The Saving Throw determines whether a spell or trap is effective or not, or whether you can run from enemy parties.
Individual saving throw uses the following formula:
SavingThrow = CharacterLevelComponent + CharacterClassComponent + LuckComponent + EquipmentComponent + Bonus
CharacterLevelComponent = Character Level / 2. Max 18.
CharacterClassComponent = +3 for Wizards, +2 for other Magic Users, and everyone else gets +1. Except Paladins. They get +1 if they are level 1-3, +2 if they are level 4-9, +3 if they are level 10-17, +4 if they are level 18-25, +5 if they are level 26-29, or +6 if they are higher than 30.
LuckComponent = Luck - 15. Minimum 0.
EquipmentComponent = +2 if a Luckshield is equipped.
Bonus is +2. Everyone gets this.
Party Saving Throw is the saving throw of the character in the first slot.
Monster Saving Throw is calculated using the following formula:
SavingThrow = MonsterIndex / 8 + Rnd(8)
MonsterIndex is the index into the list on This page. Kobold = 1. Skeleton = 10. Remainders are ignored. The Rnd(8) is a random integer from 0-7.
Whenever you cast a spell at a monster, both your Saving Throws are calculated. If your Saving Throw is higher than his, the spell is effective. Some spells can be partially resisted, for half damage. If his saving throw is within 4 of your saving throw, you still do half damage.
The same procedure happens when a monster casts a spell at you, with the throws reversed.
When you attempt to run from an encounter, your Party Saving Throw is compared with the Saving Throw of the monster in the first opposing group.
You will see these in a big way when your party members are at a very low level. When first starting out, or immediately after you change from one caster class to another. If all your casters reach the top level of the current class at the same time, you may not want to change them all to a new class simultaneously. Change one or two, and wait until they get up enough levels to not have all their spells resisted, before you change the others. If you are in an area where the monsters are above your party's ability to easily deal with, make sure your front line character has a very high luck skill. Like, 18!
For parties just starting out, consider putting a Hobbit Magician or Conjuror on the front line. A level 4 Conjuror with 18 luck can always run from any monster up to Mercenary. That means that in town during the day, you can pick and choose which encounters you want to fight. You will never get caught by a group of monsters that is above your level unless you want to. Your Monk or Bard will have to be level 6 and have 18 luck before they can do that. Paladins could do it at level 4, except Paladins can't be Hobbits, and Dwarves max out their beginning luck at 10. Your Paladin with bad luck would have to be level 10 before they could run from anything in town. By that time, your party should have been dungeon delving for quite some time.
Sometimes, even a simple level 2 Sorceror spell can be very effective. If you're pretty sure the Hypnotic Image spell will survive the Saving Throw, you can keep an entire group of high level monsters out of the action long enough for the rest of your party to handle it next round.