[RPG] What do I add to the D20 roll of a Concentration Check

Ask your DM. If you are the DM: Make a Ruling.

The rules explicitly point out that other situations may arise where a Concentration check needs to be made, based on the GM's assessment of a situation in the game.

In the description of Concentration (Basic Rules p. 79-80 ), the following comes after the three triggers for concentration to end: being incapacitated, damage and a failed Constitution save, or casting another spell which requires concentration.

The GM might also decide that certain environmental phenomena, such as a wave crashing over you while you’re on a storm‑tossed ship, require you to succeed on a DC 10 Constitution throw to maintain concentration on a spell.

These will be situational, and will follow the D&D 5e point of "rulings" where rules are not specific.

With that as a point of reference ...

• a strong gust of wind knocking someone off their feet might trigger a DC 10 Constitution check if the GM deems it to be of sufficient impact on the concentrating creature.

• Slipping and falling, depending upon the context, might do likewise. The GM may also raise or lower the DC depending upon the details of the situation or influence on the caster.

• A real earthquake (not the spell) could be a similar trigger.

On the more "cause and effect" side of things ...

Spells

A few spells directly influence Concentration:

• Sleet Storm (PHB, p. 276), influences Concentration, based on the spell save DC of the one casting Sleet Storm:

  If a creature is concentrating in the spell’s area, the creature must make a successful Constitution saving throw a against your spell save DC or lose concentration.

• Earthquake (PHB, p. 236) has an explicit influence on concentration if a failed save is made against that spell's DC.

  The ground in the area becomes difficult terrain. Each creature on the ground that is concentrating must make a Constitution saving throw. On a failed save, the creature’s concentration is broken.

• Storm of Vengeance(PHB, p. 279) has a similar effect but not with as explicit of a penalty:

  Round 5–10. ... Each creature there takes 1d6 cold damage. Ranged weapon attacks in the area are impossible. The wind and rain count as a severe distraction for the purposes of maintaining concentration on spells.

  That could be ruled as a disadvantage to the Concentration check the caster will make anyway, since the caster will be taking damage at this point in the spell. If the Warcaster feat gives Advantage to Concentration checks, this would neutralize that feature of the feat. (But it doesn't explicitly state that). Given that it is a high level spell (9th) I'd take that language in the spell description to favor a ruling of "Disadvantage" on the concentration check at that point in the spell's progression.

  Note:(from PHB, p. 173 on Advantage & Disadvantage)

  The DM can also decide that circumstances influence a roll in one direction or the other and grant advantage or impose disadvantage as a result.

Conditions

The following Conditions (Basic Rules, Appendix A) create Incapacitation as a part of the Condition:

• Unconscious
• Petrified
• Paralyzed

• Stunned

  Therefore, if the caster misses a save versus Petrification or Paralysis, or is subject to a sleep spell/sleep effect, whatever spell the caster is concentrating on ends.

Grappling

As you noted in your question, the Grappled condition does not break concentration. But, if a character with the Grappler feat(PHB p. 167) and the Mage Slayer feat(PHB p. 168) grapples the caster in question, an interesting synergy arises:

• The grappler gets advantage on attack rolls versus the one grappled

• The grappled spell caster has disadvantage on the concentration checks.

  This leads to a higher likelihood of the concentration check being failed.

Other Ways to End Concentration

Convince the caster to end the spell. The fourth way that a caster ends concentration before a spell duration expires is to choose to stop concentrating. A Suggestion or Charm spell, or an effect similar to those spells, could induce a caster to stop concentrating in a spell.

Out of combat, something like a bribe or a persuasion attempt, or an intimidation attempt, could do similarly. This again is a situation-dependent interaction.

So there are two different issues to concentrating:

1. Concentration can usually be disrupted.

2. Concentration takes your attention, read, your action.

Concentrating on a magical effect is a standard action. While you are concentrating, you cannot be doing other standard actions (usually).

So as a supernatural ability, the prayer attack cannot be disrupted. You do not need to make Concentration checks (or, equivalent, you automatically pass them, since it’s impossible to be disrupted). But you still do have to pay attention to what you’re doing. So you have to spend standard actions each round concentrating on the effect to keep it going.

In effect, the prayer attack has a duration of “Concentration” which is distinct from the idea of concentrating on something to avoid disruption.