. So yeah, my best guess.



http://keffypoo.free.fr/psu/network/bullet_resistance.png
502 x 0.5 =/= 215
Variable ATP/TP means the numbers aren't always as high as they can be. Try it, the min/max damage with resistance are actually half of what they're like without.


Edit: Not to be rude, but I'm disappointed to see things haven't changed much over the last few years. Come on, at least the people in charge should know their stuff.

[Arada]

There is no 'variance' variable. There is only 'variable ATP' -- another way of saying that weapons have a minimum as well as a maximum ATP/TP value. This is set per weapon, hence easy to test.

That's what was said. But I also mentionned I would rather treat it as a general 3-5% (more or less) random damage than try to list the variance for each weapon.
You're right to say it affects directly the weapon's ATP, though and that's it's not the end result that's directly affected.


There shouldn't be a 0.75 modifier to the element either

This modifier was introduced with AotI to "decrease the importance of elemental attribute". But they also decreased our overall damages in the process.

At least that's what I found while searching the formulas to make this guide.


Also, you forgot about the monsters' elemental stat

For attacks, I did use them. For their own defense, they just don't have one.


One last comment; you're making the formulas look really redundant using your notation

True. As I said, I'll probably rework the presentation. But the redundancy I'm showing allows people to understand the steps behind the formulas. Making it generally look like:

(Base ATP + Base ATP * elemental modifier - DFP) / 5

So yes, it's clearly not the best but I think it's the easiest to understand.
Maybe I should use the *0.2 instead of /5, though.

Thanks for the comments.

I you find anything to add/change/explain, just go. The goal here is to be complete.

[Hrith]

Variable ATP/TP means the numbers aren't always as high as they can be. Try it, the min/max damage with resistance are actually half of what they're like without.Not rly. Aikasoki damage barely varies, and certainly not by 40+

I can do it with Twin Ruby Bullet, which has fixed ATP, the result will be the same.
The DFP provided by the shield icon on the Go Vahra does not account for the 40 missing damage points.


These formulae posted above contain several (minor) errors, but since people seem to think screenshots are enough to validate formulae, I adapted the same reasoning to the opposite end.


Edit: Not to be rude, but I'm disappointed to see things haven't changed much over the last few years. Come on, at least the people in charge should know their stuff.Was that for me? =/
Makes little sense if you're talking to me.

[drizzle]

Variable ATP/TP means the numbers aren't always as high as they can be. Try it, the min/max damage with resistance are actually half of what they're like without.

Shield gives vahras 200% DFP which for a level 100 Go Vahra is another 356 DFP, or ~71 damage. So we have 502-71=431 damage. Shield also gives ranged halfguard, which cuts the final damage number in half, and the result is... 215.5.

So, Hrith's screenshot proves that halfguard gives damage * 0.5.

[Arada]

Thanks for the explanation, drizzle, I was actually looking why there was a difference. It simply came from the fact that the Shield also gives a boost in DFP.

I had totally forgotten about that.