Shove/Trip vs. Extra Attack

[Argothair]

When is it optimal to use a standard Action to knock an enemy prone?

I'm imagining a situation where a monster is already standing in melee range of the party's tank, and the tank and the monster are standing in place and duking it out for multiple rounds. The monster has no particular use for its Move, so the monster can afford to use its Move to stand back up each round before attacking. That means the only mechanical benefit (that I know of) from knocking the monster prone is that your party will gain advantage on attack rolls against the monster for the rest of the round.

One of your party members probably wants to cast a spell that doesn't rely on attack rolls. One of your party members probably already went earlier in the initiative, i.e., before the monster's turn. So maybe you have three party members who can team up on the monster. PC #1 trips the monster, knocking it prone. PC #2 attacks the monster with advantage, and PC #3 attacks the monster with advantage. Is that really better than just having PC #1, PC #2 and PC #3 all make regular attacks against the monster? Even if PC #1 has a 100% chance of knocking the monster prone, it seems like you'd need some pretty specific to-hit chances for the math to work out in favor of tripping an opponent. Of course, in a real scenario, usually the monster will have at least some chance of winning an Athletics check or something like that. So why (or when) would you ever trip or grapple a monster in combat?

[OvisCaedo]

Well... Your title suggests it's "vs" extra attack, but shove and grapple attempts are actually substitutes for a single attack out of however many extra attack grants you. Depending on turn order, sacrificing one of your attacks to gain advantage on your second as well as advantage for whoever else is in melee could certainly be helpful.

Athletics is pretty optimizable and many enemies, even if they have strength, will tend to not have actual proficiency in athletics (and there's probably even fewer enemies with a meaningful acrobatics check). A failed attempt does nothing, but so does a missed attack.

Of course, I'd probably agree that using either grapple OR shove on their own seems like a shaky proposal. The real strength is if you use both, which LOCKS the enemy to the prone position until they spend an action to attempt to beat you, and it's easy to make that weighted against them if you've taken up some form of expertise in athletics. And when they can't stand up, suddenly it will also matter that their attacks are actually at a disadvantage while on the ground. It doesn't take further actions to maintain from you unless they break out, either.

...Though the size restriction means that eventually, you might frequently come into encounters where the tactic is not even usable. Or I suppose if an enemy can just teleport out of your hands.

[Argothair]

OK, that's really cool! Somehow I'd never noticed the option to combine shove with grapple. So if you have a Level 8 Barbarian (or anyone else with two attacks per turn), can you spend one attack to shove, one attack to grapple, and then hold the monster on the ground for free on subsequent turns until the monster successfully beats your Athletics check? E.g. even if it's just the one Barbarian solo-ing against the monster, can you use your first turn to shove and grapple, and then use later turns to make two attacks per turn with advantage as long as your 'pin' holds?

[Eric Diaz]

OK, that's really cool! Somehow I'd never noticed the option to combine shove with grapple. So if you have a Level 8 Barbarian (or anyone else with two attacks per turn), can you spend one attack to shove, one attack to grapple, and then hold the monster on the ground for free on subsequent turns until the monster successfully beats your Athletics check? E.g. even if it's just the one Barbarian solo-ing against the monster, can you use your first turn to shove and grapple, and then use later turns to make two attacks per turn with advantage as long as your 'pin' holds?

Yes, that is the idea!

[Tessman the 2nd]

The shove gets alot better when the characters get a second attack at 5th.
Although it is highly dependant on party composition, great weapon master is an effect that would benefit from the advantage to possibly offset the -5 penalty.
A concern for shovers is ranged party members and giving them disadvantage.

I am not going to do the math on advantage with party vs normal extra attack because there are too many variables and im lazy.

[MaxWilson]

When is it optimal to use a standard Action to knock an enemy prone?

Well, an 11th+ level Fighter with GWM will very often find it advantageous to shove an enemy prone with his first attack any time he is planning on Action Surging. Five GWM attacks at advantage beats six attacks without advantage.

Furthermore, knocking an enemy prone and then attacking them twice, then withdrawing 20' or so, means that you take an opportunity attack at disadvantage from a prone enemy, in exchange for making two GWM attacks at advantage. So that is also worth doing, if your relative advantage on Athletics vs. Acrobatics/Athletics is great enough to make knocking the enemy prone reliable.

Beyond that, it varies depending on party composition. Valor Bards are really great at grapple/prone on enemies, which is great for giving advantage to other melee PCs/summons and bad for ranged PCs, so it's relatively more valuable in a party with a Shepherd Druid and relatively less valuable in a party with Sharpshooter fighters or skellymancers. It also depends on what other enemies are in the fight, i.e. what proportion of enemy forces you're locking down by grapple/prone.

[OvisCaedo]

OK, that's really cool! Somehow I'd never noticed the option to combine shove with grapple. So if you have a Level 8 Barbarian (or anyone else with two attacks per turn), can you spend one attack to shove, one attack to grapple, and then hold the monster on the ground for free on subsequent turns until the monster successfully beats your Athletics check? E.g. even if it's just the one Barbarian solo-ing against the monster, can you use your first turn to shove and grapple, and then use later turns to make two attacks per turn with advantage as long as your 'pin' holds?

Mhm. Though two things to keep in mind for the tactic are whether it is compatible with the party, and also whether the semi-hidden opportunity cost is worth taking. Grappling requires a free hand, which means any time you plan on grappling, you can no longer use a two handed weapon. If you were planning on wielding a shield, dropping it somehow takes an action according to the PHB, so you can't really free that hand up, meaning what you'd have to drop would be... your weapon. You might be able to argue for headbutting a guy at the normal unarmed strike damage, or using the shield as an improvised weapon. Some races probably even have a bite attack, though I forget which, and that leaves both an effective and terrifying option of shoving someone to the ground, holding them there, and tearing into them with your vicious maw.

Worth noting, though as ever requiring consideration on whether or not it fits, is that the Shield Master feat lets you shove as a bonus action with your shield, when you commit to an attack action. Sage advice has said you're allowed to take the shove first. But, if you want to use that AND grappling, you really have to make sure you have some kind of attack fallback that your GM will greenlight. Though using it without grappling has very little cost if you want to go for it, just a bonus action after all.

[Blood of Gaea]

Just as an extra tidbit, if you plan to do a lot of shoving and pushing (especially if you aren't a fighter who can get 3-4 attacks), Shield Master is great as you'll be able to do one as a bonus action.

[Xihirli]

However, you can't grapple without a free hand, so pinning them down with a grapple keeps you from using a weapon if you have a shield.

[Blood of Gaea]

However, you can't grapple without a free hand, so pinning them down with a grapple keeps you from using a weapon if you have a shield.
Sure, though you could drop your weapon or debatably your shield to go in for a grapple. You could also use the shield itself as an improvised weapon or make unarmed attacks (paired with tavern brawler perhaps?).