Qfyilyi

Which of these two would be more reliable at least in terms of consistently dealing damage?

I'm not going to take the Agonizing Blast Invocation because I'm planning to take other Invocations, so I won't get the +CHA mods on the EB's. I have 14 DEX so the Crossbow would deal 1d10+2 damage. Now, obviously 5th level EB would have out damage the Crossbow on a high roll, but on the lowest roll, EB would deal 2 damage and the Crossbow would deal 3.

There's also the fact that EB has more mods at least in terms of being able to actually hit (I have 18 CHA so +4 to hit mods, NOT including proficiency), but I could also get a Pact Weapon heavy crossbow with the Improved Pact Weapon Invocation. With that, it becomes more accurate and more damaging, but it still doesn't measure up to the maximum roll of 5th level EB, but I think it would deal much more consistent damage.

Taking everything I mentioned above into account, what is statistically the more consistent damage dealer between a Heavy Crossbow (which I have proficiency with due to Hex Warrior and an additional +2 from 14 DEX), or a 5th level Eldritch blast (which is helped by 18 CHA which gives it +4 to hit, not yet counting the proficiency)?

And what is statistically the more consistent damage dealer between a Pact weapon Heavy Crossbow (+1 to attack and damage rolls and being a Pact Weapon gives it +5 to both attack and damage rolls in total without proficiency) vs the 5th level EB I mentioned above?

Spoiler: It's always eldritch blast.

Shooting twice per turn is always going to be superior to firing once per turn, unless the one shot is vastly better. Like, not "add a stat bonus"-better, but like "this is literally a siege weapon"-better.

First off, comparing an Invocation-enhanced crossbow against an unmodified eldritch blast is obviously an unequal comparison. If you're going to throw Improved Pact Weapon into the mix in order to claim the higher stat bonus with your crossbow, you should compare that against an Agonizing Blast -- it's only fair to add an invocation to both sides of the comparison. And in that case, it's a quite simple "one attack versus two attacks" scenario. With roughly equal chances to hit and roughly equivalent damage, two blast beams is of course superior to one crossbow bolt. Even if though Improved Pact Weapon makes the crossbow count as a +1 weapon, a 5% hit rate increase and +1 damage can't come close to the benefit of just firing twice as often.

So let's ignore invocations: If we compare a standard crossbow attack to a standard blast, the blast is still the better option. You hit more often because of the higher attack bonus, and you get two attacks per turn rather than one, so you have a very high chance of hitting at least once.

The actual math would depend on what AC you're shooting against, but in general, you're talking about one attack at +5 for 1d10+2 damage versus two attacks at +7 for 1d10 damage each.

Supposing you're attacking a relatively tough AC 16, your crossbow will hit on an 11+, or 50%, which gives an average damage over time of (5.5+2)*0.5 = 3.75 damage per round.

By comparison, your eldritch blasts would hit on a 9+, or 60% of the time, and deal 1d10 damage each. So over time that would average out to 5.5*0.6 = 3.3 damage per beam. Since you're firing twice per turn, your expected damage would be double that, or 6.6 damage per round, which is vastly better than the crossbow. I ignored the impact of critical hits in the calculation here, but since you're making twice as many attack rolls with the blast, you'll crit twice as often, so that's only going to tip things even more towards eldritch blast. (Point of interest: The break-even point on damage-dealt would be at a 30% hit-rate for the blast, which I believe in this case would mean blasting with a -1 charisma modifier. Yes, the power of shooting twice is so great that the world's worst warlock is STILL a better, more consistent combatant than you with a crossbow.)

"Consistent" could be interpreted to mean "more likely to do at least some damage every turn" or "the maximum expected damage-per-round", but either way eldritch blast is the way to go for a warlock.

If I had to guess, the point of Improved Pact Weapon isn't to allow a crossbow-focused warlock, but rather to give a melee-focused warlock a ranged option that can leverage all the boosts he's pouring into his pact weapon.