Saves and To-Hit
To-hit rolls for physical attacks and saving throws against status effects both use the same basic mechanics: you pick an attack stat (accuracy, or physical, magical, or mind power) and a defence stat (defence, or physical, magical, or mind save), calculate a % chance to hit based on that, and then roll.
The rest of this article uses "attack" and "defence" to mean "the stats being used for the attack and defence parts of the roll", regardless of which actual stats these are. All the stats used in this calculation are the rescaled stats, not the raw stats.
First, attack and defence both have a lower bound of 0 applied; if the attacker has a debuff taking them to (say) -5 in that stat, they're treated as though it is 0.
Then, the to-hit chance is calculated using the following formula:
50% + (attack - defence)*2.5%
So, when the attacker and defender are evenly matched, the attack has a 50/50 chance of succeeding; each point in attack increases that chance by 2.5%, and each point in defence decreases it by 2.5%. Attack exceeding defence by 20 points or more, then, guarantees a hit (but see below); defence exceeding attack by at least 20 guarantees that the attack will fail.
Then, limits are applied. By default it can't go below 0% or above 100%; some attacks, however, impose their own limits. Most status effects, for example, have an upper bound of a 95% chance to save against them, giving the victim a 1/20 chance to fail to save no matter how good their stats are. (Note that the attack in this case is the save and the defense in this case is the power, contrary to how one might expect.) As another example, some other status effects have an upper bound of a 95% chance to apply the effect, giving the victim a 1/20 chance to save no matter how bad their stats are. (In this case, the attack is the power and the defense is the save.)
Finally, the dice are rolled and the result is applied.
Blind-Fighting and Unseen Enemies
Physical attacks have to go through one additional check: the blind-fighting check. If the enemy can't be seen, for any reason (including stealth, blindness, and invisibility), then even if the attacker makes a successful to-hit roll, they have a flat 2/3 chance to miss anyways. This applies both to the player attacking unseen enemies, and enemies attacking an unseen player. If the attacker has the "blind-fight" ability (granted, for example, by the Spectral Blade), this check is skipped entirely and the attack behaves the same as an attack on a visible target.