Applied Knowledge

Clear Rank

• The table below on the reward (Food/Resource/Magic/Money) and the number of turns shows the base value.
• Resulting reward is determined as follows, where Base Values are given in the list below.

  □Food/Resource/Magic
  [Reward] = [Base Val.] + [Difficulty]^3 * [Rank] * [Chapter]
  □Money
  [Reward] = [Base Val.] + [Difficulty]^3 * [Rank] * [Chapter] * 2
   *Difficulty  = {Easy:1, Normal: 2, Hard:3, Very Hard: 4, Nidhogg:5}
   *Rank = {S:100, A:50, B:25, C:10, D:10, E:5, F:5, G:2, H:1}

  Rank is determined as the highest one satisfying the following conditions.

  *Turns: elapsed turns in the chapter
  *Cum. Turns: cumulative elapsed turns through the game
  *Difficulty  = {Easy:1, Normal: 2, Hard:3, Very Hard: 4, Nidhogg:5}
  *INT(x): Maximum integer no greater than x.
  □Chapter 1
   [Turns] ≦ [Threshold] + [Difficulty] * 1 - 2
    *Threshold = {G:50, F:42, E:35, D:29, C:24, B:20, A:17, S:15}
  □Chapter 7
   [Turns] ≦ [Threshold] + [Difficulty] * 1 - 2 - (INT([Cum. Turns] / 25) - [Chapter])
    *Threshold = {G:45, F:37, E:30, D:24, C:19, B:15, A:12, S:10}
  □Others
   [Turns] ≦ [Threshold] + [Difficulty] * 2 - 4 - (INT([Cum. Turns] / 25) - [Chapter])
    *Threshold (Summer/Fall/Winter Nations) = {G:51, F:43, E:36, D:30, C:25, B:21, A:18, S:16}
    *Threshold (Holy Land, Chap. 6) = {G:56, F:48, E:41, D:35, C:30, B:26, A:23, S:21}
    *Threshold (Chap. 8) = {G:60, F:52, E:45, D:39, C:34, B:30, A:27, S:25}

Chapter 1

Chapters 2–5: 黄金の平原（フレイヤ）・雷神と白狼（トール）・銀世界に蛇は踊る（リグレット）

Chapters 2–5: 嵐の神域（オーディン）& Chapter 6: 鍵を手にする者

Extra Reward in Chapters 2–5 (嵐の神域) & Chapter 6: 鍵を手にする者

Chapter 7: 力を求めて

終章（ロウ・カオス共通）

Extra Reward in Chapter 7 & 終章（ロウ・カオス共通）

On the Expected Rate of Damage Increase

Surveys expected damage increase by Titles and Equips.

Status

ATK is calculated by the following equation:

ATK = power + power * sqrt(EXP) / 200 + sqrt(EXP) / 25

• power: Base ATK, EXP: experience
  • Base ATK = [ATK at Lv.1] + [bonus/penalty by titles and compatibility of moon cycle]
  • Rounded to a value between 1–999 after reflecting the change by equips and reduction by, e.g., Attack Debuff.
    • The +25% bonus for a randomly chosen unit (with yell) in encounter battles is also calculated before flooring.
  • Bonus by Style (ATK/DEF/SPD) is calculated AFTER flooring.

Whereas the bonuses by titles affect the base values, those by equips and boost/Tactics skills only affect the final values. As a result, the contribution to the damage increase ratio of the latter effects is relatively small compared with the increase of base values.

• For example, ATK bonus by Attack Tactics [8] only increases damage by +4% if the unit's ATK is 200.

Critical Attacks

Critical rate increases as SPD increases, but the maximum critical rate is 50% without Critical Boost.
The critical damage without Lethal Critical is 150%.
As a result, the maximum increase ratio (to normal attack) of the expected damage for a unit without Lethal Critical or Critical Boost is

(1 - 0.5) * 1 + 0.5 * 1.5 = 1.25,

meaning that the contribution of SPD to the critical damage is at most +25% without Lethal Critical.

Critical rate is up to 75% when the unit has Critical Boost. In this case, the increase ratio of the expected damage becomes

(1 - 0.75) * 1 + 0.75 * 1.5 = 1.375,

which means that the damage increases by at most +38% even under Critical Boost if the unit does not have Lethal Critical.

Lethal Critical

• Under Lethal Critical, the critical damage is roughly [critical damage without Lethal Critical] * (4/3) * (1+[Skill Val.]/100). Therefore, the expected increase ratio of the damage is

  (1 - crit) * 1 + crit * 1.5 * (1/0.75) * (1 + lethal/100)

• crit: critical rate, lethal: Skill Value of Lethal Critical

Examples of expected damage ratio for some critical rates and Lethal Critical values are given as follows.

• Though the variance becomes quite large, Lethal Critical considerably increases the expected damage even if the skill value is low.
  • The above argument does not consider the overkill by Lethal Critical, which decreases the effective damage.

Helmet Split

The effect of Helmet Split skills (by the unit skill, titles and equips) is additive. Since the damage is rougly inversely proportional to (100-[Skill Val.]), the damage bonus per Helmet Split [1] becomes large as the total amount of Helmet Split increases.

• Skill value is capped by 75, where damage becomes x4 (=100/(100-75)).
• Dimension Slash includes the same effect as Helmet Split [75], and Lethal Critical (when occurred) includes Helmet Split [25]. However, this effect is calculated independently from Helmet Split. For example, the damage by Dimension Slash and Helmet Split [50] becomes x8 (=100/(100-75)*100/(100-50)).

Typical examples of damage increase by Helmet Split are as follows.

(For example, the "Increase Ratio" for 30 → 50 represents the expected damage increase when Helmet Split [20] is provided to a unit that already has Helmet Split [30]).

Curse

Since Curse decreases the enemy status, it increase the damage about +11% (= 1/0.9 - 1).
Here note that the damage of the attack with Cursed Strike making the unit cursed itself is not increased. The effect appears only when an already cursed unit is attacked.

Added Attack

Damage increase ratio of additional Added Attack is inversely proportional to the current number of attacks.

• For example, damage increase ratio by title 二刀流 (Added Attack [1]) for Vampire (Added Attack [2] = 3 attacks) is +33%.

Summary

• Relative contribution to the damage ratio per 1 ATK decreases as the base ATK increases.
• Critical Boost is not effective without Lethal Critical.
• If the critical rate is not very small, Lethal Critical considerably increases the expected damage regardless of its skill value.
• Relative contribution to the damage per 1 Helmet Split drastically increases as the total skill values of Helmet Split increases.
• Relative contribution per 1 Added Attack decreases as the number of attacks increases.
• As a result, giving a title with Helmet Split is effective when the unit already have some Helmet Split. Otherwise it is effective to give titles with Added Attack (if the unit does not have high-level Added Attack) or Lethal Critical (if the critical rate is not very small).

• E.g.: Comparison between Added Attack and Helmet Split for 阿修羅:

  Titles	Equips	Number of Attacks	Helmet Split	Damage Increase Ratio
  レーザー二刀流	星割り斧 星割り斧	5	50	+262% (飛行特攻: +524%)
  レーザー二刀流	双剣・竜晶 星割り斧	7	25	+232% (飛行特攻: +464%)
  レーザー二刀流	双剣・竜晶 双剣・竜晶	9	0	+215% (飛行特攻: +430%)
  レーザー二刀流	宝鍵クルタナ 双剣・竜晶	7	0	+854%
  レーザー二刀流	宝鍵クルタナ 星割り斧	5	0	+824%
  斬鉄の狙撃の	星割り斧 星割り斧	4	70	+300%
  斬鉄の狙撃の	双剣・竜晶 星割り斧	6	45	+221%
  斬鉄の狙撃の	双剣・竜晶 双剣・竜晶	8	20	+188%
  斬鉄の狙撃の	宝鍵クルタナ 星割り斧	4	45	+703%
  斬鉄の狙撃の	宝鍵クルタナ 双剣・竜晶	6	20	+729%

• 標準の攻撃回数が多い為、攻撃回数増加の恩恵をあまり受けないことがわかる。
  • 双剣・竜晶と星割り斧の組み合わせを考える場合、星割り斧の方が双剣・竜晶よりもダメージ期待値が高い。
• 一方でクルタナの装備を前提とするなど、高いカブト割の値を維持出来ない場合はカブト割の恩恵も非常に小さくなる。
  • 二つ名、装備の違いによる攻撃力の変化は考慮されている。
  • 速度差によるクリティカル率の違いは加味していない。またオーバーキルによるダメージの無駄も考慮されていない(カブト割特化では最大で4体の敵しか倒すことはできず、殴りきれない分は無駄になる)