Skill Increase Strategy

It is also really text ugly.

A Hero has two traits you need to level up to begin maximizing its power in Battle -- Rank Level and Skill Level. Both are accomplished through the same leveling process, referred to as feeding, where you merge (or feed) up to nine other Heroes into the Hero you wish to level.

When you feed a Hero, each piece of food adds a set amount of Experience based on its own level, rank, star-category, and color. This Experience is cumulative and dictates the Hero's **Rank Level**, which is the sole determiner of its base numerical stats (Attack, Defense, and Health). A Hero starts with both a Rank and a Rank Level of 1 (which would be 1,1 in Chat shorthand). When you've fed your Hero enough to bring it to the maximum level for that Rank, any more feedings will have no effect on its Rank Level -- at this point you should Promote your Hero to the next Rank, which will also reset its Rank Level to 1 and allow you to again feed it effectively (until it reaches its overall Max).

The Hero's **Skill Level** is entirely separate from its Rank Level. The Skill Level dictates how powerful the Hero's special Skill is. The Skill is the effect described in words at the bottom of each Hero Card. Skills are often crucial in Battle so you want to make sure you get yours up as high as possible.

When you feed a Hero to increase its Rank Level, you also get a chance to increase its Skill Level. The chances are fairly small, for example feeding a single 1\* to another Hero gives a 1% chance to increase its Skill Level -- unless both Heroes are the same color, then the chance increases to 3%. That difference may seem insignificant, but makes a Skill increase three times more likely and is definitely important.

The following table shows how much XP is gained by feeding a Hero. For example, feeding a 2\* Hero of Rank Level 2,5 gives 880+5\*20 = 980 XP. Note that for purposes of feeding, a promotion is treated as one level. That is, when a Hero is promoted, its XP value as food increases by the same amount as if the Hero gained one level. Of course, the additional amount of XP per level is much less than the cost of gaining another level, so you should never level-up a Hero if you intend to use that Hero as food.

Feeding a Training Dummy to a Hero does not give the same XP that feeding a Hero of the same stars and rank does (although the chance to increase skill is the same).

 1\* Dummy 2,20
 2\* Dummy 3,40
 3\* Dummy 3,50
 4\* Dummy 4,70
 5\* Dummy 4,80

TABLE OF PERCENTS

An interesting aspect of feeding Heroes is that Skill increase chances are added up for each feeding. So if you feed the maximum at one time of nine 1\* Heroes of the same color, you get a 9 x 3% = 27% chance of an increase. This is different than if you fed those nine 1\* separately, which would be nine chances of 3% each. So which way is better?

**SHORT ANSWER:** It really doesn't matter.

*Credit = This analysis is based off of some work I was shown that someone else did for the game Empires and Puzzles, which uses a similar feeding mechanic. I disagree with the conclusion they reached however, so am expounding my own reasoning here. Would love to know if I've done anything wrong, just let me know. (Falter)*

Every Hero Star-Category (1\*, 2\*, etc.) has its own quirks for Skill leveling:

* 1\* have one auto increase, 2\* have two, 3\* have three, and 4\* and 5\* have four
* The higher the Star-Category, the more opportunities to get an increase due to more feedings required

For example, if you feed a 1\* Hero other heroes of the same color, it will almost always reach its max Rank Level (2,20) before getting even close to its max Skill Level (10/10). To maximize its Skill Level, you should feed it almost exclusively duplicates (e.g. feed Bastian only other Bastians). Feed four duplicates at once, guaranteeing a Skill increase to 2/10. Then feed four duplicates again, increasing to 3/10. Feed any one hero of any color, and then promote, increasing to 4/10. Feed four duplicates six more times will max the Skill Level at 10/10, and then two more heroes of any color will bring it to the max Rank Level (2,20). Note that if you fed 35 duplicates one at a time (instead of 4 at a time), then you would only have a 67.77% chance of reaching Skill Level 10/10.

If you feed a 2\* Hero other heroes of the same color, it will almost always reach its max Rank Level (3,40) before its max Skill Level (10/10). But, again, if you feed it many duplicates, then you can max the Skill Level. Approximately 11 duplicates and 145 1\* Heroes of the same color will give exactly the amount of XP to reach max Rank Level and have a mean expectation of getting to the max Skill Level (10/10) at the same time. But since increasing Skill Level is random, your mileage may vary. If you reach Rank Level 3,38 and do not yet have max Skill Level, then feed four duplicates at once. If you reach Rank Level 3,36 and still have Skill Level 8/10 (or lower) then feed four duplicates at a time until you get max Skill Level. Similarly if you are at Rank 3,34 and have Skill 7/10 or lower; or if Rank 3,32 and Skill 6/10 or lower. You should not feed 2\* Heroes (or higher, or any Training Dummies) to other 2\* Heroes when they are not duplicates, because that will increase their Rank Level faster than their Skill Level.

Feeding mostly 1\* and 2\* Heroes of the same color to 3\*, 4\*, or 5\* Heroes will almost always reach their max Skill Level long before their max Rank Level. For example, a 3\* Hero requires about 600 1\* Heroes or 250 2\* Heroes to reach max Rank Level, but only (on average) about 200 1\* Heroes or 120 2\* Heroes to reach max Skill Level. That means that you can feed a modest amount of higher-level Heroes or Training Dummies to 3\* Heroes and still not worry about reaching max Rank Level before max Skill Level. And 4\* and 5\* Heroes require so much more XP that it's hard to get them to max Rank before max Skill.

So that leaves 3\* as a good category to focus on, and interestingly, a 3\* takes the same number of 1\* to get its Rank Level at 3,50 as a 5\* does to reach Rank Level 2,60.

Let's start with getting a 3\* to Rank Level 2,40, which is a good midpoint in early leveling and when it starts becoming nicely powerful. Ideally we would like to reach a 10/10 Skill Level by then, or as high as possible. Using binomial probability we can calculate the likelihood of each potential outcome (2/10, 3/10 ... up to 10/10) by this point. (2/10 is the minimum possible because it starts at 1/10 and has an automatic increase with the Promotion from 1,30 to 2,1.)

*It actually takes 146 1\* to get a 3\* to 2,40, but because each Rank maxing requirement is not an even multiple of 9, I've backed the number down to the actual number of x9 feedings possible (15 feedings of x9 thus 135 of x1) -- the leftover affects each probability equally so can be ignored for our purposes here.*

 2/10
 3/10
 4/10
 5/10
 6/10
 7/10
 8/10
 9/10
 10/10

Let's look at that graphically to visualize it better:

We see probabilities for each outcome that are fairly similar, but upon closer examination, the distribution curves are different. The probabilities for middle outcomes are higher for x9 feedings and the probabilities for very good and very bad outcomes are higher for x1 feedings. This makes sense when you think about it -- with the higher probability x9 feedings, you are less likely to have failures all the time but also don't have as many opportunities for lots of successes. *As the number of chances increases, I think the distribution curves would move toward each other, eventually becoming identical at infinite chances, but we are dealing with limited chances here.*

Based on this data, in general feeding x1 is equivalent to gambling slightly on getting Skill Level increases faster at the risk of instead getting them more slowly...but let's go a step further and look at feeding a 3\* higher, to 3,50 (3/10 is the minimum Skill Level here due to the two Promotions).

 3/10
 4/10
 5/10
 6/10
 7/10
 8/10
 9/10
 10/10

Again a graphical look, but focusing on just the more likely outcomes:

This is a different distribution curve. This indicates x1 feeding is more likely to be worse. Why is that?

Since we don't care about having more than seven successes (which gives a max 10/10 Skill Level due to the automatics at each Promotion), all of the top end of the distribution curve is crushed into just the top possible outcome. This upper end crush happens in the previous example too of course, but the probabilities above 10 in that example were so small they went unnoticed.

Maxing the Skill of a 3\* by the time it has reached 3,50 is a 81.3% probability with x1 feedings and a 85.1% probability with x9 feedings...not a really significant difference, but shows x9 is slightly better.

So you should always feed x9 right? Well, not necessarily. If you are planning to use the 3\* while you are leveling it (like if building your first team), then you should consider the importance of getting increases sooner, which goes back to the earlier calculations showing x1 feeding gambles getting slightly faster increases at the risk of slower, and factor that into your decision.

So we are left with three choices. If you:

* want to try to get Skill Increases as fast as possible, then feed x1
* want to make sure you have the maximum likelihood of being 10/10 when at max Rank Level, then feed x9
* look at these tiny differences in probabilities and say "Who cares?", then feed any which way you want!
* want to know my method, I feed x9 if I have 9 to feed just because it takes less time to get your feeding done that way, otherwise I feed whatever amount is available because in my opinion ... see "SHORT ANSWER" above.