|Efficient Attribute Points Distribution|
|Last updated:||Sept 25, 2014|
In this page you will find advice on how to spend the attribute points (AP) you gain after each level up. It does not cover all use cases and it makes some assumptions. The advice given needs testing to confirm its usefulness and correctness.
The following assumptions are made throughout this guide.
- It is assumed that having double hp does not affect the damage dealt to you in any way.
- It is assumed that having double atk means dealing double damage (to the same enemy). More generally, the relation between damage dealt and atk is linear (f(x)=ax).
- It is assumed that having double def means taking half damage (from the same enemy). More generally, the relation between damage taken and def is inverse (f(x)=a/x).
A brief look at the game code proves these assumptions wrong. The guide will be updated as soon as possible. Further details at Damage.
Use cases Edit
Since the effect agi has on the total damage you deal is not straightforward and simple, agi is ignored in this guide. If you plan to spend points in agi, you could do it by spending a percentage of the points you get after each battle (ex 20%). Then distribute the rest as described below.
Also, no points are distributed in luc, for similar reasons.
So this guide is about distributing your AP in hp, atk and def efficiently. Agi and luc are up to you.
Finally, the effects of a Recover necklace are a bit complicated and will be taken into account in this guide in a future version.
Lets assume your character has 10k hp, 10k atk and 10k def. You pit that character against an enemy, and you kill the enemy. You are left with 1000 hp when the battle is over (on average).
Getting hp up to 10100 (1% increase) will make you harder to kill. The character is left with 1100 hp at the end of the battle.
Getting atk up to 10100 instead (1% increase) will also make you harder to kill, but indirectly. Since you now deal 1% more damage, the enemy will die faster, inflicting fewer hits on your character (about 1% fewer hits). Since he was dealing 9000 damage before, he will now deal 90 less, or 8910, leaving you with 1090 hp at the end of the battle. So increasing hp by 1% is a little bit better than increasing atk by 1%, but just a little bit.
Getting def up to 10100 instead (1% increase) will also make you harder to kill. Since you now take 1% less damage, instead of getting 9000 damage, you will only take 8910 damage (9000 - 90). Same effect as increasing your atk.
The difference between increasing 1% hp, or atk or def as depicted above is actually non-existent. You see a difference because the example presented is over-simplyfied. The math behind it are presented APSingnificance for anyone interested. So, the conclusion so far is that a 1% increase in either of the three attributes has the same effect as to how stronger it makes your character.
When you level up, you don't get percentages to distribute, but attribute points. Putting 1 AP in hp increases hp by 5, putting 1 AP in atk increases atk by 3, and putting 1 AP in def increases def by 3. This is further modified by your base abilities (player level), your character abilities (character level), and of course by your equipement. Base abilities and character abilities grant you a multiplying factor, while equipment grant you a fixed value increase and/or a multiplying factor. This makes 1 AP giving a different amount of hp, atk and def, than the previously mentioned values (5,3 and 3). Bottom line, the % increase that 1 AP will grant you when assigned in hp or atk or def will be (generally) different. The greater the % increase, the stronger your character will become.
There is one more thing to note before we are ready to move on to calculations. Lets assume your character has 1000hp and you spend 1AP in hp. This ups your hp to 1005. That is a 0.5% increase. Spending one more AP in hp ups your hp to 1010. This time though, you didn't get 0.5% increase, you got less (1010/1005 - 1 = 0.4975%). Further investment in hp will grant you less % increase each time. If you spend AP in the attribute that will grant you the best % increase each time, at some point the % increase you will get by spending 1AP in hp or atk or def will be the same. That in turn means that you have maximized the utility of your AP, so that is our goal.
Following the reasoning above, we are in position to calculate how to spend the AP we have available.
Naming conventions Edit
In the Status Allotment screen, you can see two numbers for each attribute. For example hp : 13653 (2174). We will refer to these numbers as 'h1'('h2') for hp, 'a1'('a2') for atk and 'd1'('d2') for def. Some items grant you a fixed increase in one attribute, such a weapon or a hp gem. We will refer to the sum of this amount (sum of fixed values from all items) as 'hf' for hp, 'af' for atk and 'df' for def. Some items grant you a multiplier for an attribute, as do base abilities and character abilities, which makes 1AP give you more than 5 hp, or more than 3 atk, or more than 3 def. We will refer to the increase you get in one attribute by spending 1AP in it as 'hm' for hp, 'am' for atk and 'dm' for def. We will refer to the % increase in hp as 'hi', in atk as 'ai' and in def as 'di'. We will refer to the total hp as 'h', total atk as 'a' and total def as 'd'. According to the game mechanics, and the naming conventions we made, that gives us the following equations:
- (1) h = h1 + h2
- (2) a = a1 + a2
- (3) d = d1 + d2
- (4) h2 = (((h1 + hf) * hm) / 5) - h1
- (5) a2 = (((a1 + af) * am) / 3) - a1
- (6) d2 = (((d1 + df) * dm) / 3) - d1
Multipliers calculation - method 1 Edit
In the equations 4,5 and 6, 'hm', 'am' and 'dm' are not known. We can infer their value from the Equipment screen, using the following three equations, which are 4,5 and 6 solved for 'hm', 'am', and 'dm':
- (7) hm = 5 * h / (h1 + hf)
- (8) am = 3 * a / (a1 + af)
- (9) dm = 3 * d / (d1 + df)
In the Equipment screen all 'h1', 'h2', 'a1', 'a2', 'd1' and 'd2' are visible, while 'hf', 'af' and 'df' can be easily calculated. So we now have the values for 'hm', 'am' and 'dm'. Every time base ablities, character abilities or equipment changes, the values for 'hm', 'am' and 'dm' have to be recalculated. At the start of the game, the values we get for 'hm', 'am' and 'dm' are not so accurate. Later on when the rest of the values grow, the values we infer are much more accurate.
Multipliers calculation - method 2 Edit
There's another way to get the values for 'hm', 'am' and 'dm'. Faster and easier, but not as accurate. After a battle, go to the Status Allotment screen and assign all your AP in hp. Don't hit OK yet. Note the the values in blue - the amount of base and bonus hp you'll get if you hit OK. Add the two blue values together and divide by the number of AP you spent. The number you get is 'hm'. Cancel and repeat for atk to get 'am' and def to get 'dm'. Every time base ablities, character abilities or equipment changes, the values for 'hm', 'am' and 'dm' have to be recalculated.
Multipliers calculation - method 3 Edit
The effect of base abilities and character abilities is known. The equipment multipliers are in their description. That means that the 'hm', 'am' and 'dm' calculation can be very straightforward. Go to Player Values#Final Multiplicative Bonus Calculations and calculate your Bonus%HP, Bonus%ATK and Bonus%DEF. Then:
- hm = 5 * (1 + Bonus%HP)
- am = 3 * (1 + Bonus%ATK)
- dm = 3 * (1 + Bonus%DEF)
Every time base ablities, character abilities or equipment changes, the values for 'hm', 'am' and 'dm' have to be recalculated.
Spending AP Edit
Spending 1AP in hp, will grant you 'hm' hp. Same goes for atk and def. We will refer to the total amount of AP we have available to spend as 'tap'. If we spend 'hs' AP in hp, 'as' AP in atk and 'ds' AP in def, then:
- (10) tap = hs + as + ds
The increase in hp ('hi'), in atk ('ai') and in def ('di') will be:
- (11) hi = hs * hm
- (12) ai = as * am
- (13) di = ds * dm
The total attributes after spending the AP will be:
- (14) newh = h + hi
- (15) newa = a + ai
- (16) newd = d + di
After assigning these AP, spending one more AP in hp or atk or def will still grant 'hm' hp or 'am' atk or 'dm' def, which translates in a % increase ('hpercent', 'apercent', 'dpercent') as in the following equations:
- (17) hpercent = hm / newh
- (18) apercent = am / newa
- (19) dpercent = dm / newd
As we already mentioned, our goal is to spend AP such as:
- (20) hpercent = apercent
- (21) hpercent = dpercent
We are almost there. We don't know three numbers: 'hs', 'as' and 'ds'. That's what we are after. We have three linear equations to help us find them: (20), (21) and (10). I'll spare you the details and present you the solution:
- (22) hs = (tap + (a / am) + (d / dm) - (2 * h / hm)) / 3
- (23) as = (tap + (h / hm) + (d / dm) - (2 * a / am)) / 3
- (24) ds = (tap + (h / hm) + (a / am) - (2 * d / dm)) / 3
NOTE: These equations can give you negative results. That happens when the attributes are too unbalanced. When they are balanced, they will give you exactly the same number.
Example 1: Edit
Looking at the Equipment screen, we see
- hp : 15000(10500)
- atk: 17100(18240)
- def: 15000(8700)
We also see we have equiped a hp gem giving 10000 hp, a weapon that gives 0 atk and an armor that gives 800 def. That means:
- h1 = 15000, h2 = 10500, h = 25500, hf = 10000, hm = 5*25500/(15000+10000) = 5.1
- a1 = 17100, a2 = 18240, a = 35340, af = 0, am = 3*35340/(17100+0) = 6.2
- d1 = 15000, d2 = 8700, d = 23700, df = 800, dm = 3*23700/(15000+800) = 4,5
So, if we have 2000 AP to distribute (tap=2000), equations (22), (23) and (24) give us
- hs = 989
- as = 289
- ds = 722
Example 2: Edit
In the example above, lets assume we spend the AP as suggested. Then:
- hp : 19945(10599)
- atk: 17967(19165)
- def: 17166(9783)
So if we have 3000 AP to spent, equations (22), (23) and (24) now give us:
- hs = 1000
- as = 1000
- ds = 1000
The attributes are now balanced.
A simple and not very good looking spreadsheet that demonstrates the above calculations can be found at https://docs.google.com/spreadsheets/d/1QNw5ShuWteVdpzYMF8hBvS4ZOWtkAjAOGsZMAI8M_i0/pubhtml. It includes all three methods mentioned in three different sheets, and minimal instructions on top. Using it without reading this guide first will not be easy.