Below is a list of formulas each stat has on game mechanics.
It does not cover everything, only the most important bits.
For more help on stats see help statistics.
Base formulas:
HD (hitdice) = level + max(0, level-90) * (level-89) / 2
LF (level factor) = (10 + level) / 100
CF (class factor) = around 1.0, see help hp mana move
Strength:
* Bonus to damroll of LF per point above 60.
* Saving throws against physical attacks made 0.2% harder per point.
Constitution:
* Bonus to hitpoints of 0.1 * HD * CF per point.
* Bonus to physical saves of -0.2 * LF per point.
Vitality:
* Hitpoint and move regeneration (directly proportional).
* Bonus to healing received from spells of 0.5% per point.
* All damage taken reduced/increased by 0.1% per point above/below 100.
Agility:
* Bonus to moves of 0.1 * HD * CF per point.
* Bonus to AC of -2 * LF per point above 60.
* Bonus to dodge chance of 0.03% per point.
Dexterity:
* Bonus to hitroll of 0.5 * LF per point above 60.
* Chance of extra attack of 0.33% per point, half again for off-hand.
* Bonus to parry and avoid dodge/parry of 0.03% per point.
Intelligence:
* Mana regeneration (directly proportional).
* Learning skills (proportional to 20 + int).
* Saving throws against spells made 0.2% harder per point.
Wisdom:
* Bonus to mana of 0.1 * HD * CF per point.
* Bonus to spell saves of -0.2 * LF per point.
Discipline:
* Threshold for injury penalty is 0.5% per point.
* Bonus to hp/mana/move of 0.05 * CF per train and point
(reduced to 0.01 * CF after reaching softcap).
Charisma:
* Max NPC follower levels is level * (200 + cha) / 100, pets excluded.
* Bonus/penalty to follower damage of 0.1% per point above/below 50.
* Bonus to minimum qp gained from quest of 0.066 per point.
Luck:
* Bonus to maximum qp gained from quest of 0.166 per point.
* Bonus of 0.1 hitroll, 0.05 damroll, -0.5 AC per point.
* Affects various checks (traps, etc.) and illu/gunny summoning spells.
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