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General information:
Stats are attributes which determine a character's overall power. The more stats a character has, the stronger he is. Additionally, they offer players a different way of customizing their character, determining their class archetype almost solely by which stats they focus on, offense, defense or a healthy mix of both.
Stats can be viewed and added by opening the Stat bar, for which the keyboard Shortcut is Alt + A.

Base stats and stat points:

There are 5 different "base" stats which the player can increase (up to 100 per stat) and stats which cannot directly be added, however, equipment gems, skills and the five base stats can alter those.
Stat points are required to increase base stats, and they are given to the player by leveling up.
4 Stat points are given at Lv1;
1 Stat point is given per level;
5 Stat points are given for every tenth level;
2 Stat points per level are given at Lv60 and above

The 5 base stats are:
Strength (STR) - Increases the attack of melee classes
Agility (AGI) - Increases Attack Speed and Dodge
Spirit (SPR) - Increases SP, SP Recovery Rate and healing/damage dealt from Magic Skills
Constitution (CON) - Increases HP, HP Recovery Rate and Defence
Accuracy (ACC) - Increases Hit Rate and the attack of ranged classes
Some of the stats mentioned above but also visible in the Stat Bar:
HP - Health Points, how much damage a character can take before dying
SP - Spirit Points, used for casting skills
Min/Max Attack - How much damage attacks and Physical Skills do
Hit Rate - Increases the chance of successfully hitting the target with attacks
Dodge - Increases the chance of dodging the enemy's attack
Defence - Reduces the physical damage taken by a flat amount
Attack Speed - Increases the speed of the character's attacks
Physical Resist - Reduces the physical damage taken by a percentage

Stats not visible in the Stat bar or anywhere else are:

Movement Speed - Increases how fast the character moves
Critical Hit Rate - Increases the chance of critically striking the target with attacks
HP Recovery Rate - The amount of HP restored every few seconds
SP Recovery Rate - The amount of SP restored every few seconds

Additional information about stats:
-Base stats scale exponentially. The more base stats one has, the higher their effect.
-Base stats give a boost every few-several points
-Base stats scale differently based on the class
-Certain passive or active skills can give permanent or temporary boosts to non-base stats
-The only Gems in the game which give base stats are Unique Gems.