Trivia about the Ability Tree System

This page introduces various information that are good to know about the Ability Tree system and might be helpful in case you want to try to use this system efficiently.

Quests that drop Principle Fruits
Both regular Principle Fruits as well as Special Principle Fruits only drop on specific Quests of chapters from Arc 2. In general, the fruits drop at boss quests. Each Quest drops 3 types of Fruits: One regular fruit, one special fruit for elemental resistance and one special fruit for increased chance of applying abnormal status effects. The following table lists all Quests that drop Principle Fruits, as well as some further information (like which fruits are dropped):

Fun facts
 * The element whose resistance gets increased is the same as the element of the boss you face. This means that quests with Hinageshi will always drop special fruits for wind resistance and never fruits for moon resistance or fire resistance (unless there is another boss of these elements in this quest).
 * There are 5 regular fruits and 5 versions of Special Principle Fruits for increased chance to apply abnormal status effects. Apparently, these two types are linked together, which means that a quest that drops Fruits of Life will always have special fruits for increased chance for confusion and never special fruits for increased chance for sleep or for paralysis.
 * The 5 regular fruits are recurring in a cycle: HP -> ATK -> DEF -> MATk -> MDEF -> HP. This means that every 5th quest that drop Principle Fruits will drop Fruits of Power. If a quest dropped Fruits of Power, the next quest that drops Principle Fruits will drop Fruits of Defense etc.

Drop rates and efficient grinding of Principle Fruits
Now that you got the list of all Quests, you might wonder what's the best Quest to get Principle Fruits. To explain this, it's needed to explain the drop rates of the drop rates of Principle Fruits.

As a general rule, the drop rate scales proportionally to the amount of stamina you need to pay to enter the quest. For regular fruits, 1 stamina is equal to a drop rate of 20% (or 5 stamina is equal to 1 regular fruit). For example, Quest 27 from Chapter 1 costs 9 stamina, thus the drop rate for the regular fruit (which is a Fruit of Life for this particular Quest) is 180%. This means that you are guaranteed to get one Fruit of Life, and in 4 out of 5 Quests, you get a second fruit as well.

This is similar for Special Principle Fruits; here, 1 stamina is equal to a drop rate approximately 0.56%. If there are 2 different types of special fruits, this probability splits equally between the two fruits. For example, Quest 31 from Chapter 1 costs 10 stamina, thus a special fruit drops with a drop rate of 5.6%, but as there are two types of special fruits, each one only drops with a drop rate of 2.8%. If there are three types of fruits (like in Quest 30 of Chapter 3), the probability is not split equally among all 3, but still, the total probability remains the same.

By these explanations, you will notice that regardless of what Quest you choose, the chances to get Principle Fruits remains the same, as the total amount of stamina needed will remain the same, at least in terms of probability.

One last question remains: What about Trial Quests?

Trial Quests cost 40 stamina, which is equal to 8 regular fruits. And indeed, you get 8 regular fruits, namingly: 2 Fruits of Life, 1 Fruit of Power, 1 Fruit of Magic, 2 Fruits of Defense and 2 Fruits of Magical Defense (these numbers are fixed). So you could get the impression that doing the Trial Quest might be a good idea. But this thinking is wrong for two reasons:
 * There are no special fruits on the Trial Quest. Since you are grinding Principle Fruits, you might as well try to get these while you are at it. Well, if you don't care for special fruits, then this doesn't make much of difference. Trial Quests would actually be the better choice, as beating this one Quest is faster than beating other Quests that cost a total amount of 40 stamina. So in terms of time efficiency, Trial Quests are recommendable.
 * As stated above, you get a fixed number of all 5 regular fruits. But in most cases, you don't want to grind all 5 types of regular fruits at the same time, but only one. As you get 1 fruit for every 5 stamina you pay, you could spend 40 stamina to get 8 fruits of the type you want instead of getting 8 fruits of different types. Thus, the Trial Quest is not recommended unless you don't care about the type of fruits you get.

Principle Fruits, Grades and the exact effects
As stated here and here, you can upgrade the level of Principle Fruits. Doing so will increase the effect the fruit will have on the character. Here, the exact effects will be introduced.

Regular Principle Fruits
Regular Principle Fruits boost a status of the character. It's an absolute boost and not a relative one, which means the boost is independent from the character's base value for the status that's to be boosted. It's not an increase by a certain percentage.

The actual boost varies slightly depending on the type of the fruit. The following list states all boosts:

Note: The "Maximum boost" can be achieved by filling Grade3 fruits of the same type in all Slots of the Ability Tree. For some characters, the passive skill from setting a Special Principle Fruit might be lucrative, thus some characters will only use 15 Grade3 fruits, while others don't need the passive skill and can thus use regular fruits on all 16 Slots. That's why there are two different numbers stated for the maximum boost.

Special Principle Fruits
A Special Principle Fruits gives a character an additional passive skill. As there is a variety of different types and versions for special fruits, the effects also vary. The following list states all effects:

Note: Only the following alterations are considered a buff/debuff: Alterations of ATK, MATK, DEF, MDEF, SPD and LUK (=critical chance). Any other alteration like taunt up or elemental resistance is not considered a buff/debuff. Thus, the duration of such an alteration is not extended by a Fruit for extended duration of buffs/debuffs. There may a different Fruit for these specific skill effects. For example, to extend the duration of taunt, you can use a Fruit for extended duration of taunt.

Note2: If a skill has the effect to charge the totteoki gauge, then this effect is not increased by the Special Fruit for increased amount of totteoki charge as this is not counted as the totteoki charge value of that skill but as the effect of that skill.

Some interesting calculations
Here, some interesting calculations regarding the Ability Tree system are displayed.

Regarding Regular Principle Fruits
As stated above, you could get a maximum boost for one status of a character if you set Grade3 fruits of the same type onto all 16 Slots of the Ability Tree. Since you need 450 Grade1 fruits to create one Grade3 fruit, you'd need 7200 Grade1 fruits to get a full set of 16 Grade3 fruits.

The calculations don't end here! As you need 5 stamina to get one Grade1 fruit, you'd need to spend 36000 stamina to get a full set of 16 Grade3 Fruits. If you tried to gather all fruits by normal stamina recovery, this would take 125 days (and you'd have to spend all stamina on Quests that drop Principle fruits). If you use gold clocks to recover stamina yourself, even with User Rank 120 you'd need to spend 249 gold clocks. Of course, if you make use of a half stamina campaign, you would only need half the amount of clocks.

If you want to have Grade3 fruits for a full party (meaning for 5 characters), you'd need to gather 5 times of the amount stated above. Whether you want all 5 character's to have the same status boosted, or whether you want different statuses boosted doesn't matter, you'd need 5 times of the stated amount, meaning a total of 36000 Grade1 fruits.

Regarding Special Principle Fruits
Similarly to Regular Principle Fruits, it is also interesting to do some calculations on special fruits.

Since for Special Principle Fruits, you need four Grade1 fruits to create one Grade3 fruit, 20 Grade1 fruits is the highest amount you'll ever need for a full party, even if you want all 5 characters to use use the same passive skill.

Two types of Special Principle Fruits (namingly those for extended duration of skill effects, and those for increased amount of totteoki charge) can only be obtained via the Item Shop and the Trade Shop, thus there are no calculations to be done here. If you want these fruits, you just buy them in the shops. If you want multiple copies of the same fruit (be it for upgrading the fruit, or be it to have the same passive skill for several characters), you just need to get the necessary amount of them. But as it's not clear yet how long it takes for a specific fruit to be offered again in the shop, there are no means to tell how much time it takes to upgrade one special fruit of these two types to Grade3.

As for the other two types of Special Principle Fruits (namingly those for elemental resistance, and those for increased chance to apply abnormal status effects), it may be interesting to calculate the estimated amount of stamina to get 1 specific fruit, to get 4 copies of that specific fruit (to upgrade it to Grade3) and to get 20 copies of that specific fruit (to get the a full party's worth of Grade3 fruits).

Most quests drop 1 special fruit for elemental resistance and 1 special fruit for increased chance to apply abnormal status effects. In this case, the drop rate for either of them is 0.28% per stamina. Thus, the expectation value to get one fruit of either type is 357.14 stamina. To get 4 copies of them, you'd need about 1428.57 stamina, and to get 20 copies (which is the maximum amount ever needed), you'd need about 7142.86 stamina. As this is less than the 36000 stamina needed to fully equip one char with a specific type of Regular Principle Fruits, you are likely to get enough Special Principle Fruits for a full party just by gathering Regular Principle Fruits for 1 character.

If a quest drops more than 1 special fruit for elemental resistance and 1 special fruit for increased chance to apply abnormal status effects (as of now (June 2021), there is only one quest to do so), the probability of 0.56% per stamina is split among 3 fruits, thus the chances to get either specific one is lower than on other quests, and you'd need to spend mote stamina to get 1 special fruit here. Thus: If you want to get a specific type of a Special Principle Fruit, you'd better choose a quest that only drops a total of 2 different types and not a quest that drops 3 or more different types.

Regarding Quest Keys - Tree
As there are only limited means to obtain Quest Keys - Tree, but you need to get a lot of them, it might be interesting to calculate the amount of time needed to get the necessary amount of keys needed to fully unlock one Scroll.

You need a total of 111 Star Beads to unlock all Slots of a Scroll, and you get 2 Star Beads per cleared Excavation Quest. Thus you need a total of 56 keys to fully unlock all Slots of a Scroll. As of now (June 2021) there are only two means to get keys. You get 5 per week from Weekly Missions, and you can get up to 20 keys per month from the Trade Shop.

If you only use the Missions to get keys (because you don't want to spend Starlight Stones in the Trade Shop), you'd need 11.2 weeks to gather 56 keys. That's about 2.5 months. If you also use the Trade Shop, it will only take about half the time, because the Trade Shop offers about the same amount of keys than the Missions: If you look at a span of 3 months, you can get up to 60 keys from the Trade Shop. But 3 months is about 13 weeks, thus you can get about 65 keys from Missions. So in case you use both the Missions and the Trade Shop to get keys, it will take about 5.6 weeks to get enough keys for one Scroll.

Is it worth to spend Starlight Stones for Quest Keys - Tree?
As just stated, it takes 2.5 months to gather enough Quest Keys from Missions to fully unlock one Scroll. And it happens that 2.5 months is about the same time they take to add a new chapter. Since everyone started with 3 Scrolls and roughly 0 Quest Keys, you could say that you naturally gather enough Quest Keys for all Scrolls added after started, but nothing more.

You can conclude 3 things from this:
 * If you buy Quest Keys from the Shop, you only need to buy enough to fully unlock 3 Scrolls. That's roughly 168 Quest Keys, which equals to 1680 Starlight Stones. It takes 8-9 months if you start now.
 * If you don't buy any Quest Keys from the Shop, you will always lack 3 Scroll's worth of Quest Keys, since all other means to gain Quest Keys are just enough for any newly added Scroll.
 * Of course, this is only true as long as Arc 2 is still on-going! Once Arc 2 is finished and they don't add any new Chapters, they will also stop adding new Scrolls. Thus you could gain the 3 Scroll's worth of Quest Keys from Missions starting from then. To gain the necessary 168 Quest Keys, it would take about 33-34 weeks starting from addition of the final chapter, which is 8-9 months'.