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For a comprehensive summary of the mechanics behind all rolls and modifiers, see Die Rolls.
A Saving Throw, also called a save, is a die roll the game makes for a creature to decide whether it can avoid or reduce the harmful effects of various threats, such as a spell, poison, trap, and so on. The creature's Ability Score Modifier and Proficiency Bonus are added to the roll.
Result =d20 + Ability Score Modifier + (optional) Proficiency Bonus
For a Saving Throw to succeed, it must reach or exceed a certain value, called its Difficulty Class (DC).
Each Saving Throw is tied to an Ability Score that determines its type. Depending on this, it can be referred to as a Strength Save, Dexterity Save, Constitution Save, and so on.
Modifiers
Saving Throws are affected by the Ability Score Modifier of the ability they're tied to. In addition to that, a creature can be Proficient in a type of Saving Throw, allowing it to add its Proficiency Bonus to the roll.
Saving Throws can also be affected by 
Advantage or 
Disadvantage. For example, Elves have Advantage on Saving Throws against being Charmed. As another example, the Bleeding condition incurs Disadvantage on Constitution Saves.
Some spells can also affect a saving throw, such as Bane, Bless, and Resistance.
Ability Score Modifier
Following is the Ability Score Modifier table based on the value of the Ability Score being used for the save:
| Ability score | Modifier value | Ability score | Modifier value | |
|---|---|---|---|---|
| 1 | -5 | 16-17 | +3 | |
| 2-3 | -4 | 18-19 | +4 | |
| 4-5 | -3 | 20-21 | +5 | |
| 6-7 | -2 | 22-23 | +6 | |
| 8-9 | -1 | 24-25 | +7 | |
| 10-11 | +0 | 26-27 | +8 | |
| 12-13 | +1 | 28-29 | +9 | |
| 14-15 | +2 | 30 | +10 |
Proficiency Bonus
As explained above, a creature needs Proficiency in the corresponding type of Saving Throw for its Proficiency Bonus to apply. Each Class provides a creature Proficiency in two types of Saving Throw:
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Following is the table of Proficiency Bonus values, by Level of the creature making the save:
| Level | Proficiency Bonus |
|---|---|
| 1 to 4 | + 2 |
| 5 to 8 | + 3 |
| 9 to 12 | + 4 |
The Difficulty Class of Saving Throws
If a creature casts a spell that forces another to make a save, the DC is determined according to the properties of the spell caster, using the following formula:
Difficulty Class = 8 + Ability Score Modifier + Proficiency Bonus
The Ability Score used to determine the Modifier depends on the class of the caster, and is the same as the one used for the Attack Roll:
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The Proficiency needed to gain the Proficiency Bonus is spell casting. All creatures capable of casting spells through their Class, Subclass, or Feats, have this proficiency. However, if a creature that can't normally cast spells uses a Scroll or other item to cast one, it will lack the Proficiency Bonus. (TODO: Verify that this is actually implemented in BG3! It's been verified for Attack Rolls, but not the Difficulty Class of Saving Throws imposed on others.)
In case of threats that don't originate from a spell caster, such as a trap that just sprung or a poisonous apple you just ate, the game sets the DC based on how serious the threat is supposed to be. For example, a rather ineffective trap could have a DC of just 5, whereas a very powerful one could have a DC of 15. A slightly spoiled tart could impose a Constitution Save of DC 5, whereas a potent venom from a snake could impose a DC 15 Constitution Save on the hapless victim.
Effects of a successful Saving Throw
Making a successful Saving Throw could mean avoiding negative effects entirely, or it could merely mean reducing the damage taken, usually by half. Depending on the threat, there could also be other rules that determine what happens on a failed or successful save.