Why aren't spells created equal?

[heavyfuel]

I think it's fair to say that some spells are straight up better than other spells at the same level. It's hard to justify Witch Bolt when you have access to Sleep. Equally as hard to justify Time Stop when you can now cast True Polymorph. I'd even place Fireball above Immolation, a 5th level spell.

So, if a spell level is a measure of how strong that spell is, why is it that some spells are considered so much better than others? Why is it that something like the Whispers of the Grave invocation something considered pretty weak to gain at level 9, when Master of Myriad Forms is considered better, but only available levels later?

This is a genuine question, though. Why is it?

[JNAProductions]

Because game designers aren’t perfect.

In Fireball’s case, that was intentionally made better, because it’s iconic.

But other spells? Witch Bolt wasn’t intended to suck-it just happened that way. Because humans mess up-a lot.

[MrStabby]

Some are unequal because they are circumstantial and it may depend on what comes up in a given campaign.

If you are fighting a rakshasa then fireball or counterspell wont be useful but lower.level spells very much might be.

[sophontteks]

Some spells just straight up don't work, like find trap and enthrall. There's a good amount of human error in them. In many other cases it just doesn't look like they were aiming to make them balanced. That's fine. Balanced can be boring. But it would be nice to remove the straight trap options.

[Unoriginal]

I think it's fair to say that some spells are straight up better than other spells at the same level. It's hard to justify Witch Bolt when you have access to Sleep. Equally as hard to justify Time Stop when you can now cast True Polymorph. I'd even place Fireball above Immolation, a 5th level spell.

So, if a spell level is a measure of how strong that spell is, why is it that some spells are considered so much better than others? Why is it that something like the Whispers of the Grave invocation something considered pretty weak to gain at level 9, when Master of Myriad Forms is considered better, but only available levels later?

This is a genuine question, though. Why is it?

A spell level is a range, not a point. Some spells are strong for their level, others are weak for their level.

Furthermore, as pointed out above, the creators aren't perfect. Even without counting the mistakes, sometime tactical considerations the spell-creator didn't think about or didn't think as relevant make a spell much more or much less useful than intended. Sleep is much less useful than Witch Bolt against two Ogres the group's frontliners can prevent from reaching the caster entirely, but against a bunch of low-HPs mooks Sleep is pretty great. It just happens that one situation is "any source of damage is nice" while the other is "a good AoE turns the table here", making Sleep more noticeable useful.

In-universe, the creators of the spells and the principles they relied on for their creation aren't equal in everything, either. Mordenkainen managed a feat when he created his Faithful Hound, but his Sword is pretty inferior to Bigby's famous force constructs, despite the similarities.

[Damon_Tor]

Because game designers aren’t perfect.

In Fireball’s case, that was intentionally made better, because it’s iconic.

But other spells? Witch Bolt wasn’t intended to suck-it just happened that way. Because humans mess up-a lot.

My understanding is that Witch Bolt isn't intended to be used by players, it's a spell designed to be used by NPCs against the players. It makes much more sense when you think about it in that context.

[Sigreid]

Some spells just straight up don't work, like find trap and enthrall. There's a good amount of human error in them. In many other cases it just doesn't look like they were aiming to make them balanced. That's fine. Balanced can be boring. But it would be nice to remove the straight trap options.

IMO find trap for example would be set right if it had a duration of at least an hour.

[DwarfFighter]

This is a genuine question, though. Why is it?

Really?

The real answer is: Spells are different and therefore they will be of different use in different circumstances. Suggestion is going to win you more friends than Fireball, after all.

Even if you had an offensive spell with identical properties except for damage type, one of those would be considered better than the other by applying a mix of objective and subjective preferences: A fireball-clone that deals force damage instead of fire would cause an upset in the community because of how uncommon are resistance and immunity to force damage!

But I guess you mostly care about spells that are used to in the same manner, as offensive hammers, right? Why spend a really difficult full minute with lvl 3 Witch Bolt to deal 30d12 lightning damage when you can deal 8d6 no-brain fire damage (save for half) with a Fireball? Well, sometimes you need to grind, sometimes you need to blast. You can't make that distinction by just looking at the numbers on the page, you gotta play the game to see what situations you get into.

-DF

[heavyfuel]

To answer some general points that have come up:

Yes, human error is a thing. The designers over/under estimating a spell's capabilities is definitely one of the reasons. But it doesn't explain everything.

Take Invocations, for example. I'm pretty sure it would be considered overpowered if level 9 Warlocks could pick an invocation of at-will Shield. So why isn't it overpowered that they can pick at will Jump? If Shield and Jump are both 1st level, they should have roughly the same power/versatility. So either Shield is underleveled or Jump is overleveled. And if so, why?

Also, it's obvious that spells having different uses doesn't mean that one is stronger than the other. Yeah, Suggestion is better in social situations than Fireball. That's so beside the point it shouldn't even merit an answer.

But, in a lot of cases, spells that serve similar purposes are still at odds. Magic Missile (plus cantrips) out-damages Witch Bolt in pretty much every scenario, except the super contrived ones people will point out trying to prove me wrong. MM and WB are both single target damage spells, but one is clearly superior to the other.

[Asisreo1]

Some spells just straight up don't work, like find trap and enthrall. There's a good amount of human error in them. In many other cases it just doesn't look like they were aiming to make them balanced. That's fine. Balanced can be boring. But it would be nice to remove the straight trap options.

Find Traps is a product of DMs playing differently than the designers intended.

How finding traps, in general, is supposed to work is that they must make a Wisdom (Perception) check to notice anything that seems off in the surroundings while it takes an Intelligence (Investigation) check to determine how exactly to disarm it. It then takes theives' tools or any action that would reasonably disarm the trap to disarm it.

The players should rarely ever know if something is a trap. They should just know that something odd is happening. Allow me to demonstrate with a Hidden Pit trap.

Step 1. The players walk into the room with the trap.

Step 2. The DM asks the party for their passive perception.

Step 3. The DM describes the room, if they beat the PP check, he includes the trap's visual description: "The 20 x 20 room holds military supplies. A tapestry of the kingdom of Leden is draped over the wall. A locked chest stands in the corner of the room. In the center of the room, there is a section of the floor with an unusually light amount of foot traffick."

Step 4. The players investigates the clean area. If they succeed a DC 15 Investigation check, they realize its actually a pit.

Step 5. The players decide what they want to do next.


Find Traps is a spell that skips 2, 3, & 4 for the purposes of finding traps. As soon as you cast it, you know that the floor is trapped but the tapestry, door, and chest are not. Its useful for exploration and can even detect invisible traps or hazards.

Unfortunately, DMs skimp out on mapmaking and trap-setting so it hardly matters in those games.

[stoutstien]

Mio the real big reason why there is such a big discrepancy across the spell list is because it's too darn big.

[SharkForce]

Sleep is much less useful than Witch Bolt against two Ogres the group's frontliners can prevent from reaching the caster entirely, but against a bunch of low-HPs mooks Sleep is pretty great. It just happens that one situation is "any source of damage is nice" while the other is "a good AoE turns the table here", making Sleep more noticeable useful.

nah, I'd still rather have sleep. once those ogres are whittled down, sleep could become an amazingly effective spell against them. witch bolt, if all the stars align perfectly for it, might manage to achieve "a little better than casting a cantrip"... but then again, it might not, even then.

Find Traps is a product of DMs playing differently than the designers intended.

How finding traps, in general, is supposed to work is that they must make a Wisdom (Perception) check to notice anything that seems off in the surroundings while it takes an Intelligence (Investigation) check to determine how exactly to disarm it. It then takes theives' tools or any action that would reasonably disarm the trap to disarm it.

The players should rarely ever know if something is a trap. They should just know that something odd is happening. Allow me to demonstrate with a Hidden Pit trap.

Step 1. The players walk into the room with the trap.

Step 2. The DM asks the party for their passive perception.

Step 3. The DM describes the room, if they beat the PP check, he includes the trap's visual description: "The 20 x 20 room holds military supplies. A tapestry of the kingdom of Leden is draped over the wall. A locked chest stands in the corner of the room. In the center of the room, there is a section of the floor with an unusually light amount of foot traffick."

Step 4. The players investigates the clean area. If they succeed a DC 15 Investigation check, they realize its actually a pit.

Step 5. The players decide what they want to do next.


Find Traps is a spell that skips 2, 3, & 4 for the purposes of finding traps. As soon as you cast it, you know that the floor is trapped but the tapestry, door, and chest are not. Its useful for exploration and can even detect invisible traps or hazards.

Unfortunately, DMs skimp out on mapmaking and trap-setting so it hardly matters in those games.

actually, you don't know that. the spell doesn't give you a location, it just tells you that somewhere in range that you can see, there is a trap. you still have to check the chest, you still have to check the tapestry, and you still have to check the door.

[Asisreo1]

nah, I'd still rather have sleep. once those ogres are whittled down, sleep could become an amazingly effective spell against them. witch bolt, if all the stars align perfectly for it, might manage to achieve "a little better than casting a cantrip"... but then again, it might not, even then.



actually, you don't know that. the spell doesn't give you a location, it just tells you that somewhere in range that you can see, there is a trap. you still have to check the chest, you still have to check the tapestry, and you still have to check the door.

It does still leaves much to be desired as intended, don't get me wrong. Its not entirely clear if it tells you the number of traps within the line of sight but it does tell you the general nature of the trap.

What that means is kinda up to the DM. He could be as explicit as "There's a pit trap with spikes somewhere." Or he could be as vague as "A hidden trap will activate by proximity."

Interestingly enough, its not on any spell list except for Druid, Cleric, and Ranger. I don't think its ever worth it on the Ranger though it could be somewhat flavorful. The Druid and Cleric has the versatility to take this spell, though, if they suspect they'll be facing alot of hidden threats in their adventure.

Also also, Find Traps doesn't really specify if it can detect harmful creatures that are indiscernable from its environment or an object. A generous DM could let the caster detect an ambush by invisible creatures like Stalkers or Pixies or by object-like creatures like Mimics and Animated Armors.

I don't think its wrong to do so.

[kingcheesepants]

Also worth noting are that a lot of spells are adapted from older editions or sometimes different settings and the rules don't always port over well leading to under/overpowered or really niche spells. True strike is a pretty good example of this, in 3e it gave a +20 insight bonus and there were a some more powerful spells that utilized spell attack rolls back then. However there's no such thing as an insight bonus anymore, 5e uses bonded accuracy and so a +20 to hit would be insane and spells that require an attack roll are few and most all of them are low level. So instead of an insight bonus it's advantage and there really isn't anything worthwhile to pair it with. It becomes doubly useless since there are other easier ways to get advantage that don't use up your entire action. Could the spell have been ported over in a more usable form? Almost certainly, but it's easy to understand how it got messed up. I think if you look at a lot of the most egregious examples of bad spells (either way too good or too bad) you'll see the same thing. Simulacrum wasn't nearly so OP before but in simplifying the spell for 5e it got a big buff, Weird was never great but it used to be okay at least, etc etc.

[lall]

Equality most likely wasn’t the designers’ top priority. Plus, spells don’t exist in a vacuum. I may vastly prefer a ‘lesser’ spell for a particular build.

[holywhippet]

Another reason is due to differences in what classes are meant to be capable of in order to maintain balance. Fireball, for example, isn't available to all spell casting classes. A bard can take it via magical secrets, but at the cost of not taking something else. They usually have to use weaker AoE spells instead.

[MaxWilson]

I think it's fair to say that some spells are straight up better than other spells at the same level. It's hard to justify Witch Bolt when you have access to Sleep. Equally as hard to justify Time Stop when you can now cast True Polymorph. I'd even place Fireball above Immolation, a 5th level spell.

So, if a spell level is a measure of how strong that spell is, why is it that some spells are considered so much better than others? Why is it that something like the Whispers of the Grave invocation something considered pretty weak to gain at level 9, when Master of Myriad Forms is considered better, but only available levels later?

This is a genuine question, though. Why is it?

In my spell research rules, it's because mediocre spells take less time, talent, gold, and luck to create than highly optimized, overpowered spells. A first level wizard could probably recreate Witch Bolt in a single week, but Find Familiar would be orders of magnitude harder and more expensive.

The PHB/DMG have essentially no spell research rules at all so you might as well adopt my explanation until proven otherwise, even if you're not using spell research rules. It makes sense, and explains the existence of awful spells and terrific spells alike.

[Valmark]

Spells within the same level being stronger or weaker then others can be either designer error, campaign-dependancy (meaning that depending on context spells can be stronger or weaker) and/or personal taste (as an example you say Whispers of the Dead is considered pretty weak when I think the opposite).

As far as spells being put on different levels... Well, obviously it's the designer's judgement on which one goes at which level. Spells with apparently bigger effects will need an higher level.

[Merudo]

I think it's fair to say that some spells are straight up better than other spells at the same level. It's hard to justify Witch Bolt when you have access to Sleep. Equally as hard to justify Time Stop when you can now cast True Polymorph. I'd even place Fireball above Immolation, a 5th level spell.

So, if a spell level is a measure of how strong that spell is, why is it that some spells are considered so much better than others? Why is it that something like the Whispers of the Grave invocation something considered pretty weak to gain at level 9, when Master of Myriad Forms is considered better, but only available levels later?

This is a genuine question, though. Why is it?

Because the Lead Rules Designer, Jeremy Crawford, is absolutely terrible at evaluating game balance.

Seriously - he's awful at it. Any experienced player visiting this forum is likely more capable of evaluating the balance of spells, subclasses, feats, and the likes than he is.

Without a lead designer with a strong grasp of game balance, the spells end up all over the place. The same spell level that offers you the OP Simulacrum also gives you junk like Mordenkainen’s Sword.

[Guy Lombard-O]

Why spend a really difficult full minute with lvl 3 Witch Bolt to deal 30d12 lightning damage when you can deal 8d6 no-brain fire damage (save for half) with a Fireball?

Whoa! 30d12?

Has there been some huge errata to Witch Bolt that I should know about?!?

[Theodoxus]

On top of the really great answers - and I love your take, MaxWilson - there is very little 'formulaic' construction around spell making. Beyond MW's notation of a lack of in-universe rules for it, there's also a very obvious lack of such rules for the designers to follow.

It kinda sorta works for damaging spells. They sorta follow a internal rule schema, until they don't. But utility spells are all over the place. Defensive spells tend to be overpowered for their level, but curative spells are massively underpowered for their level except for bloat exceptions (which get errata-nerfed anyway).

Then there's the 5E philosophy of upcasting, which is new to D&D and I think the devs (probably JC) thought that fixed everything. If a spell is underpowered at the level you get it, simply upcast it! I originally thought it was a pretty slick solution. I have come to loathe it. I want my Caster Level back, my automatically boosted spells like Magic Missile. And maybe make it a hybrid system, where you can upcast it, and not only does it Heighten the spell, but grants a different, new rider effect. All those "At Higher Level" could be re-written with something nifty happening at higher level than just affecting more targets or dealing/healing more damage.

[Hael]

There’s also class balance at stake. Certain spells are basically class features for all intents and purposes.

Also there are a number of spells that would essentially obsolete another classes strong point if they were ported as they once were. For instance, Wizards aren’t given many mass summon spells and many of their summons spells are counterbalanced by DM dependant wording. There’s a reason gate isn’t as strong as it was in previous editions and that their high lvl summons are mostly inferior to druids conjure animals, a third lvl spell.

I’m pretty sure a number of spells were actively nerfed and buffed as direct class buffs during play testing without regard for spell balance within their own tier.

[Asisreo1]

There’s also class balance at stake. Certain spells are basically class features for all intents and purposes.

Also there are a number of spells that would essentially obsolete another classes strong point if they were ported as they once were. For instance, Wizards aren’t given many mass summon spells and many of their summons spells are counterbalanced by DM dependant wording. There’s a reason gate isn’t as strong as it was in previous editions and that their high lvl summons are mostly inferior to druids conjure animals, a third lvl spell.

I’m pretty sure a number of spells were actively nerfed and buffed as direct class buffs during play testing without regard for spell balance within their own tier.

Precisely.

I consider spell lists when thinking about class balance and its the reason why so many spells can be difficult to balance from just a "this spell is this level" perspective.

Lets say I wanted to create a spell called "Divine Movement," which is just a teleportation spell but on the cleric's spell list. Let's say I modeled it after Misty Step and did something like BA able to teleport 15ft in a direction they choose. Basically half distance but doesn't require sight. Not broken, right?

Well, teleportation on clerics are extremely valuable because they don't have many means to do so. If a cleric gets swallowed or restrained, they'll usually have to either cast a 4th-level freedom of movement spell or find some other escape condition. If a cleric is trapped, they rarely have excellent mobility options to free themselves.

What does this mean? It means that every cleric will probably default to this spell. No cleric will not have it always prepared and it shores up a weakness that the arcane casters had over them.

[LudicSavant]

Why is it that something like the Whispers of the Grave invocation something considered pretty weak to gain at level 9, when Master of Myriad Forms is considered better, but only available levels later?

Eh? Who said Master of Myriad Forms is better than Whispers of the Grave? Many Faces can make disguises without eating your Concentration like Myriad does. And water breathing is just an all-day ritual that also does not eat your Concentration. And we have a thread about how good Whispers is on the front page right now.

Aside from that, occasionally imbalance is intentional, especially in the case of iconic "like a class feature" spells, but often it's just the result of the devs not doing a great job of balancing. I'm betting whoever made Witch Bolt just sort of failed to do the math there.

In my spell research rules, it's because mediocre spells take less time, talent, gold, and luck to create than highly optimized, overpowered spells. A first level wizard could probably recreate Witch Bolt in a single week, but Find Familiar would be orders of magnitude harder and more expensive.

The PHB/DMG have essentially no spell research rules at all so you might as well adopt my explanation until proven otherwise, even if you're not using spell research rules. It makes sense, and explains the existence of awful spells and terrific spells alike.

I really like when mechanics are narratively associated like this. That's a fun take: Fireball is as good as it is because generations of mages have been refining it to perfection.

Reminds me of the story Keith Baker had for 3.5e metamagic mechanics and Eberron's technological development.

[Snails]

There’s also class balance at stake. Certain spells are basically class features for all intents and purposes.

Hunter's Mark, for example, is basically a class feature for the Ranger to simply up damage, while falling short of being 100% reliable. That is shows up on the spell list for the Oath of Vengeance Paladin is pretty path defining, as well.

So, it is true that a few spells are simply better than is typical for spells of that level and that is an implied significant class feature. Eldritch Blast, Hunter's Mark, Hideous Laughter and Fireball are the obvious examples.

OTOH, some spells are simply weak because the designers shoehorned them into 5e mechanics without thinking carefully, often just keeping the spell level of a previous edition without serious consideration of where it fits in the new edition. For example, Protection from Energy and Flame Arrows would not be considered notably good if they were 2nd level instead of 3rd level.

[Veldrenor]

In addition to the other great ideas here, the idea of system mastery might also be at play. WotC has definitely talked about this in the past about why they intentionally create bad Magic: the Gathering cards. A newcomer to the game doesn't know yet that there are "good" spells and "bad" spells, and so they'll use whatever spells look neat to them. As they play, though, they'll get a feel for how the game works and the actual utility and power of the different spells. They'll learn the limitations of Witch Bolt, or the strength of Fireball. That increased knowledge is an accomplishment. Becoming more skilled at the game, understanding which spells are "good" and which are "bad" and how best to apply them, makes people feel good and smart.

[Galithar]

Whoa! 30d12?

Has there been some huge errata to Witch Bolt that I should know about?!?

I believe he mistakenly applied the damage increase to the damage on subsequent turns, which would actually make the spell a million times more powerful and very usable. Along the lines of heat metal except more damage, no target restriction, and a less resisted damage type.

[Asisreo1]

Witch Bolt was a difficult spell to balance anyways. There's no real guarantee that an enemy will just leave your range or threaten your concentration. Sure, they could, but its not like there's a mathematical formula to predict how often your character gets threatened or how likely your DM will have your enemies play 30ft ballerina.

The fact of the matter about the spell, however, is that if neither of those are forced, the spellcaster casted a 1st-level spell to have a better tier 1 cantrip. Having auto-hit and damage higher than firebolt is interesting and, if not for the other conditionals, would be a powerful tier 1 spell.

Now, you may be thinking "This only accounts for tier 1. Why bother taking a spell that gets shafted later?" Well, you can think of it like a temporary spell. Look at the characters with access to it. They are known casters that can switch their known spell upon level up (aside from wizards). As soon as they enter tier 2, they can safely retire that spell for maybe a second 3rd-level spell.

As for the restrictions themselves, make of them what you will. Its generally commonly accepted that a monster would prioritize getting rid of Witchbolt which seems ridiculous to me. If a fighter is engaged in combat with a monster and that monster has Witchbolt on him, that fighter is probably threatening 10 damage on the monster as an AoO. If they have a 65% chance of hitting, well, they take an average of 6.5 damage anyways. This isn't including any sort of fighting style/feats the fighter may have.

From the monster's PoV, its strictly worse to move out of the way. Look at what they're trading: they take their movement and 6.5 damage against the fighter's reaction to avoid what would have been 6.5 damage on the caster's whole action. The only reason a DM would move the creature in this scenario is to spite the caster.

The caster, however, is free to use their action for something like firebolt, ray of frost, or even another higher level spell slot. This isn't a good trade for the monster and they're better off keeping the witchbolt until the situation changes somehow.

[Luccan]

Witch Bolt was a difficult spell to balance anyways. There's no real guarantee that an enemy will just leave your range or threaten your concentration. Sure, they could, but its not like there's a mathematical formula to predict how often your character gets threatened or how likely your DM will have your enemies play 30ft ballerina.

The fact of the matter about the spell, however, is that if neither of those are forced, the spellcaster casted a 1st-level spell to have a better tier 1 cantrip. Having auto-hit and damage higher than firebolt is interesting and, if not for the other conditionals, would be a powerful tier 1 spell.

Now, you may be thinking "This only accounts for tier 1. Why bother taking a spell that gets shafted later?" Well, you can think of it like a temporary spell. Look at the characters with access to it. They are known casters that can switch their known spell upon level up (aside from wizards). As soon as they enter tier 2, they can safely retire that spell for maybe a second 3rd-level spell.

As for the restrictions themselves, make of them what you will. Its generally commonly accepted that a monster would prioritize getting rid of Witchbolt which seems ridiculous to me. If a fighter is engaged in combat with a monster and that monster has Witchbolt on him, that fighter is probably threatening 10 damage on the monster as an AoO. If they have a 65% chance of hitting, well, they take an average of 6.5 damage anyways. This isn't including any sort of fighting style/feats the fighter may have.

From the monster's PoV, its strictly worse to move out of the way. Look at what they're trading: they take their movement and 6.5 damage against the fighter's reaction to avoid what would have been 6.5 damage on the caster's whole action. The only reason a DM would move the creature in this scenario is to spite the caster.

The caster, however, is free to use their action for something like firebolt, ray of frost, or even another higher level spell slot. This isn't a good trade for the monster and they're better off keeping the witchbolt until the situation changes somehow.

You can't move out of range either, making it easier for the monster's allies to break your concentration and perhaps more importantly leaving yourself in melee range of said allies even if you maintain it. You also have to spend your action every round to maintain the spell, which means it basically eats everything you can be doing in combat except your bonus action and reaction. In tier 1 you might not even have a bonus action and you'll probably be spending your reaction on Shield since you're only ever 30ft from the front line. So Y
Uou're standing there pinging an enemy for 1d12 a round and it's not transferable after the foe drops, so it's not worth it except on something with a lot of HP*. You have to give up every tactical decision in order to use this spell to its maximum effect and all the casters that know it are in some way limited on the spells they pick-up. It's too niche and restrictive to be picked.

*As you pointed out this spell is not suited for higher than tier 1.

[LudicSavant]

Witch Bolt was a difficult spell to balance anyways. There's no real guarantee that an enemy will just leave your range or threaten your concentration. Sure, they could, but its not like there's a mathematical formula to predict how often your character gets threatened or how likely your DM will have your enemies play 30ft ballerina.

The fact of the matter about the spell, however, is that if neither of those are forced, the spellcaster casted a 1st-level spell to have a better tier 1 cantrip. Having auto-hit and damage higher than firebolt is interesting and, if not for the other conditionals, would be a powerful tier 1 spell.

Witch Bolt isn't really an "auto-hit." Yes, you don't need to roll on rounds 2+, but that doesn't change the fact that the damage was still contingent upon an all-or-nothing attack roll landing, and this affects the math accordingly.

To understand how bad Witch Bolt is, you have to understand how the math for it works. Some people seem to labor under the assumption that it deals 6.5 expected DPR on rounds after the first. But that's not really how it works, because that 6.5 damage is dependent on an event that doesn't have 100% probability: Landing the initial bolt on round one. The DPR calculation is less like Magic Missile and more like an all-or-nothing single target Damage Over Time effect that requires you to invest actions for every tick (e.g. even worse than Immolation).

So the real DPR formula is:
Round 1: (hit% * 6.5) + (crit% * 6.5)
Round 2: ((chance Witch Bolt hit on round 1 and remained active into the current round) * 6.5) + ((DPR of whatever you'd use if Witch Bolt wasn't active anymore) * (chance Witch Bolt missed on round 1 or got interrupted))
Round 3+: As round 2, except the chance that Witch Bolt is interrupted typically rises each round.

The result is that Witch Bolt is quite unattractive for a first level spell slot even if a designer were to assume that the tether is rarely broken.