How former FGO players play Azur Lane

This year, I got into Azur Lane. I used to play FGO, but after waiting for the story of the Chinese server to catch up with the Japanese server, I decided to quit the game. Anyone who gives money to Chen Rui is an idiot.

I've been playing for half a year, so I consider myself somewhat experienced. However, many habits from FGO have had a deep impact on my gameplay in Azur Lane.

Traditions of FGO Players#

When playing FGO, there are four things you must do: card counting, optimizing card order, using support servants, and stacking buffs. If you haven't done these things, it means you haven't really gotten into FGO, or you're just copying others.

Card counting is self-explanatory. It involves counting cards and aiming for critical hits. This is also common in Azur Lane.

Clearing daily quests, doing 3T~6T setups, preserving skills, and soloing battles all require optimizing card order. One classic example of optimizing card order is the "Meteor Shower" setup. Some players have used excellent card order techniques to solo the "Meteor Shower" quest with Mashu. Others have even used amazing card order techniques to clear a stage that was designed to be impossible, such as the "13-stroke Command Seal Challenge."

Even if many players are not familiar with the damage calculation formula in FGO, they probably know about the four types of buffs (A, B, C, D) and how buff stacking works.

In simple terms, buffs of different types multiply, while buffs of the same type add up. Let's say one buff provides a damage increase of $a$ , and another buff provides a damage increase of $b$ . If the two buffs are of the same type, then the combined effect is $(1+a+b)$ . But if the two buffs are of different types, the combined effect is $(1+a)(1+b)=1+a+b+ab>1+a+b$ .

Due to the design of FGO, even for daily quests, you often need to stack multiple buffs. If a newcomer wants to get into FGO, they must have the following servants to stack enough buffs (as of when I quit the game): Merlin, Tamamo no Mae (Caster), Shuten Douji, Zhuge Liang (El-Melloi II), Scathach (Caster), Paul Bunyan, Florence Nightingale, Skadi, Artoria Pendragon (Caster), Oberon...

Bringing FGO Techniques into Azur Lane#

Buff stacking is a given, and I believe most people are familiar with the buff system of Unicorn, Yuubari, Ayanami, and Akashi. But this is far from the limit of buff stacking.

Consider the BINAH team: Unicorn, Yuubari, Mizuho, Akagi, Ayanami, and Akashi. A fully buffed Unicorn would have the following buffs:

49.4% penetration effect (Unicorn's skill)
26.6% attack increase (Unicorn's skill)
24.2% increase in damage dealt (Unicorn's skill)
Half EX cost
16.1% attack increase (Yuubari's EX)
25.9% critical rate increase (Yuubari's skill)
45.9% attack speed increase (Yuubari's skill)
70.1%+28.9% penetration effect (Mizuho's EX and skill)
43.1% attack increase (Mizuho's skill)
37.7% defense reduction on the enemy (Akagi's EX)
39.5% critical rate increase (Ayanami's EX)
73.3%+17.3% critical damage increase (Ayanami's EX and skill)
105% attack increase (Akashi's EX)
Evasion is not important, so it can be ignored

In total, the buffs are:

Half EX cost
148.4% penetration effect
190.8% attack increase
24.2% increase in damage dealt
65.4% critical rate increase
45.9% attack speed increase
37.7% defense reduction on the enemy
90.6% critical damage increase

With so many buffs, even in FGO, they are quite rare and usually only achievable through card counting and optimizing card order.

Accumulating buffs requires skill in optimizing card order. Since Azur Lane is based on time rather than turns, the card order optimization in Azur Lane is more similar to the precise card order optimization in Civilization 6 rather than the rough card order optimization in FGO.

In general, the card order optimization in Azur Lane is based on seconds, as most buffs have a duration in whole seconds. However, sometimes, due to the short duration of multiple buffs, card order optimization may require intervals of 0.5 seconds or even 0.1 seconds. Some actions, such as delaying a skill activation (for example: using Unicorn's EX but not detonating it yet, then using Akashi's EX to slightly increase damage), also require precise timing. Therefore, the card order optimization experience in Azur Lane is completely different from FGO.

Next, let's talk about how to apply the damage formula in Azur Lane.

Damage Formula#

The damage calculation formula in Azur Lane is similar to FGO, except for the defense part. The defense formula in Azur Lane is similar to League of Legends' $\frac{100}{100+D}$ .

The formula may look long, but it's actually just a simple multiplication of factors.

Part 1: Damage Calculation Starting Point#

Similar to FGO, the starting point of damage calculation in Azur Lane is:

Atk \times Skr \times Hitr \times Us

Base stat $Atk$
Skill damage multiplier $Skr$
Hit distribution $Hitr$
Damage fluctuation $Us$

However, unlike FGO, the damage fluctuation in Azur Lane is variable. The fluctuation is determined by the stability value $Stb$ , which varies between characters. The fluctuation range is: it fluctuates to $Us$ times the original damage based on the stability value $Stb$ , where

Us \in\left[ \frac{Stb}{Stb+1000}+0.2, \ 1 \right]

Unicorn has a relatively low stability value, only 1376, and in IS mode, the Orochi reduces stability by 50%, so the minimum damage Unicorn can deal is only 61% of the original damage.

Part 2: Attribute Advantage, Terrain, and Level Multiplier#

After the starting point, there is the attribute advantage, terrain, and level multiplier $Atr$ .

$Atr$ is calculated by multiplying three factors.

Level: For every 1 level lower than the enemy, damage reduction is 2%, up to a maximum of 60% reduction.
Terrain: Varies in increments of 10%, with a maximum of +30% for advantageous terrain and a minimum of -20% for disadvantageous terrain.
Advantage: Deals 200% damage when advantageous, 50% damage when disadvantaged, and 150% damage when effectively advantageous.

Unlike the significant buff dilution in FGO, the buff dilution in Azur Lane is much milder. In Azur Lane, only buffs of the same name are diluted, and there is no issue of buff type dilution like in FGO (in FGO, attack increase and defense reduction are the same type of buff, calculated by addition).

Part 3: Buff Factors#

The buffs that affect damage are:

Enemy defense $Arm$ (can be reduced by buffs)
Critical damage multiplier $Crr$ (affected by multiple factors)
Enemy damage reduction $Red$
Ally damage increase $Inc$
Advantageous effect $Eff$

These factors are all multiplied together.

The calculation of defense reduction is similar to League of Legends. For an enemy with defense $Def$ , the actual damage they receive is

\frac{\frac{5000}{3}}{\frac{5000}{3} + Def}

I don't know why they chose the strange number $\frac{5000}{3}$ , as League of Legends uses 100. However, interestingly, the IS Orochi with 5000 defense actually takes $\frac{1}{4}$ damage, which is a visually pleasing fraction. Other bosses may have similar mechanics.

For flat and percentage defense reduction, the flat reduction is calculated first. In other words, the actual defense is (initial defense - flat reduction) * (1 - percentage reduction).

The changes in damage reduction and damage increase are both calculated as flat reductions.

The advantageous effect is an independent increase in damage when your damage is advantageous against the enemy's armor. For example, Mizuho deals an additional 99% damage when attacking light armor in EX mode. This doubling of damage is directly multiplied, separate from the advantageous factor in $Atr$ . So Mizuho deals 4 times the damage instead of 2 times.

The calculation of critical damage multiplier is somewhat complicated, as there are buffs that increase critical damage multiplier and buffs that decrease the damage received from critical hits.

First, on your side, the critical damage multiplier is (base critical damage multiplier 200% + equipment critical damage multiplier + skill-based increase) * (1 + percentage-based increase).

On the enemy's side, the critical resistance multiplier is (base critical resistance 50% + equipment critical resistance + skill-based increase) * (1 + percentage-based increase).

The final critical damage multiplier used in the damage calculation is: critical damage multiplier - critical resistance multiplier.

Card Order Optimization#

Card order optimization in Azur Lane is much simpler than in FGO.

In general, FGO requires you to defeat enemies within 3 to 6 turns, but you only have 6 characters, 18 skills, and 6 Noble Phantasms, and only 3 characters can be on the field at the same time. Many buffs in FGO have a duration of 3 turns, and some powerful buffs last only 1 turn (such as Merlin's skill that provides 100% critical damage for 1 turn). Some enemies have multiple health bars, and you can only deplete one bar per turn (with a few exceptions), and when you deplete a bar, the enemy will unleash a powerful skill, which can be challenging. Sometimes, it is even necessary to use algorithms like dynamic programming to defeat enemies with 4 or more health bars in the shortest possible time.

Azur Lane, on the other hand, is not as complex. Generally, you cannot use two rounds of skills within the duration of a powerful buff, and the effects of the same skill will overwrite each other, so there is no need to meticulously optimize card order to stack buffs excessively. However, swimsuit Hanako is an exception. Hanako's passive skill allows her to use her EX skill three times in a row, and her EX skill only costs 2, so she can unleash incredible bursts of damage.

Additionally, the passive skills in Azur Lane bring buffs with obvious periodicity. As long as the cost is controlled within a reasonable range, it is generally easy to make good use of the buffs brought by each passive skill. The timing of using active skills is also not difficult to control.

Mathematical Modeling and Optimization Problems#

Next, let's talk about a technique commonly used in Azur Lane but not in FGO: mathematical modeling.

Fortunately, game designers rarely create things as mathematically challenging as Heartsteel in League of Legends. In Azur Lane, most of the time, mathematical modeling involves simulating battles and does not require dealing with differential equations or other complicated situations. This rough modeling can often accurately calculate the damage that can be dealt.

However, there are exceptions. The damage caused by Unicorn's EX skill depends on the target's current health compared to their maximum health, and in this case, differential equations are necessary. I have previously modeled and calculated how Unicorn's damage is affected by various factors, but unfortunately, the only copy of that file was shared in a Telegram group that has since been disbanded. I may recalculate it in the future.

In general, for regular attacks, the damage can be considered uniform. Due to the law of large numbers, the effects of stability and critical hits on regular attacks can generally be ignored. Therefore, in most cases, it is sufficient to calculate the cooldown and damage of skills and EX skills. The simplest method is to always assume that EX skills are used with full buffs, while small skills have no buffs.

In some battles, finding a suitable model is difficult because they heavily rely on specific mechanics, and simple calculations cannot take those mechanics into account. For example, Gregory.

In addition to damage, sometimes it is necessary to consider healing and tankiness. Typical examples include Bishop's healing and Mizuho fighting Orochi. These can also be calculated simply based on skill cooldowns and values.

The real challenge lies in calculating the total damage in multi-round battles.

Assuming you have $n$ front-line students and $m$ back-line students to choose from, without considering borrowing, at round $t$ , you have

\prod_{i=0}^{t-1} C_{n-4i}^{4}C_{m-2i}^{2}

possible team compositions.

Approximately, you have $\Theta(n^{4t})$ possible team compositions.

In terms of the number of rounds, simulating battles to find the optimal solution has exponential time complexity, while in terms of the number of available students, the time complexity is polynomial.

Taking myself as an example, I have 36 back-line students and 76 front-line students. If I want to do 3 rounds, I have approximately $1.88*10^{26}$ possible team compositions. Simulating each battle one by one is clearly not feasible.

However, if a single battle can be accurately modeled, an approximate optimal solution can be explored through reinforcement learning methods. Although it still requires a lot of time, at least it can be calculated in a crowded situation.

Positioning and Control#

In some total damage battles, positioning is very important. For example, Goz requires reaching the true form in the second phase, and Black and White can dodge skills through positioning. FGO does not have positioning, but it has taunting. Generally, taunting in FGO is effective against bosses because it is a buff effect rather than control over the boss.

Most bosses and high-difficulty quests in FGO do not have immunity to control effects, and they generally do not have immunity to debuffs either. Therefore, many bosses, especially male bosses, can be controlled to death. A typical example is the "Gorgon Sisters' Dynamic Team." In Azur Lane, control skills are not very useful and are usually only used in total damage battles that rely on control, such as Hod. Debuffs that do not increase damage are also not very useful, but there are a few bosses that rely on the number of debuffs, such as Gregory. However, in FGO, these debuffs are often used to reduce survival pressure and can even be used to defeat bosses, such as the classic "Maze That the Demon King Can't Escape From."

Conclusion#

Although both Azur Lane and FGO require a high number of characters, the gacha difficulty in Azur Lane is much lower than in FGO. The story in FGO is mostly good, and even now, I still follow the story of FGO. It is common sense not to play the Chinese server, and anyone who plays BGO or Middle East Archives is an idiot.

Both Azur Lane and FGO belong to games with little gameplay but interesting stories. However, Azur Lane has auto-battle for daily quests, and you don't need to meticulously plan team compositions for daily quests, which is more comfortable. In the end, FGO is still too grindy. Calculating multiple rounds is a challenge that FGO does not have, and the various techniques in FGO can be effectively applied.

I will always love Azusa Shirasaki!