D&D 5E Shield Master vs Two Weapon Fighting on a rogue

So I build a shield Master rogue and I’m wondering if two weapon fighting is better damage wise. The rogue has a +7 in Athletics and has proficiency in heavy armor since are table allows UA. (Eldritch Armor) Now mathematically what is better damage wise? Two separate attacks without advantage or one with advantage?
In my opinion it depends on exactly what you mean by 2-weapon fighting.

Shield master is a feat, while figting with 2 weapons is free (as long as both are light). If you are considering the daul wielding feat vs the shield master feat for said rogue, shield master is better unless you have some powerful magic rapiers or whips you want to wield.

That said I don't think using the feat for this is a good way to spend a feat and in general it is not how I would go for a rogue (maybe for a fighter rogue who was mostly fighter.

A few things to consider:
1. There are a lot of ways to get sneak attack, especially if you are swashbuckler. Shield master could generate the needed advantage, but other things can get you that SA opportunity too. For example disengage as a bonus action then moving to flank an opponent, and said opponent does not get a save on this.

2. If you are looking for a way to simply make advantage more common go with magic initiate and get find familiar. Your familiar can use "help" and give you advantage plus you still get your bonus action for whatever you want. Additionally you can get some cantrips that work really well with a rogue.

3. two weapon fighting is more flexible in terms of action economy - make your first attack, if you miss then use your bonus action to get an offhand SA. If you hit with the first attack, use cunning action to do something else (disengage or hide being the most common). By taking the shield master route you have to use the BA first to get advantage.

4. You will not always win your shove and some monsters can't be shoved prone. With a +7 you will a lot, but you will still lose some, using cunning action for mobility or hiding is a better way of getting SA in general.

5. A rogue gets evasion which makes the save bonus with the feat less useful.
 
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Everyone when is talking about shield master is quoting only about "prone" part. But it's improving dex saves. Yes Rogue has proficiency and on 7th lvl have evasion, but Shield master adds his bonus to Rogue - 1 lv. Vhuman rogue with shield master will have +7 dex save and half/nothing... (6 lvls before evasion) not bad. On 5th lvl, after ASI to dex, +3 proficiency bonus it's +9. So you can be targeted by your wizard with the fireball.

But if you are thinking how to do more DPR, it's not best way,
 

Everyone when is talking about shield master is quoting only about "prone" part. But it's improving dex saves. Yes Rogue has proficiency and on 7th lvl have evasion, but Shield master adds his bonus to Rogue - 1 lv. Vhuman rogue with shield master will have +7 dex save and half/nothing... (6 lvls before evasion) not bad. On 5th lvl, after ASI to dex, +3 proficiency bonus it's +9. So you can be targeted by your wizard with the fireball.

But if you are thinking how to do more DPR, it's not best way,
Already thought about it. It’s called Pact of The Chain with Two Weapon Fighting since Invisible Imp is very good for the help action.
 


So I build a shield Master rogue and I’m wondering if two weapon fighting is better damage wise. The rogue has a +7 in Athletics and has proficiency in heavy armor since are table allows UA. (Eldritch Armor) Now mathematically what is better damage wise? Two separate attacks without advantage or one with advantage?

Remember that it's not just the rogue who will hit with Advantage, but the rest of the party too.
 

Everyone when is talking about shield master is quoting only about "prone" part. But it's improving dex saves. Yes Rogue has proficiency and on 7th lvl have evasion, but Shield master adds his bonus to Rogue - 1 lv. Vhuman rogue with shield master will have +7 dex save and half/nothing... (6 lvls before evasion) not bad. On 5th lvl, after ASI to dex, +3 proficiency bonus it's +9. So you can be targeted by your wizard with the fireball.

But if you are thinking how to do more DPR, it's not best way,
Shield master only gives you a bonus to dex saves if you are the only target. So you get a +2 vs Disintegrate and a couple other spells like (maybe) Acid Splash.

The feat as written with Crawford's "clarification" that it has to happen after the attack is pretty pointless IMHO.
 


Already thought about it. It’s called Pact of The Chain with Two Weapon Fighting since Invisible Imp is very good for the help action.
It is three levels of Warlock to get to that subclass. Magic initiate is easier and Arcane Trickster is easier still, albeit with a weaker familiar.
 

Everyone when is talking about shield master is quoting only about "prone" part.

OP's question was literally, "Now mathematically what is better damage wise?" We answered that question because that's what was asked.

Remember that it's not just the rogue who will hit with Advantage, but the rest of the party too.

In aggregate, half of the rest of the party, since the opponent is prone until their next turn when they stand up, not until the Rogue's next turn. Also, prone grants disadvantage to ranged attack rolls so it penalizes any characters doing that.

It's only a benefit for other melee characters, and, in aggregate, they're only able to take advantage of the benefit some of the time. And that's not even discussing whether or not the other melee characters can reach the prone target!
 


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