In D&D 3.5e, there were various "blast shape" invocations available to warlocks, five of which were included in the video game Neverwinter Nights 2 (which is based on 3.5e and is all I really know of 3.5e): Hideous Blow, Eldritch Spear, Eldritch Chain, Eldritch Cone and Eldritch Doom.
Now, I know that warlock invocations worked differently in 3.5e to 5e (primarily based on how they're implemented in the video game compared to how I know they work in 5e), but I wanted to convert some of these into 5e Eldritch Invocations.
Arguably, Hideous Blow could be thought of as being roughly equivalent to Eldritch Smite from 5e (XGtE, p. 56; even though it doesn't actually modify eldritch blast), and Eldritch Spear already exists in 5e (as a way to increase the range of eldritch blast), so the remaining three are the ones I have attempted to convert.
Here are my attempts at each of the three invocations, with some commentary below each one to explain my thought process and design decisions.
Prerequisite: 5th level, eldritch blast cantrip
This blast shape invocation allows you to improve your eldritch blast by turning it into an arc of energy that "jumps" from the first target to others. When you cast eldritch blast, on a hit, you can choose to target an additional creature of your choice within 30 feet of the target with the same beam. Make a ranged attack roll against the additional creature, which takes half of the damage dealt to the target on a hit. You can only use this invocation once per turn with one beam, although you may choose to do so after you know whether a beam hits its target.
When you reach 11th level, your chain can target two additional creatures, both of whom take half of the damage dealt to the original target on a hit, and when you reach 17th level, your chain can target three additional creatures, all of whom take half of the damage dealt to the original target on a hit. You choose the targets in succession, and each subsequent target must be within 30 feet of the previous target of the chain (not the original target). The chain cannot target the same creature more than once (although it can target a creature hit with a different beam that turn), and on a miss, the chain ends and you cannot target any further creatures with the chain.
In NWN2 (and presumably 3.5e), Eldritch Blast only ever fired one beam, and Eldritch Chain was a way of making that hit more enemies, but each additional enemy only took half damage. Considering that eldritch blast in 5e can target multiple creatures already, I wanted to come up with something that felt unique.
I considered having each beam jump to only one addition target to deal half damage, but then a level 17 warlock could hit eight creatures with this thing, which seemed overpowered (and wouldn't "look right" compared to what it looked like in NWN2, where the one beam would jump to different targets, not four different beams that each jump to one other target).
In the end, I decided to have it target a few additional creatures, but for half damage (Agonizing Blast would be taken into consideration for the original target's damage, so isn't added again to each of the chain's targets), which is the same as in 3.5e, but only on one of the beams, not each beam. Yes, this still increases the number of creatures you can hit each turn, and therefore increases the damage output of eldritch blast, but hopefully the half damage mitigates that somewhat; also, you've still got to roll to hit them, so there's a chance that you'll simply miss and then it's no different to not having the invocation at all.
That said, it's still a clear improvement on RAW eldritch blast, so if it needs to be nerfed further, I could reduce the range to 10 feet or something, although unless the targets are spread out, this won't really matter. Losing the second paragraph when you reach higher levels is also something that can be dropped, but hopefully not since that would also nerf the look/flavour of Eldritch Chain. I'd still like to keep it as an "at-will" ability, but increasing the damage output of a cantrip is pretty big, so another way to nerf it is to say that you must use it or Agonizing Blast (per beam, so your non-chain beams can still use Agonizing Blast). Depends on how powerful it is as-written above...
Also, I did in fact mean "spell attack", as Cubic's answer points out (I would update the above, but then the Q and A are out of sync, but for any future answers, yes, I did mean "spell attack").
Prerequisite: 12th level, eldritch blast cantrip
This blast shape invocation allows you to invoke your eldritch blast as a 15-foot cone. Each creature within the cone must make a Dexterity saving throw. A creature takes 1d10 force damage on a failed save, or half as much damage on a successful one.
For Eldritch Cone, I've simply used the standard cone spell implementation, like burning hands, but it only does the same amount of damage as one beam, to balance out the fact that you can hit multiple enemies with it. My intention is for Agonizing Blast to be included in this damage, so it's actually 1d10 + 5 force damage for an optimised warlock.
I originally had it as a 30-foot cone that did 3d10 force damage, same as the normal damage output for eldritch blast (which would have increased to 4d10), but that was so powerful that I could only justify that as being once per rest or something, and I'd prefer to keep these as being something that can be used "at-will" to keep that 3.5e feel, so hopefully having a cone shaped cantrip is useful enough to justify only dealing 1d10 damage in a 15-foot cone to be balanced; I'm not sure if even having a cone cantrip is inherently overpowered, or whether the small damage and range somehow makes it underpowered, but hopefully it's balanced.
Prerequisite: 18th level, eldritch blast cantrip
This blast shape invocation allows you to invoke your eldritch blast as the dreaded eldritch doom. This causes bolts of mystical power to lash out and savage all targets within a 20 foot area originating from a point you can see within 120 feet of you. Each creature within that area must make a Dexterity saving throw. A creature takes 1d10 force damage on a failed save, or half as much damage on a successful one.
For Eldritch Doom, I've implemented it as basically a force fireball, dealing the same damage as a single beam. As above, my intention is for Agonizing Blast to be included in this damage, so it's actually 1d10 + 5 force damage for an optimised warlock.
I originally had it at 4d10, same as all four beams combined, and had the range at 30-feet, but this would be massively overpowered without a "once per rest" cap on it, but these caps kinda go against what blast shape invocations were about, so as before, I hope that the AOE shape alone is worth an invocation, since you now have a weak at-will force fireball, but without that being inherently overpowered.
Are these three invocations balanced when compared to the other Eldritch Invocations? Specifically, do they make eldritch blast overpowered in a way that dealing reduced damage and taking up a choice of an Eldritch Invocation doesn't counterbalance?