User blog:LadyAzur/Calculation Combat

Do you like maths? No? Then you shouldn't read any further. I really like mathematics and calculations and I am very curious about how Habitica calculates things. But the wiki does not contain all formulas, so I need to guess how something is calculated. This week I fiddled out how the Brutal Smash damage is calculated if you get a Critical Hit.

Some days ago, I changed my class to Warrior to help my Party with Quests. I changed my Equipment accordingly, to get a high Strength-Bonus. With my Perfect Day-Bonus I'll get a STR of 197. If I am using Brutal Smash, I will do 40.6 damage to the boss.

You can find the formula on the Warrior wiki page:
 * $$( 55 * STR / (STR + 70) )$$

So with STR = 197 you'll get:
 * ( 55 * 197 / (197 + 70) )
 * = 10835 / 267
 * = 40.58 (rounded to 40.6)

Ok. That was easy. But sometimes I got a pop-up with 48.9 damage to the boss. And I wondered why.

Because it was more than my normal damage, it must have been a Critical hit. But the Warrior wiki page shows only the formula without a critical hit, and I wanted to know how the extra damage was calculated.

The Critical Hit wiki page shows a formula for the overall damage multiplier:
 * $$1.5 + { ( 4 * STR ) / ( STR + 200 ) }$$

And somewhere at the bottom you'll find the hint, that "The frequency and size of the critical hit depends on one of the player's attributes: Brutal Smash - Constitution".

I did not pay attention to this little sentence at the bottom of the page and tried to calculate an overall damage multiplier with my strength value of 197 and insert it into the Brutal Smash formula. No, this wasn't right!

"The size of the critical hit depends on the attribute Constitution" - if you read the sentence carefully enough, you will come to the conclusion that you have to replace STR with CON to get the overall damage multiplier for the skill:
 * $$1.5 + { ( 4 * CON ) / ( CON + 200 ) }$$

That was easy, because I had a constitution value of 100:
 * 1.5 + { ( 4 * 100 ) / ( 100 + 200 ) }
 * = 1.5 + { 400 / 300 }
 * = 1.5 + 1.33
 * = 2,83 (rounded)

This is the CON-based damage multiplier that needs to be inserted into the Brutal Smash formula:
 * $$(55 * STR * CriticalHitDamageMultiplier) / ((STR * CriticalHitDamageMultiplier) + 70)$$

The damage calculation is based on STR, so you have to multliply your STR value with the critical hit damage multiplier.
 * (55 * 197 * 2,83) / ((197 * 2,83) + 70)
 * = 30663,05 / (557,51 + 70)
 * = 30663,05 / 627,51
 * = 48,86 (rounded to 48,9!)

Yay! I got it!