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Certain damage kickers are put into effect at the attacker's option after it is determined that an attack is a hit. Examples include:

The rules on a critical hit seem pretty clear (PHB. 196):

Roll all of the attack’s damage dice twice and add them together.…

… If the attack involves other damage dice, such as from the rogue’s Sneak Attack feature, you roll those dice twice as well.

It seems clear that (a) the player decides to apply the kicker after seeing the die roll, and (b) "all of the attack's damage dice" includes the kicker. But this gives the player quite an advantage to choose to apply a damage kicker on a known critical hit, so I am seeking to confirm (or correct) my understanding.

Can the attacker wait to add optional damage dice until after seeing if the roll is a critical, knowing that the additional damage dice will be doubled?

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Yes

You've already listed the related rules. Yes, additional damage dice are doubled on a critical hit. Yes, that means you can choose to smite when you see you've got a critical hit. Yes, it's pretty good.

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  • \$\begingroup\$ The question has changed dramatically and some information that was there is gone. Can you explain how the rules allow for this behavior? \$\endgroup\$ – Premier Bromanov Apr 27 '16 at 15:22
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    \$\begingroup\$ Actually, I believe the entire question is covered by the phrase "when you hit a creature with a melee weapon attack," or more specifically "when you hit." Since the effect is triggered on the hit rather than the attack, you already know the result of the roll (and therefore whether it's a critical) before triggering it. \$\endgroup\$ – Passage Apr 27 '16 at 20:35
  • \$\begingroup\$ The question's been updated. You might wish to review the change to see if you need to alter the answer or adjust what it emphasises. \$\endgroup\$ – SevenSidedDie Apr 28 '16 at 5:49
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The extra damage from these abilities can be applied after you hit a creature.

In order to know if you've hit a creature, you (usually) need to know the result of your d20 attack roll. So regardless of whether or not the roll ends up being a critical, you can wait until after the die roll to apply the extra damage.

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Divine smite yes because it is "special" it doesn't require a bonus action to activate. All other smite spells, no they have to be cast beforehand. You can also stack one of those divine smites with the other bonus action smites.

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The answer is yes.

But it should be no, IMHO.

I would rule that the PC can add the kicker damage if they want but that it's not doubled.

A critical hit's damage is doubled because you've hit the opponent's head or struck particularly sweetly. Why would the divine power of your God be doubled however? It is a fixed amount.

Similarly I'm struggling to see how a Trip attack could be critical and do more damage.

The other powers I'm not so familiar with.

But anyway mechanically and aesthetically I'd rule there should be no doubling kicker damage. Especially not on smite as it would be disproportionately powerful given all the dice involved!

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  • \$\begingroup\$ Welcome to the site... please, take the tour and you should quote places to underlay your answer. \$\endgroup\$ – Trish Apr 12 '18 at 11:25

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