If you roll a 1 on a saving throw against a damage spell, do you take extra damage?

Question

For example:

Fireball Each creature must make a DEX saving throw. A target takes 8d6 fire damage on a failed save, or half as much damage on a successful one.

If a target caught in the fireball rolls a 1 on their saving throw, which is an automatic fail, does the target take any form of extra damage?

Answer 1

No extra damage is taken

Saving throw for fireball is "pass/fail".

3. Compare the total to a target number. If the total equals or exceeds the target number, the ability check, attack roll, or saving throw is a success. Otherwise, it’s a failure. The DM is usually the one who determines target numbers and tells players whether their ability checks, attack rolls, and saving throws succeed or fail (page 4, Basic Rules)

"which is an automatic fail" (there isn't one)

There is no specific rule in this edition for a d20 result of 20 or 1 on a saving throw -- except the specific rule for the death saving throw when a PC is at 0 HP. (See below; Basic Rules p. 76). Without a specific rule like that for fireball, the general rule for saving throws is how it works.

A missed save is a missed save. The damage for a save is per the spell description. Fireball's spell description does not call for boosted damage due to a given result on the saving throw. Damage is whatever comes up on the damage dice rolled; damage is halved if the save is made.

Saving Throws (Basic Rules, p. 62)(Chapter 7)

The result of a successful or failed saving throw is also detailed in the effect that allows the save. Usually, a successful save means that a creature suffers no harm, or reduced harm, from an effect.

What about Criticals?

A Critical hit (20 on a d20) and an automatic miss (1 on a d20) are confined to spell attacks and weapon attacks that require an attack roll. The fireball spell does not require an attack roll, it only requires a saving throw. The 1 rolled on the saving throw is as good as the 13 if the save required was a 14: it is a failed save (no modification to damage done).

• The DM can use the die roll as a cue on how the failed save is described during play. A low roll might be described as "you are caught squarely by a burst of flame" while a roll that "just missed" could be described as "you try to dodge but your wounds slowed you down just enough to catch the full heat of the fireball." How a DM describes the events in combat can add a lot to the game, regardless of the mechanical pass/fail points.

What automatic fail?

• For a spell cast with a low DC against a creature with a substantial saving throw bonus (let's say a proficiency bonus of +6 and another bonus (+3 from an item or a spell buff) versus a DC of 10) -- sometimes even a 1 won't fail to save.
  • Conversely, the only form of "automatic fail" is at the other end of the d20 rolling continuum. An orc (without some kind of buff to a saving throw) can't roll the 21 he needs to save versus an Ancient Red Dragon's Frightful Presence. (DC 21 versus a Wisdom saving throw ... no bonuses for a standard Orc). His d20 roll isn't an automatic success, since he is not rolling an attack roll.

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Death Saving Throws are an exception to the saving throw general rule.

Death Saving Throws (p. 76 Basic Rules)

Whenever you start your turn with 0 hit points, you must make a special saving throw, called a death saving ... Unlike other saving throws, this one isn’t tied to any ability score.{snip}
Rolling 1 or 20. When you make a death saving throw and roll a 1 on the d20, it counts as two failures. If you roll a 20 on the d20, you regain 1 hit point.

Rules in the PHB are the same as in Basic Rules on this matter.