Thread:SPEAR GOBLIN/@comment-29396184-20170122141203/@comment-25856498-20170311154411

Everyone knows that the stats of most cards, especially health and damage, are increased by about 10%. However, this does not always seem to be the case, and the change in stats appears to be erratic. Consider the level 2 Prince and the level 3 Inferno Dragon. Both have 1,210 health (even though they are not equivalently leveled, I'm using both of them for this case). When both the Prince and the Inferno Dragon level up by 1 level, the Prince gains 121 health, as expected. But, the Inferno Dragon only gains 120 health. So what seems to be the reasoning behind this?

The answer lies in internal values within the game's code known as the "PowerLevelMultiplier". These values govern most statistics. They are shown in the table below: The value of PowerLevelMultiplier for a certain level can be found given that you have the value of PowerLevelMultiplier for the previous level. Take the value of the previous level's PowerLevelMultiplier, multiply it by 1.10, then round down the answer to the lower integer. In other words, the values can be represented in the functions below: where $$M_n$$ is the PowerLevelMultiplier for that level, $$M_1 = 100$$

$$M_{n+1} = \lfloor1.1M_n\rfloor$$ So how does these values apply to the stats of cards? The answer is simple. Simply multiply the base stat of the card (the stat of the card at level 1) by the PowerLevelMultiplier for the level given above. Divide the result by 100 and round down the answer to the lower integer.

Let's apply this to the level 2 and 3 Prince and level 3 and 4 Inferno Dragon from before to see this discrepancy:

The base health (at level 1) for the Prince and Inferno Dragon is 1,100 and 1,000 respectively.

The health of the Prince at level 2 = $$\Biggl\lfloor\frac{1,100*110}{100}\Biggr\rfloor = 1,210$$

The health of the Prince at level 3 = $$\Biggl\lfloor\frac{1,100*121}{100}\Biggr\rfloor = 1,331$$

The health of the Inferno Dragon at level 3 = $$\Biggl\lfloor\frac{1,000*121}{100}\Biggr\rfloor = 1,210$$

The health of the Inferno Dragon at level 4 = $$\Biggl\lfloor\frac{1,000*133}{100}\Biggr\rfloor = 1,330$$

Now you can see how the leveling system really works, and why certain levels get increases of far less than 10%, somewhere in the range of 9.6% rather than 10%. This is especially prevalent between level 7 and level 8, and hence prevalent in the final upgrades of Epic cards.

Second example: Dart Goblin and Princess. Both have 216 health at tournament standard but there is a difference in health between level 9 Dart Goblin and level 3 Princess (Dart Goblin has 260 health and Princess has 261).

This can be visualised as follows:

The base health (at level 1) of the Dart Goblin and Princess is 123 and 216 respectively.

The health of Dart Goblin at level 7 = $$\Biggl\lfloor\frac{123*176}{100}\Biggr\rfloor = 216$$

The health of Dart Goblin at level 9 = $$\Biggl\lfloor\frac{123*212}{100}\Biggr\rfloor = 260$$

The health of Princess at level 1 = $$\Biggl\lfloor\frac{216*100}{100}\Biggr\rfloor = 216$$

The health of Princess at level 3 = $$\Biggl\lfloor\frac{216*121}{100}\Biggr\rfloor = 261$$

The health and damage increases of the King's Towers and Arena Towers work in a similar fashion. Up to level 9 (tournament level), they gain 7% per level and 8% per level respectively rounded down, rather than 10%. Above level 9, they gain 10% a level in a similar fashion.

This can be represented below:

Using this, we can extrapolate the King's Tower health and Arena Towers' health at level 14 to be 6,408 and 4,032 respectively. They will also do 133 and 144 damage respectively.

Sorry for long post but I hope that clears up everything.

Additional note: The Clan Battle Kings' Tower has 4,810 health. This does not fit the formula for any base health (closest is around 2,880) given a PLM of 167. A base health of 2,880 gives 4,809 health at level 9 while a base health of 2,881 gives 4,811 health at level 9. So the system might be revamped soon.