Minions of the Fickle Muse

For those who really wanna Min/Max – I found an articular over at Sithwarrior.com with all the formulas used for combat ingame. Due note – While I'm posting a version here – these numbers might change as the game goes on and more people are able to break down what the game is doing.

Original Artical – SWTOR formula list @ Sithwarrior.com

The purpose of this formula list to to assist the SW:ToR community in theorycrafting and making guides. Special thanks to LagunaD, Takira and the theorycrafting community at Sithwarrior.com – Freehugs

Note: Bonuses from Buffs and Skills are additive to whatever stat they apply. For example a 5% crit buff adds 5% to your total crit, there's no fancy math there.

About the tooltip bug for Skill trees
The tooltips of damage and healing abilities in the skill trees do not scale properly with level, but the abilities themselves do. So the formula's for damage and healing abilities below will give you high values than you will see on these tooltips until this bug is fixed.

Ability Damage Min = ( AmountModifierPercent + 1 ) * MainHandMin + ( AmountModifierPercent + 1 ) * OffHandMin * 0.3 + Coefficient * DamageBonus + StandardHealthPercentMin * StandardHealth

Ability Damage Max = ( AmountModifierPercent + 1 ) * MainHandMax + ( AmountModifierPercent + 1 ) * OffHandMax * 0.3 + Coefficient * DamageBonus + StandardHealthPercentMax * StandardHealth
AmountModifierPercent is the weapon damage modifier for min and max values and all ranks of the ability
Coefficient is the force/tech/melee/ranged damage bonus modifier for min and max values and all ranks of the ability
StandardHealthPercent is the base damage modifier, which can vary for the min and max values of the ability
StandardHealth is a damage number from the StandardHealth Lookup Table table near the bottom of this thread
DamageBonus is on your character screen (e.g. Melee Damage Bonus for a melee attack)
You can find all these values on your character screen or at TORHead if you expand the effect details on an ability page. Ability damage is always calculated per tick of a DoT or Flurry attack.

Force and Tech attacks don't use main-hand or off-hand damage.
OffHand is 0 is you have no off-hand to attack with or if the attack doesn't use the off-hand. Off-Hand damage is rolled as a separate attack to the main hand, so one hit will be x*MainHand + y*Bonus + z and the other x*OffHand*0.3. As a result the off-hand hit is much smaller than the main-hand hit.

Attack and Damage Types (thanks Kor)
There are four damage types: Kinetic, Energy, Internal, Elemental. The first two are mitigated by armor, the latter two are not.
There are also four attack types: Melee, Ranged, Force, Tech. Attack type and damage type have no correlation, you can have any combination of the two sets (though not all combination exist in game). The first two are subject to defense (avoidance) and shield (partial mitigation), the latter two are subject to resistance. Resistances (which are just avoidance for Force and Tech attacks) are present as a mechanic, but very very few effects in the game grant them, so they can essentially be ignored.
Thus you can very easily have an attack that bypasses armor yet can be dodged or shielded (an internal melee attack, for example), or an attack that bypasses defense and shield yet is armor mitigated (an energy force attack, for example).

The Two-Roll System
SW:ToR uses a two-roll system to determine attacks. The first roll determines hit or miss (or dodge/parry/resist, which are effectively just different names for miss).
The second roll determines of a successful attack crit, was shielded, or was a normal hit. In the event that crit % + shield % is greater than 100%, crit chance overrides shield chance.

Ability Healing Min = Coefficient * HealingBonus + StandardHealthPercentMin * StandardHealth

Ability Healing Max = Coefficient * HealingBonus + StandardHealthPercentMax * StandardHealth
Coefficient is the force/tech/melee/ranged healing bonus modifier for min and max values and all ranks of the ability
StandardHealthPercent is the base healing modifier, which can vary for the min and max values of the ability
StandardHealth is a healing number from the StandardHealth Lookup Table table near the bottom of this thread
HealingBonus is on your character screen (e.g. Force Healing Bonus for a Sith Sorcerer)
You can find all these values on your character screen or at TORHead if you expand the effect details on an ability page. Ability healing is always calculated per tick of a HoT.

Strength/Willpower/Aim/Cunning Damage Bonus = (Strength or Willpower or Aim or Cunning) * 0.2

Force/Tech Power Damage Bonus = (Force or Tech Power) * 0.23

Power Damage Bonus = Power * 0.23

Willpower/Aim/Cunning Healing Bonus = (Willpower or Aim or Cunning) * 0.14

Force/Tech Power Healing Bonus = (Force or Tech Power) * 0.17

Power Healing Bonus = Power * 0.17

Crit Chance % = 5 + 30 * ( 1 – ( 1 – ( 0.01 / 0.3 ) )^( ( PrimaryStat / max(Level,20) ) / 2.5 ) ) + 30 * ( 1 – ( 1 – ( 0.01 / 0.3 ) )^( ( CritRating / max(Level,20) ) / 0.45 ) )
Crit chance can also include a bonus from a secondary stat. Have a look at your damage or healing bonus on the character screen, if it includes a bonus from a secondary stat it will also have a small crit bonus from that stat calculated as + 30 * ( 1 – ( 1 – ( 0.01 / 0.3 ) )^( ( SecondaryStat / max(Level,20) ) / 2.5 ) )

Crit Size % = 50 + 30 * ( 1 – ( 1 – ( 0.01 / 0.3 ) )^( ( SurgeRating / max(Level,20) ) / 0.11 ) )

Basic Accuracy % = 90 + 30 * ( 1 – ( 1 – ( 0.01 / 0.3 ) )^( ( AccuracyRating / max(Level,20) ) / 0.55 ) )
Accuracy over 100% reduces the Defense of the target. Only your free level 1 attack is Basic.

Basic Off-Hand Accuracy % = 57 + 30 * ( 1 – ( 1 – ( 0.01 / 0.3 ) )^( ( AccuracyRating / max(Level,20) ) / 0.55 ) )
Off-hand attacks are rolled separately to main hand attacks

Special/Force/Tech Attack Accuracy % = 100 + 30 * ( 1 – ( 1 – ( 0.01 / 0.3 ) )^( ( AccuracyRating / max(Level,20) ) / 0.55 ) )
Accuracy over 100% reduces the Defense of the targe

Special/Force/Tech Off-Hand Accuracy % = 67 + 30 * ( 1 – ( 1 – ( 0.01 / 0.3 ) )^( ( AccuracyRating / max(Level,20) ) / 0.55 ) )
Off-hand attacks are rolled separately to main hand attacks

Activation Speed = CastingTime * ( 1 – ( %AlacrityFromSkillsAndBuffs / 100 ) – 0.3 * ( 1 – ( 1 – ( 0.01 / 0.3 ) )^( ( AlacrityRating / max(Level,20) ) / 0.55 ) ) )
Alacrity does not affect instant cast spells or the rate at which DoT's and HoT's tick, but does improve all cast time spells and channeled spells.

Armor Damage Reduction % = ArmorRating / ( ArmorRating + 200 * Level + 800 ) * 100
Caps at 75%, although this is not achievable with current gear and buffs

Defense Chance % = 5 + 30 * ( 1 – ( 1 – ( 0.01 / 0.3 ) )^( ( DefenseRating / max(Level,20) ) / 0.55 ) )

Shield/Glance Chance % = BonusOnSheildGenerator + 50 * ( 1 – ( 1 – ( 0.01 / 0.5 ) )^( ( GlanceRating / max(Level,20) ) / 0.32 ) )

Shield/Glance Absorption % = BonusOnShieldGenerator + 50 * ( 1 – ( 1 – ( 0.01 / 0.5 ) )^( ( AbsorbtionRating / max(Level,20) ) / 0.18 ) )

PvP Damage Bonus % = 20 * ( 1 – ( 1 – ( 0.01 / 0.2 ) )^( ( Expertise / max(Level,20) ) / 0.72 ) )

PvP Damage Reduction % = 20 * ( 1 – ( 1 – ( 0.01 / 0.2 ) )^( ( Expertise / max(Level,20) ) / 0.72 ) )

PvP Trauma Ignore % = 20 * ( 1 – ( 1 – ( 0.01 / 0.2 ) )^( ( Expertise / max(Level,20) ) / 0.72 ) )
Trauma ignore overcomes the Trauma (-30% healing received) debuff that players get in PvP, so it effectively improves healing.

Max Health = BaseHealth + Endurance * 10

Heath Regen = ? + Endurance * 0.03

Bonus Companion Health = Presence * 5

Bonus Companion Damage = Presence * 0.2

Bonus Companion Healing = Presence * 0.14

Code: (See original artical)

A Note on the formula used for Ratings, which was worked out by LagunaD
You'll notice that the formula's for ratings are all basically the same. Their values are not arbitrary but have specific meaning. Lets look at this example:
PvP Damage Bonus % = 20 * ( 1 – ( 1 – ( 0.01 / 0.2 ) )^( ( Expertise / max(Level,20) ) / 0.72 ) )
This first underlined section is the % cap for this rating and the second underlined section is the % cap divided by 100. In this case the cap is 20%. Remember this is the cap for the rating, not the stat, so you can't get more than 20% PvP Damage Bonus from stacking Expertise but you may be able to get more from a skill or buff (if any exist). Since these formula's give diminishing returns, you will never actually achieve a 20% PvP Damage Bonus from Expertise.
The third underlined section is 1/50th of the amount of rating needed to get 1% of the stat at level 50. So in this case 50 * 0.72 = 36 Expertise Rating to get 1% PvP Damage Bonus at level 50.

For calculation purposes, here's the base stats at Level 50
Code: (See original artical)

To calculate the stats at lower levels you can use these formula's, and round the results DOWN to the nearest whole number:
Primary Stat = 50 + Level * 4 i.e. Cunning for the Smuggler
Secondary Stat = 20 + Level * 1.6 i.e. Willpower for the Sith Warrior
Tertiary Stat = 10 + Level * 0.8 i.e. Strength for the Trooper
Endurance = 45 + Level * 3.6