The Ready action occurs when the trigger finishes (PHB p.192):
Sometimes you want to get the jump on a foe or wait for a particular circumstance before you act. To do so, you can take the Ready action on your turn so that you can act later in the round using your reaction.
First, you decide what perceivable circumstance will trigger your reaction. Then, you choose the action you will take in response to that trigger, or you choose to move up to your speed in response to it.
When the trigger occurs, you can either take your reaction right after the trigger finishes or ignore the trigger.
Seems simple enough.
For the purposes of this question, please assume that a creature casting a spell is a "perceivable trigger" - that is worthy of a question on its own (I'll link it when I write it).
With respect to casting a spell as a trigger it seems that the player/creature can choose 2 possible timings:
- "when a spell is cast" meaning the spell is completed and the reaction can then be taken, or
- "when a spell starts being cast" meaning when the caster pulls out his components/focus and waves his hands etc.
There are advantages to both timings. The ones related to 2. being most obvious i.e. you can do something before the spell happens. For example, you might be able to move out of the area of affect, render the caster unconscious, cast a Silence spell on them, attack them before their Barkskin comes into effect etc. The advantages of no 1. are that it can be advantageous to follow on from an ally's spell or attack the caster after his concentration spell is finished in order to break concentration etc.
To my mind, 1. is uncontroversial and works with 1 reaction and 1 action casting times; it has an issue with multi-round casting times but a common-sense approach of allowing the reaction after the caster's first turn readily overcomes this.
So, is it permissible for the player to opt for the second timing?