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This may be quite obvious, but I want to be certain.

As a Draconic Bloodline sorcerer with Elemental Affinity to fire, do I get to add my Charisma modifier to each ray of scorching ray, or just one of the three?

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Only once

From the PHB errata:

Elemental Affinity (p. 102). The damage bonus applies to one damage roll of a spell, not multiple rolls.


Original Text

The original (pre-2016 errata) text read the following:

Starting at 6th level, when you cast a spell that deals damage of the type associated with your draconic ancestry, add your Charisma modifier to that damage.

Which was ambiguous, since you only cast the spell once, but the spell might deal damage more than once. This was later corrected in the above mentioned errata.

Corrected (post-errata) text

The current print reads as follows.

Starting at 6th level, when you cast a spell that deals damage of the type associated with your draconic ancestry, add your Charisma modifier to one damage roll [of that spell]1.

From this, it's clear that the damage is only applied once, as stated in the errata.

1 This part of the sentence ("of that spell") is seen in the Roll20 version, which is probably the SRD version.

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    \$\begingroup\$ The description of Elemental Affinity on DNDBeyond includes the "of that spell" text, and my copy of the PHB seems to include it as well... So I'm confused about your footnote about it. \$\endgroup\$ – V2Blast Aug 7 '18 at 7:49
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No, as per the feature's text, you only add it to one damage roll.

Elemental Affinity
Starting at 6th level, when you cast a spell that deals damage of the type associated with your draconic ancestry, add your Charisma modifier to one damage roll.

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    \$\begingroup\$ Note that this is a post-errata version of the text. The original stated "Starting at 6th level, when you cast a spell that deals damage of the type associated with your draconic ancestry, add your Charisma modifier to that damage." \$\endgroup\$ – HellSaint Aug 7 '18 at 7:32
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Just one

Elemental affinity reads:

Starting at 6th level, when you cast a spell that deals damage of the type associated with your draconic ancestry, add your Charisma modifier to one damage roll.

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    \$\begingroup\$ Note that this is a post-errata version of the text. The original stated "Starting at 6th level, when you cast a spell that deals damage of the type associated with your draconic ancestry, add your Charisma modifier to that damage." \$\endgroup\$ – HellSaint Aug 7 '18 at 7:33

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