How do former FGO players play Azur Lane?

This year, I got into Azur Lane. I used to play BGO, but after waiting for the story in the Chinese server to catch up with the story I had already seen in the Japanese server, I decided to quit the game. Whoever gives money to Chen Rui is an idiot.

I've been playing for half a year, so I guess I'm considered a beginner. However, many habits from FGO have had a deep impact on how I play Azur Lane.

Traditions of FGO Players#

When playing FGO, there are four things you must do: card counting, card order optimization, using specific team compositions, and stacking buffs. If you haven't done these things, it can be said that you haven't really gotten into FGO, or you're just copying others' strategies.

Card counting is self-explanatory. It involves counting cards to maximize the chances of getting the cards you want, such as getting critical cards or specific Noble Phantasms. This is also common in Azur Lane.

Optimizing card order is essential for farming daily quests, doing 3T~6T setups, preserving skills, and soloing. One classic example of card order optimization is the "Meteor Shower" setup. Some players have even used excellent card order optimization techniques to defeat challenging stages that were designed to be impossible to win, such as the "13-stroke Command Seal kill on the Captain".

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

In simple terms, buffs of different types are multiplied together, while buffs of the same type are added together. 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 usually 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, Altria Pendragon (Caster), Oberon...

Bringing FGO Techniques into Azur Lane#

Stacking buffs is a given, and I believe most people are familiar with the buff system of Unicorn, Yuudachi, Ayanami, and Javelin. However, this is not the limit of buff stacking.

Consider the team composition of BINAH: Unicorn, Yuudachi, Yukikaze, Akashi, Ayanami, and Javelin. A fully buffed Unicorn should have the following buffs:

49.4% Armor Penetration (Unicorn's skill)
26.6% Attack Increase (Unicorn's skill)
24.2% Damage Increase (Unicorn's skill)
50% Reduction in EX Cost
16.1% Attack Increase (Yuudachi's EX)
25.9% Critical Rate Increase (Yuudachi's skill)
45.9% Attack Speed Increase (Yuudachi's skill)
70.1%+28.9% Armor Penetration (Yukikaze's EX and skill)
43.1% Attack Increase (Yukikaze's skill)
37.7% Enemy Defense Reduction (Akashi'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 (Javelin's EX)
Ignore Evasion (ignored for simplicity)

In total, the buffs are:

50% Reduction in EX Cost
78.3% Armor Penetration
190.8% Attack Increase
24.2% Damage Increase
65.4% Critical Rate Increase
45.9% Attack Speed Increase
37.7% Enemy Defense Reduction
90.6% Critical Damage Increase

Having so many buffs is quite rare, even in FGO. Usually, only with card shuffling and preservation can you achieve such a high buff stack.

Stacking buffs requires skill in optimizing card order. Since Azur Lane is based on real-time combat rather than turn-based combat like FGO, the card order optimization in Azur Lane is more similar to the precise card order optimization in Civilization VI rather than the broad 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 overlapping, card order optimization may require intervals of 0.5 seconds or even 0.1 seconds. Some operations, such as backstabbing (for example: using Unicorn's EX and then using Akashi's EX before Unicorn's EX detonates, which slightly increases 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 the one in 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 Attack $Atk$
Skill Damage Multiplier $Skr$
Hit Splitting $Hitr$
Damage Float $Us$

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

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

The Stability Value of Unicorn is relatively low, only 1376. Under the effect of IS, the Stability Value of Orochi is reduced by 50%, which means that Orochi can only deal a minimum of 61% of the original damage.

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

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

$Atr$ is calculated by multiplying three factors.

Level: For every level lower than the enemy, damage reduction is 2%, up to a maximum of 60% reduction.
Terrain: It increases or decreases damage by 10% increments, with a maximum of +30% (Sunglasses) and a minimum of -20% (Crying).
Advantage: Dealing 200% damage when having an advantage, 50% damage when being at a disadvantage, and 150% damage when having an effective advantage.

Unlike FGO's severe buff dilution, Azur Lane's buff dilution is much milder. Azur Lane only dilutes buffs of the same name, without the issue of buff type dilution in FGO (in FGO, attack increase and defense reduction are the same type of buff, calculated by addition).

Part 3: Buff Factors#

Buff factors that affect damage include:

Enemy Defense $Arm$ (can be reduced by buffs)
Critical Damage Multiplier $Crr$ (affected by multiple factors)
Enemy Damage Reduction $Red$
Ally Damage Increase $Inc$
Advantage Effect $Eff$

These factors are all multiplied together to calculate the final damage.

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 weird number $\frac{5000}{3}$ , League of Legends uses 100. However, interestingly, the damage received by IS Orochi with 5000 defense is $\frac{1}{4}$ , which is unexpectedly a nice fraction. Maybe other bosses are the same.

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).

Both damage reduction and damage increase are calculated with flat reduction taking priority.

Advantage effect is an independent damage increase when your damage has an advantage against the enemy's armor. For example, Mizuhara deals an additional 99% damage against light armor in her EX. This damage increase is directly multiplied independently, separate from the advantage factor mentioned earlier in $Atr$ . So Mizuhara deals 4 times the advantage damage instead of 2 times.

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

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

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

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

Card Order Optimization#

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

In FGO, you usually need to defeat enemies within 3 to 6 turns, but you only have 6 Servants, 18 skills, and 6 Noble Phantasms in total, and only 3 Servants can be on the frontline at the same time. Many buffs have a duration of 3 turns, and some powerful buffs only last for 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 powerful skills, which can be quite 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 the card order to stack buffs excessively. However, swimsuit Hanazuki is an exception. Hanazuki's passive skill allows her to use her EX three times in a row, and her EX only costs 2, so she can unleash astonishing 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, players can easily make 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 that is commonly used in Azur Lane but not in FGO: mathematical modeling.

Fortunately, game designers rarely introduce things that are difficult to handle mathematically, like Heartsteel in League of Legends. In Azur Lane, most of the time, mathematical modeling involves simulating battles, without the need to deal with differential equations and 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 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 the damage caused by Unicorn's EX is affected by various factors, but the only copy of that document was shared in a Telegram group that has since been disbanded. I may recalculate it in the future.

In general, for normal attacks, the damage can be considered uniform. Due to the law of large numbers, the effects of Stability Value and critical hits on normal attacks can generally be ignored. Therefore, in most cases, it is sufficient to calculate the damage and effects of skills and EX skills. The simplest way is to always assume that EX skills are used with full buffs, while small skills do not have 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 also necessary to consider healing and tankiness. Typical examples include Bishop's healing and Yukikaze's fight against Orochi. These can also be calculated simply based on skill cooldowns and values.

The real challenge lies in calculating the overall damage in multi-turn battles.

Assuming you have $n$ front-line ships and $m$ back-line ships to choose from, without considering borrowing ships, at turn $t$ , 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 turns, the time complexity of simulating battles to find the optimal solution is exponential, while in terms of available ships, the time complexity is polynomial.

Taking myself as an example, I have 36 back-line ships and 76 front-line ships to choose from. If I want to do 3 turns, I have approximately $1.88*10^{26}$ possible team compositions. Simulating battles 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. Although it still requires a lot of time, at least it can be calculated in a crowded situation.

Positioning and Control#

In some multi-turn battles, positioning is crucial. For example, Goz requires you to reach its true form in the second phase, and Black and White can dodge skills by 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 usually do not have immunity to debuffs either. Therefore, many bosses, especially male bosses, can be controlled to death. A typical example is Gorgon's "Don't Move Team". In Azur Lane, control skills are not very useful, except in total force 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".

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 generally 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 less gameplay but interesting stories. However, Azur Lane has auto-battle for farming, 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 multi-turn battles is a challenge that FGO does not have, and the various techniques in FGO can be effectively applied.

I will always love Azusa Shirasaki!