While Darts are only a 1d4, you can still make this work my optimizing damage modifiers and extra damage. The difference in expected damage between a 1d4 (darts) and 1d10 (heavy crossbow) is 3 damage.
Basically, you need to compensate for your lower damage with having more opportunities to hit/crit, and having more damage dice to roll, or damage modifiers. Sadly, most of the abilities that increase static damage are focused on Melee weapons. A shame you can't use a thrown spear instead of a dart.
To start, I would take 6 levels of Fighter as a human variant, and then continue on as a Rogue Assassin.
With this you can take the following:
- Extra starting feat: Sharpshooter, extends your range, ignore cover, and can convert -5 to hit to +10 damage (helping negate the low damage of the darts)
- Fighter options:
- level 1 : Archery for a +2 to your thrown weapons.
- level 2 : Action surge - for extra throws.
- level 3 : Champion for increased Crit to roll twice your damage dice.
- level 4 : Extra feet - Skulker to prepare you for Rogue/Assasin
- level 5 : Extra attack - more throws.
- level 6 : Ability score improvement - 18 dex.
Then at level 7, take rogue and keep on going with the Assassin path. This will give you sneak attack damage dice, to compensate for your lack of good damage dice on your weapon. You miss out on one last ability score improvement/feat but you won't be needing it.
A few important things you need to do.
- Put your highest stat in Dex to maximize your accuracy so you can feel confident in adding your +10 to damage.
- At levels, 10 increase dex to 20 and then level 14 take the Alert feat, then at 16 and 18 you can take any feat you like, or improve other stats such as CON
- Always use your bonus action to throw two darts if you aren't using it for something else.
The Assassin will allow you to make more critical strikes compensating for the lower weapon damage die. Your d4 won't even be noticed under the mountains of d6s you will be rolling.
For completeness sake, here is the average damage per round at level 20 for comparison of different builds using the same feats but different weapons:
- Phil Taylor: 12.5 (5d4 weapons + Action surge) + 28 (8d6 sneak attack) + 4 (crit * 10%) + 10 (dex mod) = 54 or 64 damage.
- Rogue Assasin: 7 (2d6 weapons) + 35 (10d6 sneak attack) + 1.8 (crit * 5%) + 5 (dex mod) = 48.8 or 58.8 damage.
- 2 handed Fighter: 7 (2d6 weapons ) * 8 (Action surge) + 5.6 (critical* 10%) + 5(str mod) = 61 or 71 damage
- Phil Taylor with Homebrew Feat: 14 (4d6 weapons + Action surge) + 28 (8d6 sneak attack) + 4.2 (crit * 10%) + 20 (dex mod) = 66.2 or 76.2 damage
House rules: You might want to ask your DM to convert Crossbow Expert to Dart Expert giving you the same benefits, but uping the damage of the dart to a 1d6 rather than ignoring the loading property, and allowing your bonus action to be used to throw a second dart. Such a house rule might allow you to go pure rogue assassin or maybe just 1 level dip in fighter for the bonus accuracy.