At what point is it statistically better to take Tavern Brawler over an increase to Str or Dex if 1/3 of all your attacks are made with an improvised weapon?
Example: A Thief rogue 4/Champion fighter 5, with 16 Dex.
You make two attacks a turn with the Attack action, and one (throwing an acid vial) with the Fast Hands thief feature:
Two attacks with dagger: +7 to hit 1d4+3 (6)
If one of daggers hit assume sneak attack applies 2d6 (8)
One attack with an acid vial: +3 to hit 2d6+3 (11)
Statistically, would it be better to take Tavern Brawler for all 3 attacks to be at +7 to hit?
Or should I put the ASI into Dex for two +8 to hit and +4 to hit?
Best Answer
The two options for you are actually stunningly close, statistically.
Mechanically, Tavern Brawler is statistically better if you are fighting enemies with an AC of 18 or above, while the ASI is better for AC 17 or below. However, the difference never amounts to more than 0.4 DPR.
Link to statistical analysis: https://anydice.com/program/1343d
My analysis assumes that you are always attacking without advantage, but that sneak attack is always possible. If you have advantage on your first attack, you will likely be better off with the ASI. I also assume that you are not attacking with STR or that the +1 to STR/CON from Tavern Brawler would not round out your STR score to an even value.
Because these two options are so close in combat, it may be worth considering out of combat mechanics as well. Vials of acid are both costly and consumable, so they may not always be available. Additionally, putting an ASI into DEX would improve your AC, stealth, sleight of hand, and many other useful abilities.
On the other hand, Tavern Brawler does create many useful roleplaying opportunities.
tl;dr The two options are nearly identical in combat, so other abilities and character traits should be the basis of your decision.