For a pact of the chain warlock, spell damage is going to nearly all of the damage inflicted as the cantrips are as effective as a ranged weapon would be.
Eldritch Blast is the bread and butter
It's a cantrip, so this is the default and aligns well with the consistent non-resource intensive option. It may not do the most damage in a day, but it's going to be the most consistent and most used spell.
The damage can be improved with the agonizing blast invocation (adds charisma bonus to damage).
At L17, you're rolling four spell attacks each doing 1d10 + cha bonus damage.
Eventually gets you the hurl through hell feature that does 10d10 once per long rest on a hit. By the time this feature is available, eldritch blast has 3 chances per casting.
The pact of chain doesn't have a lot of accessories that can contribute to class features for added damage.
- a robe of archmagi adds 2 to your spell attack bonus and your spell DC.
- a rod of magi will give you a +2 to your spell attack and a couple free fireballs a day. (Rod of pact keeper would give +3, but no free fireball)
- a leadership ioun stone gives a +2 to charisma which frees up an ASI for something else like a feat or maybe some more dexterity.
Race & Ability Score Increase (ASI)
Tiefling grants a charisma bonus of 2. Using a standard array, that starts the stat at 16.
Using a single ASI to get to 18 and the Ioun stone to get to 20 essentially maxes out charisma bonus to +5.
Only needing 1 ASI to get a 20 charisma leaves 4 ASIs to buy feats.
- Lucky: Smoke 'em if you got 'em. 3 extra d20 rolls per long rest gives you a chance to roll more 20's. Always use one during the first combat after a long rest. Extra chance to crit or convert a miss to a hit. (Maybe save the remaining to re-roll any natural 20's against you or a crappy saving throw.)
- Spell sniper. Learn ray of frost and ignore any cover but full.
- Elemental adept (cold) for bonus damage with hunger of hadar, frostbite, and ray of frost (from spell sniper)
- Agonizing blast to add charisma modifier to eldritch blast damage
- Minions of chaos to use a spell slot to summon an elemental
Result at L17
- 10 turns per combat
- 1 combat per short rest
- 3 short rests per long rest
Makes a round assumption of 30 rounds of combat a day.
Long rest recharging stuff
Big ticket items that you only get a limited number of per long rest. These are going to have the possibility of doing the most damage, but might be countered, resisted, or not entirely applicable in each situation.
- 2-7 7th level fireballs/lightning bolt/conjure elemental a day from the staff. Each fireball 11d6 fire damage with DC 21. Assuming two castings (66)
- 4 spell slots for hunger of hadar, shatter, or conjure elemental (Spell DC 21). Huger of hadar does 2d6 cold + 2d6 acid damage for 10 rounds (120). Assuming elemental does 10 damage a round for 10 rounds (120)
- 1 hurl through hell use that coincides with a successful spell attack hit. 10d10 damage (50)
Elementals and the area of effect (AOE) spells are more difficult to estimate the total damage done. It depends greatly on the number of enemies being faced, resistances, etc. Grossly assuming mean damage to single target gloss over variable duration, saving throws, and number of targets.
2 fireball (66) + 4 hungar of hadar or elemental (480) + 1 hurl through hell (50)
Approximately 600 damage from long rest or daily recharging abilities.
Leaves 17-24 rounds for cantrip casting.
17 attack actions with 4 blasts each doing 1d10 + 5 of force damage. Each blast has a +15 to hit (prof 6 + cha 5 + robe of archmagi 2 + staff of magi 2). Average 20 damage for all four blasts together.
Approximately 350 damage per adventuring day from eldritch blast.