Guides

Intro

I was curious about how damage is calculated, so I started taking a bunch of data and analyzing the results. I've figured out the formulae, so I thought I would share. :)

I also have a calculator tool that can make use of all of the formulae for you. The first mode (enemy requirements) will tell you how much STR you need to KO enemies with certain skill combos. The second mode (calculator) will let you calculate skill effects. The third mode (enemy stats) contains charts per venue of enemy stats with their elements and ability info. Click here for the skills and stats tool.

Note: This guide focuses on skill mechanics related to the amount of damage / healing / effects and how skill calculations are made. It does not describe all the details of each Battle Stone. For specific Battle Stone info, please visit Maki's Battle Stones guide.

Mathematical terms

round: Take the whole number that is closest, with anything below .5 taking the lower number and anything .5 or above taking the higher number. (Ex: round(3.2) = 3, round(3.5) = 4)

floor: Round down to the nearest whole number. (Ex: floor(2.9) = 2)

ceiling: Round up to the nearest whole number. (Ex: ceiling(3.1) = 4)

modulo (%): Remainder of division. (Ex: 5 % 3 = 2)

Health

Health is a function of the VIT stat and the level. Each contributes a certain amount of points that add up to the total health.

Every VIT point adds 20 health.

Every Level adds 30 health.

The health gained from VIT and Level are added together for the total health.

* All dragons, enemies, and bosses follow this formula for Health. Bosses have more health because they get a lot more stat points to spend.

Damage from skills

All damage dealt is based on some function of the caster's offensive stat and the target's defensive stat. The function varies depending on the skill.

For physical attacks, the offensive stat is STR, and the defensive stat is DEF.

For magic attacks, the offensive stat is INT, and the defensive stat is MND.

The minimum damage for a hit is 1. A critical hit's effect will be applied after the minimum damage rule, meaning that crits at minimum damage will cause 2 damage.

Damage may be modified in several ways including critical hits and elemental effectiveness multipliers (listed in the Skill effect modifiers section below). Check the additional information section for details on some edge cases of order of application and rounding.


Damage from skill special effects

Some skills have special effects, and the calculation modifiers vary.


Skill effect modifiers

There are multiple ways that skill damage or skill healing may be modified. The following list includes the various modifiers that may be applied in each situation.


Healing from skills

Some skills can heal their targets.


Buffs

Some skills can buff stats or add other effects. Many of these stats and effects can modify damage or healing in some way.


Miscellaneous

Some skills don't quite fit in the other categories and do not cause damage or healing on their own.

Rounding and order of application

Skills and stat calculations are rounded in a certain way. Knowing the rounding mechanics is important because it affects the edge cases; if our understanding is incomplete, it would be possible to experience off-by-1 situations.

In addition, this section describes the order in which skills and effects are applied in situations where the order might not be clear. It is important to understand the order of application because the calculations can be affected depending on which skills and effects are considered first.

• The 5% stat camping bonus introduced in Coliseum 2.0 rounds up to the nearest whole number, or in other words, performs a ceiling. This means that a 117 STR dragon will have 123 STR with a 5% STR camping bonus, and a 5 MND dragon will have 6 MND with a 5% MND camping bonus.
• Anticipate will calculate damage reduction based on the target’s defensive stats. Buffs are applied before this calculation, meaning that Bolster will add DEF that will then benefit Anticipate.
• When multiple bonuses are active, critical hit bonus is applied after other bonuses but before rounding. For example, an elemental attack that should do 347 damage normally will do round(347/2) as an ineffective element, which is 174 damage, but if that attack crits, it will do round (347/2 * 2), which is 347 damage, NOT round(347/2) * 2, which would be 348 damage.

Additional skill mechanics

• Reflect always applies the effects based upon the offensive stat of caster of the Reflected spell and the defensive stat (if applicable) of the recipient of the Reflected spell. Reflected spells can be dodged based on the AGI stat of the recipient of the Reflected spell.
• Bite can only be learned by Coliseum enemies. It deals the same damage and builds the same Breath as Scratch.
• Pollen can only be learned by Coliseum enemies. It grants the same base Breath as Meditate (30), but it can never be buffed by Discipline since enemies cannot equip that stone. It also does not cause Meditate Exhaustion.
• Flutter can only be learned by Amaranth Moth. It does not have any effect besides wasting a turn.
• A caster under the influence of the Berserk debuff will always use the move "Scratch" (even if it doesn't know the move normally) and damage is calculated according to its own STR and all the other normal damage rules.

Current bugs

These bugs currently still occur and can be the cause of confusion when making skill effect calculations.

Currently no known bugs that cause calculation issues. The devs have squashed a bunch!

Archived bugs

These bugs used to happen, but they have since been fixed. This archive maintains a record for curiosity's sake.

• Concentration used to not apply its stat buff even though the buff was displayed (similarly to Berserker stones). At some point, this was fixed; the behavior is evident when comparing pre-buff to post-buff Regeneration values.
• All the Buff-type skills used to contribute a small amount of healing equivalent to the caster's INT. When applied, it did not show up during the battle where the buffs were cast, but they healed the target immediately, for as many times as the buff was cast. The fact that the healing did not show up on the battle was simply a display error. (This is why sometimes our dragons may have seemed to have 0 HP but did not get KOed; the extra instant health from the buffs made it able for our dragons to survive.) With the release of Coli 2.0, both these bugs were squashed.
• In the past, flights with Dominance would show an extra +1 stats when displaying the dragon's battle stats. This caused issues such as expecting +1 STR for the dragon's damage or wasting Tincture of Dissolution. The incorrect stats were removed from dragons' Coliseum pages while using Tinctures after Coliseum 2.0 was released, but they remained for some time on the dragon profiles. The revamp to the dragon profiles during Flight Rising's 7th Anniversary seems to have gotten rid of the confusing profile stats as well.

Disclaimers

Q: "Will you share your tool data in a specific format for me / review my calculations for my own projects / help me work on my own projects?"

A: I'm afraid that I'll have to decline. I'm happy to answer specific questions regarding my guide and/or tool, but seeing as I'm very far behind on my own personal projects myself, I can't commit to providing tailored services for yours. The guide and tool provide all the information that you need; please feel free to put in the expected minimal effort required to convert the data for your own use. Inquisitive minds should be willing to do their homework. ;)

Tool updates

If you'd like to be pinged whenever there is a major update to the coliseum skills + enemies calculator tool, please subscribe to the ping list. :)

Special thanks

• lemondrop for the original iteration of the Coliseum monster stat chart, without which stat-damage observations would not have been possible.
• The FR Devs, for saying that grabbing the monster data is absolutely okay! As of Dev 4, 2019, data mining became unnecessary, as the devs gifted us with the wonderful Game Database. Thanks again!
• Salmastryon, whose Battle Stones guide was a helpful quick-reference.
• Cyradis4 for noticing that Enfeeble damage is different than the other elemental special damage and for providing the data to calculate Enfeeble's formula, along with additional data for other elemental specials to confirm that they follow the first pattern. Also for relaying the method for collecting monster stat data so that I can look up new monster data that isn't yet available.
• nika for providing the data for Clobber.
• Kiena for inspiring me to make the tool with her Coliseum grinding and exalting guide and for providing me with all the support that motivated me to continue developing the tool. Also for helping to provide monster data and find bugs.
• Maki for suggesting improvements to the tool, testing a bunch of stuff, providing a ton of data (including data during the dark days of Coli 2.0 before the Game Database), and alerting me when discovering any new info. Also for the lovely new Battle Stones guide!
• car340 for helping to grab monster data.
• Meredith44 for noticing that the elemental ultimate damage multiplier for super effective attacks did not match the numbers in the calculator tool. This helped me to find out that the code for the elemental ultimate and elemental bolt were subtly wrong so that I could fix it. Also, for continuing to help report whenever an old monster's stats have been changed!
• RageAsylum for pointing out that the health formula listed in the guide didn't match the true functionality in the tool, and for providing data on turn order.
• Zamirathe for finding a workaround for the tool's Firebase host not being accessible to some people (see this post).
• Serpenthyne, Munchcatto, and Lililira for volunteering with data collection during the dark days of Coliseum 2.0 before the Game Database was introduced.
• schafpanda for confirming that Bite now grants 6 Breath like Scratch.
• gn0me for pointing out the confusing wording of the old Reflect description.
• LunchBox1211 for pointing out that Regeneration is now buffed by Concentration; it's very likely that Concentration had a bug in the past that did not apply the stat buff even though the buff was displayed.
• Anyone else who has helped to improve this guide through comments, volunteer work, and extra help. Thank you! :)

@nika - Yeah it's definitely a no-no to report values that were inflated with those items! Since they don't actually contribute damage, the stat level would be incorrect if those effects aren't removed. For simplicity's sake I avoided buffs/debuffs too; it's entirely possible to calculate the correct base damage off of those but it just makes reporting require more details.

Berserker is supposed to give 5 STR each, so 3 * 5 = 15 and 49 - 15 = 34 base STR.

I think those numbers are good enough to work with, thank you :)

@nika - I've got a question for you, when you fought Longneck Mender did you happen to be hit by Contuse?

@nika - Naw, I'm 100% sure you were hit by Contuse. Your data's fine, I just need to go interpret it. Thank you :)