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Your mage cast the spell. They need to cast using the spell throw.
The target needs to cast the saving throw.
If someone tries to push you, you save yourself by pushing against that force. That is why strength.
If someone tries to make you slip with a spell, that is where you make a dexterity saving throw.
So if you cast telekinesis, as an example, against a living creature, they can resist it using their strength saving throw.
https://bg3.wiki/wiki/Saving_Throw
You as the caster need only your casting stat to be high. They need their Str to be high to resist.
Also, items that increase your spell save DC (you'll find plenty) will make it harder for the target to resist your saving throw spell.
While 8 no mods difficulty is the same as base 12 AC for basic light armor, I think saving throw spells are harder to land compared to attack throw spells (eg fire bolt) due to lots of ways to create hit advantage and lots of save throw buffs on serious enemies.
So, my guess is to use savethrow spells on pure mage only, while semi-mages should use attack throw casts or even certain hits.
But my current char is a CoS Bard with 20 DEX and 16 CHA, with nothing to boost spellcasting. Best (as in most useful for me) spells I can cast are Counterspell (guaranteed success if cast at same spell level) and Invisibility.
Also the Friends cantrip, the MVP spell of my playthrough.
https://bg3.wiki/wiki/Saving_Throw
https://bg3.wiki/wiki/Spells
https://bg3.wiki/wiki/Proficiency
https://bg3.wiki/wiki/Telekinesis
To put it simply, casting spells that have an Ability Score Save (STR Save, WIS Save etc) simply means that your spell targets that specific Ability Score (STR, WIS etc) of your enemy.
Your enemy has to make a dice roll (called a Saving Throw) for that particular Ability Score (STR, WIS etc) to determine if he will resist the spell or not.
In your case You cast Telekinesis that has a STR Save.
Your target has to do a Saving Throw using his STR as defense.
Your STR value has no bearing on this.
Your spells power is determined by a completely different value.
Now there are two things to consider here:
Your spell power or more correctly called in this game "The Difficulty Class of Saving Throws", "Save DC" or "DC" for short.
The higher it is, the lower the chance enemies will have to resist it.
This is the formula to determine the DC of your casting spells:
DC = 8 + Proficiency Bonus + Spellcasting Ability Modifier
In your case since you are a Mage, the Spellcasting Ability Modifier would be Intelligence (INT), so increasing your INT further would increase the DC of your spells.
Every 2 INT above the base value of 10 will give you +1 to add to your DC.
There are some spells that instead use a specific Ability Modifier but let's ignore it, it's very rare. (Ex. Fire Bolt given to all high elves).
Proficiency for Spells is called Spellcasting.
in BG3 everyone has it so don't worry about it, the bonus automatically increases at some specific level intervals.
Another thing to consider is the opponent's Saving Throw for the Ability Modifier your spell targets (In your case your opponent's STR Saving Throw).
The higher the enemy's saving throw is, the higher chances to resist they have.
This is the formula that determines the total of the opponent's saving throw:
Opponent Saving Throw = D20 + Ability Score Modifier + Proficiency Bonus (if proficient)
What that means is that your opponent rolls a dice of 1-20, add up any bonuses he has for STR Saving Throws (STR Ability Score Modifier + STR Proficiency Bonus) and then it compares it to your character's Save DC to determine if the spell will be resisted or not.
Final Result: Compare Spell's DC to Opponent's Saving Throw
If the target's saving throw value is equal or higher to your Spell Save DC, he will resist it, otherwise it will affect him.
Example:
You cast Telekinesis on a target/enemy. Telekinesis has a STR Save.
You are a Mage Level 4 (Spellcasting Proficiency Bonus +2), You have 16 INT (INT Score Modifier +3), base DC is 8.
You have 8+2+3= 13 Save DC.
Target/Enemy is also level 4, has STR proficiency (Proficiency Bonus +2), has 12 STR (STR Score Modifier +1) and has a passive condition/aura that adds +1 to All Saving Throws (+1).
He has = 1+2+1 = +4 STR Saving Throw
Target makes a D20 roll + 4 to determine his Saving Throw against your 13 Save DC.
Let's say he rolled 9 + 4 = 13 Opponent Saving Throw.
Final Result: 13 Saving Throw == 13 Save DC, so he resists your spell.
TL;DR:
TELEKINESIS has a STR Save, which means your spell targets the STR score of your target/enemy. Your target/enemy needs to roll a Saving Throw using his own STR Saving Throw Bonus to try and resist. It has nothing to do with your own STR.
You can increase your own Spells Save Difficulty Class (Spells power) by increasing your Ability Score (INT for Mages) and items or buffs that specifically give +Save DC or Advantage.
Press TAB to see your Save DC or hover over the STR Save part of a spell to see your Save DC number.
You can reduce your enemies specific Saving Throws chances, in your case STR, by reducing their STR score, STR Saving Throws or cause a disadvantage on STR Saving Throws.
It does not affect your characters strength, it is an indicator to help guide you to see if an enemy will be likely to resist it or not.
I hope this helped, as I just learned about this 2 days ago myself :)