Be prepared; this section contains all the math and calculations needed to play. All of these calculations are very easy and can be performed using the calculator on a phone or even with a simple Excel sheet. All the math involved in creating and implementing these calculations are included. Remember that all values are rounded to the nearest whole number only at the end of a calculation.

Dodge and Parry Calculation
You chance for success for avoidance is based on the attacker’s Hit SVS (A Hit) and the defender’s Dodge SVS (D Dodge) in the case of the dodge roll or the defender’s Hit SVS (D Hit) in the case of the block / parry roll. The defender’s stat is divided by the sum of the defender’s stat and the attacker’s Hit SVS; this result is multiplied by 100%.

Dodge and Parry Roll
In order to determine the target roll, subtract your dodge or parry chance from 100% and the resulting number (sans percentage sign) will represent your target roll on a 100 sided die. If your roll matches or beats this target, your dodge or block / parry attempt is successful.

EXAMPLE:
-Dave has a Hit of 500
-Kenneth has a Hit of 300 and a Dodge of 600

Dave makes a physical attack against Kenneth. He declares a dodge roll and calculates his target roll:

Kenneth types “/random 100” and the result is a 33. His dodge attempt fails.

Kenneth has a STR PVS of 219 and Dave has a STR PVS of 350, meaning that he may attempt a parry attempt with the quarterstaff he is holding. He declares a parry roll and calculates his target roll:

Kenneth types “/random 100” and the result is a 63. His parry attempt is successful. He may avoid all damage by describing his parry in the “reaction” half of his prep. Since he parried, he cannot attack or use his quarterstaff on his turn.

Sidebar
A clever mathematical mind may come to the conclusion that if you subtract the success rate from 100% then use that as a target roll, you are actually committing an error. If you have a 50% chance of success, subtract that from 100%, then come up with 50 as your roll to match or beat, then you actually have 49 chances of failure (any roll from 1-49) and 51 chances of success (any roll from 50-100). This is an absolutely valid argument.

Even if “rounding errors” are attributed, this error in calculation is still ever-present. However, the ease of calculation in its current (though flawed) form makes it desirable. Also, this error is always in favor of the defender, so if you are trading blows with an enemy, you will take turns reaping the benefits of this skewed calculation, leaving the battle, in its entirety, fair to all involved.

Base Damage Calculations
A character’s base physical damage is equal to the sum of his Body SVS and the attack value of the weapon used, if any. The weapon’s attack value is equal to the character’s Proficiency SVS times the weapon’s attack rating (ATT).

A character’s base energy damage is equal to the character’s Mind SVS times his energy potency.

A character’s base elemental damage is equal to the character’s Spirit SVS times his elemental potency.

There are a few abilities (mainly job class capabilities) that can raise or lower base damage. That means that when calculating base damage, these bonuses or penalties come into effect. These will almost always be in the form of “half base damage” or “double base damage” but can also raise base damage by a numerical amount. These calculations must be done before unmitigated damage is calculated and must be calculated in this order.

Unmitigated Damage Calculations
Your unmitigated damage is your base damage plus any bonuses. Treat penalties as negative bonuses.

If you have multiple damage bonuses, these bonuses (and penalties) are additive. That means if you have two effects that give you 10% bonus damage, you then have a 20% bonus to damage. If you have a 20% bonus to damage and a 50% penalty to damage, you have an overall 30% penalty to damage.

Damage Reduction Calculations and Chart
Do determine damage reductions, you first need your character’s defenses. There are three defenses (and three damage reductions) that represent the three types of damage. The defenses of each are determined by the character’s stats and the character’s armor’s defensive values – armor defensive values are based off of the armor physical (PDEF) and force (FDEF) ratings and the character’s Proficiency SVS.

Note that an armor’s force defense value increases both energy and elemental defense.

Your damage reduction values are based off of an offset degrading function with dependence on defense. A function is just a fancy word for an equation or calculation and it having dependence on defense just means that defense is a variable in the equation. The offset means that the function will constantly be 0% until a certain values is reached. Degrading means that as your defense rises to greater values, each point of defense will be less effective at raising your damage reduction than the last. Meaning it takes more defense to raise from 20% to 30% DR than it does from 10% to 20%, meaning that it is relatively simple for a character to achieve a reasonable damage reduction, but it should take some work in order to maximize all of a character’s damage reductions.

The damage reduction function is the same for each type of damage reduction – each is based off of the respective defense (i.e. to find Physical Damage Reduction, use the equation substituting in Physical Defense where it simply says “defense”).

This function is shown as a “piece-wise” function, meaning that you use a different equation depending on the values of defense. If your defense is less than 100, then your damage reduction will be 0%, but if your defense is greater than 100, then your damage reduction is based off of that second equation. If you were to use a defense less than 100 in the second equation, you may end up with a negative damage reduction, which is never possible in Solaris.

On a character’s Vital Stats Page, the character’s (and his companion’s) damage reductions are calculated and shown. These values will always be relevant, so the only reason for you to need this function is if you wanted to look at a hypothetical case.

Mitigated Damage Calculations
Mitigated damage is very simple to calculate. You subtract reduced damage from unmitigated damage (in a sense, mitigating it). To determine how much is removed, you take a percentage of the incoming attack based on a character’s damage reduction. Remember that the type of damage determines which of the three Damage Reduction values you will use.

If you want to do some substitution and simplification, you can makes a more condensed formula. If this formula does not make sense to you, the above will work just the same, so you are welcome to use whichever form you like.

Stat Changes Calculations
The following stats can be changed (as described in the Vital Stats Guide): Hit and Dodge SVS; Base Physical, Energy, and Elemental Damage; Bonus Physical, Energy, and Elemental Damage; and Physical, Energy, and Elemental Damage.

When changing Hit and Dodge SVS, all bonuses and penalties are additive, meaning you can just take the different bonuses and add them up (penalties count as negative bonuses). This means that if you have a 10% bonus, and 20% bonus, and a 30% penalty all to your Hit SVS, this adds up to 10% + 20% - 30% = 0% or an overall nullification of bonus.

When changing base damage values, as described above in Base Damage Calculations, you must apply any change before calculating unmitigated damage. If you have an effect that doubles/halves base damage and an effect that increases/decreases base damage by a numerical amount, the calculation must be done with the multiplicative benefit first and the numerical amount second.This means that any "doubling" or "halving" is done first, and any bonus or penalty of a numerical amount is done last.

Bonus damage, as described above in Unmitigated Damage Calculations, are done in the same way as bonuses to Hit and Dodge SVS.

Changes in damage reduction are additive to the character’s normal damage reduction value. Meaning that if you have a Phys. D.R. of 25%, have a Phys. D.R. bonus of 10% and a Phys. D.R. penalty of 5%, your Phys. D.R. will total at 25% + 10% - 5% = 30%. Remember that if a character’s damage reduction is ever over its respective cap, then you will treat your character as having damage reduction equal to the cap. Also, if a damage reduction penalty would reduce any damage reduction below 0%, it is instead lowered to 0%.