So, your fist isn't a weapon but when you attack with your fist it is a weapon attack.
You can make a weapon attack with something that isn't a weapon.
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Inspiration is a really interesting addition to Dungeons & Dragons. Finally, the world's premier roleplaying game has actual rules and mechanisms for roleplay!
Except there are some problems in execution here:
- There aren't a lot of guidelines about when the DM is supposed to award Inspiration to the players, but what is there on paper states that you should award Inspiration when a player roleplays in a way that is connected to their character's personality, ideals, bonds, and flaws. Which sounds good, but in practice this means that the DM will need to keep track of five traits per character and be on the lookout for them in play. The DM already has enough stuff to keep track of.
- Spending Inspiration give you advantage on a roll, but it's a bit hamstrung by the fact that it has to be spent prior to making a roll. Both dice might show successful results, which seems like a waste of a precious commodity. (You can only have one "point" of Inspiration at a time.) In this case, it would make more sense if spending Inspiration got you a re-roll or advantage on a roll.
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Take a look at the ranger's capstone 20th level special ability, then compare it against any other late-level ability from the other classes. Foe Slayer is so bad that you can roll it into the ranger's 1st level Favored Enemy ability and it in no way unbalances the game. If a ranger in any of my games made it to 20th level, we'd definitely be coming up with a replacement ability.