Let's start with a baseline dart thrower
If we are building a net and dart character, we will want them to be at least better than a basic dart thrower. The simplest optimized dart thrower that I could come up with is a Custom Lineage Fighter 1/Ranger (Gloom Stalker) 5 with the Piercer and Sharpshooter feat.
Thus the relevant factors for our damage are:
- 18 Dexterity
- 2 attacks with Extra Attack (3 with Dread Ambusher on the first turn; which we will call 1/3 of turns)
- 50% chance to hit with Sharpshooter attacks (includes the Archery Fighting Style, and using the expected AC of 15 for a solo monster in a medium difficulty encounter according to the Dungeon Master's Guide)
- One reroll on damage with the Piercer feat
- Extra critical hit damage with the Piercer feat
- 10 extra damage with Sharpshooter
- 2 extra damage with the Thrown Weapon Fighting Fighting Style
Calculating this damage, we get 22.75 DPR:
$$(\frac{2}{3}*2+\frac{1}{3}*3)*(50\% *(\frac{2.5+2.5+3+4}{4}+4+10+2)+5\%*5)=22.75 \text{ DPR}$$
What does the net do?
If we replace one throw of the dart with a net, we get the following changes to the damage factors:
- No dart attacks on the first turn
- When our net hits (75% of the time), our remaining dart throws improves to 75% chanced to hit, and are chance to score a critical hit improves to 9.75%
Calculating this damage, we get 17.988 DPR:
$$(\frac{2}{3}*2+\frac{1}{3}*0)*((\frac{3*75\%}{4}+\frac{50\%}{4}) *(\frac{2.5+2.5+3+4}{4}+4+10+2)+(\frac{3*9.75\%}{4}+\frac{5\%}{4})*5)=17.988 \text{ DPR}$$
As you can see, we lose considerable damage because that first round is spent on the net. Firstly, Gloom Stalker ranger is wasted with this strategy, but more importantly, we need to find a way to deal damage during that first turn or to be able to guarantee the restrained condition.
Optimizing for the net
The first basic solution is to get our hands on Action Surge so we can attack on the turn we use the net. Unfortunately, Action Surge forces us into straight Fighter to maintain our Fighting Styles (using the level 6 ASI to gain the Fighting Initiate feat).
Let's say we have Action Surge about half of our first turns. Our new damage is 22.484 DPR:
$$(\frac{5}{6}*2+\frac{1}{6}*0)*((\frac{3*75\%}{4}+\frac{50\%}{4}) *(\frac{2.5+2.5+3+4}{4}+4+10+2)+(\frac{3*9.75\%}{4}+\frac{5\%}{4})*5)=22.484 \text{ DPR}$$
Now we are fast approaching parity with the dart thrower and we haven't even included our subclass yet. But before we get to that, let's talk a bit about nets.
What if they break out of the net?
If the target breaks free from the net, our damage drops precipitously. While it is nice to have wasted their turn, calculating the drop in damage on the proceeding turns, we get 17.497 DPR:
$$(\frac{2}{3}*2)*(50\% *(\frac{2.5+2.5+3+4}{4}+4+10+2)+5\%*5)+$$
$$(\frac{1}{6}*2+\frac{1}{6}*0)*((\frac{3*75\%}{4}+\frac{50\%}{4}) *(\frac{2.5+2.5+3+4}{4}+4+10+2)+(\frac{3*9.75\%}{4}+\frac{5\%}{4})*5)=17.497\text{ DPR}$$
As such, we want to make breaking free as hard as possible. And the best way to do that is with the hex spell:
Also, choose one ability when you cast the spell. The target has disadvantage on ability checks made with the chosen ability.
As a Fighter 5/Warlock 1, we miss out on the Piercer feat, setting our Dexterity to only 17 (lowering our chance to hit as well) and we don't get the rerolls on damage dice and extra damage. However, hex (and Genie's Wrath from our patron choice) gives us a bit of that damage back, and helping maintain the net restraint is very worth it.
Our chance to hit is now 45% without the net, and 69.75% with the net. The net attack now has a 70% chance to hit instead of 75%.
Our new damage with hex and Genie's Wrath is 22.025 DPR:
$$(\frac{5}{6}*2+\frac{1}{6}*0)*((\frac{7*69.75\%}{10}+\frac{3*45\%}{10}) *(2.5+3.5+3+10+2)+(\frac{7*9.75\%}{10}+\frac{3*5\%}{10})*(2.5+3.5))+(\frac{5}{6}*((1-(1-(\frac{7*69.75\%}{10}+\frac{3*45\%}{10})^2))*3)+\frac{1}{6}*(70\%*3))=22.025 \text{ DPR}$$
We miss out on about 0.75 DPR compared to a quick-and-dirty dart throwing build, but get the benefit of applying the net for our party to possibly benefit from.
What subclass to play
We could eek out a little more damage with Battle Master, but I think the best course of action is to help guarantee the restrained condition. Hex is making a difference, but there is still a chance they will break free despite the disadvantage.
For these situations, I recommend the Rune Knight subclass for the Fire Rune on your shield:
In addition, when you hit a creature with an attack using a weapon, you can invoke the rune to summon fiery shackles: the target takes an extra 2d6 fire damage, and it must succeed on a Strength saving throw or be restrained for 1 minute. While restrained by the shackles, the target takes 2d6 fire damage at the start of each of its turns. The target can repeat the saving throw at the end of each of its turns, banishing the shackles on a success. Once you invoke this rune, you can’t do so again until you finish a short or long rest.
It also gives a bit of extra damage between short rests (4d6+ instead of 4d8), and can reengage that restrained condition on those occasions where the target breaks free.
You also get Giant's Might for a bit more sustained damage in fights where you use it.
As for warlock, I chose The Genie for a bit of extra damage per round, but you could certainly choose something else at the cost of about 2.5 DPR.
The final build
Our character is Custom Lineage for the Fighting Initiate feat (Archery) with the following classes:
- Fighter 5 (for Thrown Weapon Fighting, Action Surge, Fire Rune, Giant's Might, the Sharpshooter feat, and Extra Attack)
- Warlock 1 (for hex and Genie's Wrath)
Taking the build further
Going much higher with this build, our net will be less and less reliable. You will start to run into huge enemies, or combats with multiple enemies more often. Additionally, the Strength scores will be high enough to break free of the net despite the disadvantage.
Against such enemies, you should basically fall back on that baseline dart thrower and skip the net.
Here's how I would level this character past level 6:
- Fighter 6 for the Piercer feat getting our Dexterity to the much needed 18
- Warlock 2 for the extra spell slot for if we ever lose Concentration or if our combats are more than an hour apart. Take whatever Invocations you like
- Fighter 7 for the Storm Rune and Runic Shield which are both quite potent to help with or against key attacks and saving throws
- Fighter 8 for Dexterity 20
- Fighter 9 for Indomitable (helps with Concentration on hex)
- Fighter 10 for Constitution 18
- Fighter 11 for improved Extra Attack
- Ranger 1
- Ranger 2
- Ranger 3 for Dread Ambusher
- Ranger 4 for Constitution 20
This build is "viable" at higher levels, but not very optimized. As the net falls off, you are better off just switching to a hand crossbow and picking up the Crossbow Expert feat. If I were playing this character, I'd do this at 10th level and delay maximizing my Dexterity for those extra attacks.