I honestly have never met someone who goes down the minutia of hit chance when considering average damage because hit chance changes from encounter to encounter, target to target.
Also... because of how probability works, an individual can occasionally see a disparity in the expected number of hits and the actual number of hits. Some people roll consistently bad. Each die roll has a 5% chance to result in a given number on the d20, but if you roll 100 d20's you very much can see deviations from the expected average value. When we are talking low levels, you only have a couple spell slots, you can EASILY roll five or less when looking at a sample size that small... does that mean that we should consider the average damage of Attack Roll spells as 0 because we never hit? This is why looking at the effect of the spell when it has an effect is more useful. Your same argument could be applied to 'save or suck spells' like hold person. Sure it paralyzes him, but you have a 50% chance of it not working, so why bother using it at all?
Sure, lets take your version for average damage. Magic Missile does 10.5 and Guiding Bolt does 7.35. A difference of 3.15 damage. Guiding Bolt still grants advantage to the next hit. That could be anything from a 1 damage Sorcerer Slap to a variant human Great Weapon Master to another cast of Guiding Bolt from another party member. In most cases that extra 3 points of damage will be paid forward as a direct result of your cast, as advantage boosts average damage as well using your to-hit basis.
And what about the Shield spell? Sure it will make Guiding Bolt much less likely to hit, but it completely negates the Magic Missile spell. I'm not saying that players always find themselves fighting casters, but rather that there is ALSO a situation that reduces Magic Missile's damage completely, while Guiding Bolt gets to see its average damage simply plummet... but not to zero. If we are going to look at the 'misses' of attack rolls we need to also consider the situations where Magic Missile 'misses'.
This is why I just look at the bald effect of a given ability instead of mathing out hit percentages -- there is ALWAYS going to be some situation that alters the equation, and not just in a niche sense as there are many DIFFERENT factors that can arise on regular basis. Things like cover, advantage/disadvantage, direct counters, unforeseen resistance or immunity... It is a level of granularity that is an interesting exercise but less than practical.
I've never had an enemy shield on me to ruin a magic missile.
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Any time an unfathomably powerful entity sweeps in and offers godlike rewards in return for just a few teensy favors, it’s a scam. Unless it’s me. I’d never lie to you, reader dearest.
Yep, I did misread the VoA bit. Considering an Order Cleric can cast Guiding Bolt, I assumed that was the case, my bad.
I think you are also making an assumption of my position, however. I do consider the ability to crit to be a big benefit, but I at no point meant to infer that the ability to crit alone was worth picking a spell for. My comment on critical hits was much more of the nature of "If a critical hit happens, it can give you a victory instead of a TPK". That isn't something that Magic Missile can do due to its static damage output. Even with max damage on a cast of magic missile, it won't reach the same single round output that an attack roll spell can achieve.
Crit fishing is also a player preference, so it is much more variable table-to-table. I have seen plenty of players go for it. I can understand if its not something you are used to, but Elven Accuracy is a feat -- and it applies to all spell attack rolls that have advantage. You very much can make a spell caster that is a crit-fisher, and in many cases it is one of the most effective version of crit fishers.
The average damage of attack rolls depends on the specific AC of the target, which is why I don't factor them in. You can just as easily be fighting a monster with very low ac but high HP as you could be fighting a monster with high AC and midling to low HP. It is a variable that effects damage per round on an encounter-to-encounter basis and thus shouldn't be used to determine averages. Some DM's particularly favor one sort of enemy over others. Some tables may only ever see creatures with 18+ ac, others might never see one with an AC over 16. It is a meaningless level of granularity that assumes too much.
Good for you? Considering magic missile prompts multiple concentration checks (so sayeth the jcrawford), it is something that most characters with access to the Shield spell should want to do. If your DM's aren't taking advantage of actions available to some creatures, then that is to your benefit, but your personal experience is anecdotal at best. Shield DOES negate Magic Missile.
Any time an unfathomably powerful entity sweeps in and offers godlike rewards in return for just a few teensy favors, it’s a scam. Unless it’s me. I’d never lie to you, reader dearest.
yes it does, but not nearly as often as bad rolls or high ACs negate guiding bolt.
EDIT: Shield can make guiding bolt miss too.
Yes it can make Guiding Bolt miss. But Guiding bolt has a chance to not miss even when shield is in effect (either by a high enough roll or by a crit). Magic missile is entirely negated. The point of bringing up shield was to rebut using to-hit in calculating average damage. I suggest you review the conversation i've been having with a couple others on this point, in this thread.
Oh I've reviewed it. I just think you're way off base. You're arguing very situational facts....situational to the point I find them to be mostly irrelevant. 9 rounds out of 10, magic missile is going to out perform guiding bolt.
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Any time an unfathomably powerful entity sweeps in and offers godlike rewards in return for just a few teensy favors, it’s a scam. Unless it’s me. I’d never lie to you, reader dearest.
I like to assume the best about people, but I guarantee you that your DM, if they are going to pop Shield at all, is going to do so after having seen your attack roll. You are not going to hit with Guiding Bolt against a Shield-ed opponent. :)
I do grant that getting into weighting the likely to-hit% on top of the average damage gets too mathy to generally be worth discussing. But that's because generally we're weighing two options that will be at least similarly impacted by to-hit... do I optimize my Hexblade for Eldritch Blast, or for using his Hex weapon? Either way, I have to hit AC, so if I disregard it from the equation, it's kind of balanced. But in the specific scenario of comparing an AC-targeting spell vs. an auto-hit spell, it is an important part of the conversation, and not one that can be glossed over.
I will concede that Guiding Bolt gets a worse rap than other spells like Chromatic Orb, probably because it's most often discussed in the context of being a Cleric spell. Right or wrong, most groups will give their Clerics side-eye when they spend rounds and precious spell slots doing attack spells instead of healing or support, since that isn't really their party role... and I think all of us have seen that side-eye evolve into open grumbling from the group or self-loathing from the Cleric when the spell misses (which anecdotally it always does!). It always sucks to miss and "waste" a spell slot, but it EXTRA sucks for a Cleric to spend a round missing and wasting a could-have-been-a-Cure Wounds slot during a boss battle!
This thread popped up in the context of a Sorcerer, and of all the caster classes, Sorcerers probably care the least about "wasting" a spell slot by missing because of their Font of Magic. So credit where it's due, while a Cleric usually has MUCH better uses for their round than attacking (and certainly better uses for their spell slot than missing!), a Sorcerer is supposed to be slinging attack spells and Guiding Bolt may be an attractive one to throw instead of Chromatic Orb or something for whatever reason (but Divine Souls get access to Cleric spells, so usually I see them getting played like weird alt-Clerics, not like Sorcerers at all).
So... yeah it's not all bad. I give Guiding Bolt a D- as a Cleric spell, but I suppose for a Divine Soul Sorcerer that doesn't have anything better to do than attack, it's probably on par with other options. Heck, Divine Souls have Favored by the Gods, so if anyone in the history of D&D is ever going to land a Guiding Bolt, I suppose the Divine Soul is going to be the one to do it!
I feel your pain. I had the opposite experience. My GB (twinned) hit most of the time and it was very exciting and much appreciated by my party members - especially the cleric who preferred to cast Inflict Wounds but for some reason the dice were never in her favor unless she had advantage. Everyone's experience is different. If my rolls for GB constantly missed, I would hate it. I have the same feelings when it comes to Chromatic Orb. I hate that spell because my rolls almost always missed. I'm convinced that spell is cursed :-)
Magic Missile is more damage on average, when one accounts for actually needing to land a hit. Other than that, sure.
That is not correct. In general, Guiding bolt does more damage than magic missile, if you include the advantage into your combat calculation. Consider for example a simple situation of 1 on 1 fight, where you hit 50% of the time and repeatedly choose only one spell. Note, 50% is fairly LOW chance to hit, usually your prof + spell stat => AC.
Given that situation, every round magic missile does: 3d4+3, which averages out to 10.5, every round.
Guiding bolt, does (if it hits) 4d6 in the first round, averaging out to 14. Times 1/2 (for missing half the time) PLUS another 14/20 (chance of a crit, which always hits) = 7.7 damage the first round, before including the advantage.
After the first round it gets advantage, so the formula becomes 14 * .75 (as it has advantage) + 14 /10 (rough chance of a crit now) = 11.9 damage on average each round after the first.
In a 1 on 1 situation Guiding Bolt vs Magic Missile, Guiding bolt does 2.8 less damage the first round, but does 1.4 more each successive round. 4th round or later it beats Magic Missile.
If you have a Rogue, it does more damage in the 2nd round of combat. You see, that is the silly situation where you are using Guiding Bolt for your own advantage. If you do it right, the Rogue takes the advantage, and gets the sneak attack on top of the increased chance to hit and the increased chance of a critical. Or not a Rogue - a Paladin that is SMITING but only when he crits.
Magic Missile does have certain other advantages. Mainly because the advantage of Force damage over Radiant, but no Monster Manual creature is immune to Radiant (6 published are immune), only 4 MM are resistant (9 other published are resistant) and 9 are vulnerable (2 from the MM). If you are not fighting Celesitals or Aeorians consistently, then Guiding Bolt is a FAR better spell than Magic Missile.
Everyone likes to talk about the ability to spread it out among multiple monsters, but that only helps when you are facing a horde of weaklings. I mean really, when do you know that only 3.5 damage or even 7 (two missiles) will be enough? The rest of the time you concentrate your fire to kill creatures.
Guiding Bolt is a statistical better spell than Magic Missile, unless you are an evil SOB attacking Celestials and Aeorians.
yes it does, but not nearly as often as bad rolls or high ACs negate guiding bolt.
EDIT: Shield can make guiding bolt miss too.
Yes it can make Guiding Bolt miss. But Guiding bolt has a chance to not miss even when shield is in effect (either by a high enough roll or by a crit). Magic missile is entirely negated. The point of bringing up shield was to rebut using to-hit in calculating average damage. I suggest you review the conversation i've been having with a couple others on this point, in this thread.
You have to use hit chance to calculate average damage. It's mostly impossible to get a truly accurate result there, because it's not feasible to figure out what the average AC for an enemy is (we could get the average AC of every monster in the Monster Manual, but that doesn't take into account the frequency at which each might appear), which is why we make assumptions like "probably a 50% hit chance," which is the assumption the balance of the game makes. Factors like Shield are deliberately excluded because they complicate things unnecessarily, and their actual impact on the numbers is tiny. "Just assume it hits" in a game where the possibility of failure is constant is just flat-out incorrect.
The reason hit chance doesn't usually come up in discussions of expected damage is that the things being compares almost invariably have the same hit chance (greatsword vs. greataxe, 2H vs. two-weapon fighting, etc.). The fact that, in this case, the hit rates are not the same, makes hit chance extremely important. If you ignore it, you will be misled.
yes it does, but not nearly as often as bad rolls or high ACs negate guiding bolt.
EDIT: Shield can make guiding bolt miss too.
Yes it can make Guiding Bolt miss. But Guiding bolt has a chance to not miss even when shield is in effect (either by a high enough roll or by a crit). Magic missile is entirely negated. The point of bringing up shield was to rebut using to-hit in calculating average damage. I suggest you review the conversation i've been having with a couple others on this point, in this thread.
You have to use hit chance to calculate average damage. It's mostly impossible to get a truly accurate result there, because it's not feasible to figure out what the average AC for an enemy is (we could get the average AC of every monster in the Monster Manual, but that doesn't take into account the frequency at which each might appear), which is why we make assumptions like "probably a 50% hit chance," which is the assumption the balance of the game makes. Factors like Shield are deliberately excluded because they complicate things unnecessarily, and their actual impact on the numbers is tiny. "Just assume it hits" in a game where the possibility of failure is constant is just flat-out incorrect.
The reason hit chance doesn't usually come up in discussions of expected damage is that the things being compares almost invariably have the same hit chance (greatsword vs. greataxe, 2H vs. two-weapon fighting, etc.). The fact that, in this case, the hit rates are not the same, makes hit chance extremely important. If you ignore it, you will be misled.
You do have to use hit chance, but only having a 50% chance seems small. At first level, you probably have a +5 to hit, and I doubt most enemies have 15 AC.
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A fool pulls the leaves. A brute chops the trunk. A sage digs the roots.
I like to assume the best about people, but I guarantee you that your DM, if they are going to pop Shield at all, is going to do so after having seen your attack roll. You are not going to hit with Guiding Bolt against a Shield-ed opponent. :)
I do grant that getting into weighting the likely to-hit% on top of the average damage gets too mathy to generally be worth discussing. But that's because generally we're weighing two options that will be at least similarly impacted by to-hit... do I optimize my Hexblade for Eldritch Blast, or for using his Hex weapon? Either way, I have to hit AC, so if I disregard it from the equation, it's kind of balanced. But in the specific scenario of comparing an AC-targeting spell vs. an auto-hit spell, it is an important part of the conversation, and not one that can be glossed over.
I will concede that Guiding Bolt gets a worse rap than other spells like Chromatic Orb, probably because it's most often discussed in the context of being a Cleric spell. Right or wrong, most groups will give their Clerics side-eye when they spend rounds and precious spell slots doing attack spells instead of healing or support, since that isn't really their party role... and I think all of us have seen that side-eye evolve into open grumbling from the group or self-loathing from the Cleric when the spell misses (which anecdotally it always does!). It always sucks to miss and "waste" a spell slot, but it EXTRA sucks for a Cleric to spend a round missing and wasting a could-have-been-a-Cure Wounds slot during a boss battle!
This thread popped up in the context of a Sorcerer, and of all the caster classes, Sorcerers probably care the least about "wasting" a spell slot by missing because of their Font of Magic. So credit where it's due, while a Cleric usually has MUCH better uses for their round than attacking (and certainly better uses for their spell slot than missing!), a Sorcerer is supposed to be slinging attack spells and Guiding Bolt may be an attractive one to throw instead of Chromatic Orb or something for whatever reason (but Divine Souls get access to Cleric spells, so usually I see them getting played like weird alt-Clerics, not like Sorcerers at all).
So... yeah it's not all bad. I give Guiding Bolt a D- as a Cleric spell, but I suppose for a Divine Soul Sorcerer that doesn't have anything better to do than attack, it's probably on par with other options. Heck, Divine Souls have Favored by the Gods, so if anyone in the history of D&D is ever going to land a Guiding Bolt, I suppose the Divine Soul is going to be the one to do it!
Ah yes, because there is no chance that shield could have been popped earlier in the round and DMs never make a simple math mistake in the middle of battle. For a caster with Guiding bolt this essentially boils down to a target with 20ish ac now (compared to around 15, assuming mage armor) but the magic missile user is SOL.
I think the auto-hit nature of Magic Missile is an important benefit/factor in considering it, i just don't weigh probability into the effectiveness of spells beyond considering if a spell targets a bad attribute for the task at hand. I think most players who have multiple options will choose to NOT use an attack roll against a high AC target and will choose an appropriate saving throw based spell. It is just one more reason why using to-hit or saving throw percentages is less useful -- in a vacuum it matters, but a CHARACTER has multiple options and will choose the best of them for a given situation.
I also VEHEMENTLY disagree with the peculiar social stigma of clerics playing anything other than a healbot, but that is not the topic of this thread.
You seem to have missed why i included shield. It was because assuming that a player will choose to make a spell attack roll against a high ac target is directly analogous to assuming a player will choose to cast magic missile against a character with the shield spell. It is assuming the player will take a course of action with the least chance of success.
It was also pointing out that we are "just assuming it hits" for magic missile when there is a specific counter for it that is easy to access. I have never met an arcane caster my dm made (nor made an arcane caster npc) that DIDN'T have shield as a spell. I can understand that not every table has the same experiences, but in my experience casters generally are present post lvl5 unless the quest is specifically about monsterous beasts.
No spell is perfect for all situations. Magic Missile is capable of being a multi target spell, but it performs terribly in this capacity compared to specifically designed aoe spells. Reading the description allows us to compare the applications of different effects. We should compare what the spells themselves DO.
I like to assume the best about people, but I guarantee you that your DM, if they are going to pop Shield at all, is going to do so after having seen your attack roll. You are not going to hit with Guiding Bolt against a Shield-ed opponent. :)
I do grant that getting into weighting the likely to-hit% on top of the average damage gets too mathy to generally be worth discussing. But that's because generally we're weighing two options that will be at least similarly impacted by to-hit... do I optimize my Hexblade for Eldritch Blast, or for using his Hex weapon? Either way, I have to hit AC, so if I disregard it from the equation, it's kind of balanced. But in the specific scenario of comparing an AC-targeting spell vs. an auto-hit spell, it is an important part of the conversation, and not one that can be glossed over.
I will concede that Guiding Bolt gets a worse rap than other spells like Chromatic Orb, probably because it's most often discussed in the context of being a Cleric spell. Right or wrong, most groups will give their Clerics side-eye when they spend rounds and precious spell slots doing attack spells instead of healing or support, since that isn't really their party role... and I think all of us have seen that side-eye evolve into open grumbling from the group or self-loathing from the Cleric when the spell misses (which anecdotally it always does!). It always sucks to miss and "waste" a spell slot, but it EXTRA sucks for a Cleric to spend a round missing and wasting a could-have-been-a-Cure Wounds slot during a boss battle!
This thread popped up in the context of a Sorcerer, and of all the caster classes, Sorcerers probably care the least about "wasting" a spell slot by missing because of their Font of Magic. So credit where it's due, while a Cleric usually has MUCH better uses for their round than attacking (and certainly better uses for their spell slot than missing!), a Sorcerer is supposed to be slinging attack spells and Guiding Bolt may be an attractive one to throw instead of Chromatic Orb or something for whatever reason (but Divine Souls get access to Cleric spells, so usually I see them getting played like weird alt-Clerics, not like Sorcerers at all).
So... yeah it's not all bad. I give Guiding Bolt a D- as a Cleric spell, but I suppose for a Divine Soul Sorcerer that doesn't have anything better to do than attack, it's probably on par with other options. Heck, Divine Souls have Favored by the Gods, so if anyone in the history of D&D is ever going to land a Guiding Bolt, I suppose the Divine Soul is going to be the one to do it!
Ah yes, because there is no chance that shield could have been popped earlier in the round and DMs never make a simple math mistake in the middle of battle. For a caster with Guiding bolt this essentially boils down to a target with 20ish ac now (compared to around 15, assuming mage armor) but the magic missile user is SOL.
I think the auto-hit nature of Magic Missile is an important benefit/factor in considering it, i just don't weigh probability into the effectiveness of spells beyond considering if a spell targets a bad attribute for the task at hand. I think most players who have multiple options will choose to NOT use an attack roll against a high AC target and will choose an appropriate saving throw based spell. It is just one more reason why using to-hit or saving throw percentages is less useful -- in a vacuum it matters, but a CHARACTER has multiple options and will choose the best of them for a given situation.
I also VEHEMENTLY disagree with the peculiar social stigma of clerics playing anything other than a healbot, but that is not the topic of this thread.
Yeah, I'm not too sure what Chicken_Champ is talking about. First, he doesn't seem to know that Shield ALWAYS is activated after the attack roll is seen. Secondly, healing in general is pretty trash in 5e, and is absolutely not what any Cleric besides a Life Cleric should be specializing it. I'd recommend having 1 healing spell just to get an unconcious ally off the ground, but doing that every round is really not good in 5e. Thirdly, Guiding Bolt is widely thought to be one of the best 1st-level Cleric spells, and one of the better 1st-level spells in general. Also, he seems to be implying that Sorcerers care less about their spell slots, which makes absolutely no sense.
Now, I disagree with Barathol_Creed in that considering chances of success is one of the first things you should be looking at when determining effectiveness. For example, if you just assume everything will succeed, then why don't you spend every dollar you have on lottery tickets? If you win, you'll get more bang for your buck than with anything else. This is the exact same principle, but on a smaller scale. Would you take a 10% chance to win $5, or an 80% chance to win $1? You're saying that since 5 is more than 1, you'd go for that bet. However, if you actually look at it, the $1 bet is more profitable. Also, it's actually really easy to calculate damage with chance of success in mind. Also, you say that we have multiple options, but we don't have all the options in the world; that's why we're considering taking one or the other. For a 1st-level damage spell, the character in question will only have one, and we are determining which one. Frankly, the "multiple options" would be either whatever we pick with this, a Cantrip or a Light Crossbow. This is a Sorcerer character; one of their main weaknesses is the LACK of having a lot of spell options on their sheet.
On the other hand, Barathol_Creed is totally right about Clerics. Maybe a Life Cleric would try to be a "healbot," but for any other subclass, that's pretty much the least effective role they could pick. Healing Word is pretty decent because of its range and casting time, but the other healing spells all suck until you get to Heal and Mass Heal (which are both actually amazing). Frankly, your "healer" should be the shopkeeper who sells you the potions. Clerics have great offensive spells, like Spirit Guardians (absolutely amazing), Spiritual Weapon (simply fantastic), and Bless, all at low levels. These are what the Cleric should be casting, not a Cure Wounds on the Fighter who took 4 damage.
Magic Missile is more damage on average, when one accounts for actually needing to land a hit. Other than that, sure.
That is not correct. In general, Guiding bolt does more damage than magic missile, if you include the advantage into your combat calculation. Consider for example a simple situation of 1 on 1 fight, where you hit 50% of the time and repeatedly choose only one spell. Note, 50% is fairly LOW chance to hit, usually your prof + spell stat => AC.
Given that situation, every round magic missile does: 3d4+3, which averages out to 10.5, every round.
Guiding bolt, does (if it hits) 4d6 in the first round, averaging out to 14. Times 1/2 (for missing half the time) PLUS another 14/20 (chance of a crit, which always hits) = 7.7 damage the first round, before including the advantage.
After the first round it gets advantage, so the formula becomes 14 * .75 (as it has advantage) + 14 /10 (rough chance of a crit now) = 11.9 damage on average each round after the first.
In a 1 on 1 situation Guiding Bolt vs Magic Missile, Guiding bolt does 2.8 less damage the first round, but does 1.4 more each successive round. 4th round or later it beats Magic Missile.
If you have a Rogue, it does more damage in the 2nd round of combat. You see, that is the silly situation where you are using Guiding Bolt for your own advantage. If you do it right, the Rogue takes the advantage, and gets the sneak attack on top of the increased chance to hit and the increased chance of a critical. Or not a Rogue - a Paladin that is SMITING but only when he crits.
Magic Missile does have certain other advantages. Mainly because the advantage of Force damage over Radiant, but no Monster Manual creature is immune to Radiant (6 published are immune), only 4 MM are resistant (9 other published are resistant) and 9 are vulnerable (2 from the MM). If you are not fighting Celesitals or Aeorians consistently, then Guiding Bolt is a FAR better spell than Magic Missile.
Everyone likes to talk about the ability to spread it out among multiple monsters, but that only helps when you are facing a horde of weaklings. I mean really, when do you know that only 3.5 damage or even 7 (two missiles) will be enough? The rest of the time you concentrate your fire to kill creatures.
Guiding Bolt is a statistical better spell than Magic Missile, unless you are an evil SOB attacking Celestials and Aeorians.
Again, I'm bad at math, so I fully concede I could be doing this wrong. It would be easier to compare if we could agree on a target to measure against.... so let's just assume 2nd level characters (attack stat is +3, Prof is +2, 3 slots to burn) against an AC 16 target? That gives the Guiding Bolt user a 50% base chance to hit like you say.
Using all three spell slots, the Magic Missile user will do no less than 6 damage per round, nor any more than 15 damage per round (10.5 avg), but will do it each round. So no less than 18 total, no more than 45 total, avg. 31.5.
In the first round, the Guiding Bolt user will have a 50% chance of doing 0 damage, a 45% chance of doing 4-24 damage (14 avg), and a 5% chance of doing 8-48 damage crit (28 avg crit). Together, that's an average of (14*.45)+(28*.05)=7.7 in the first round, 2.8 less than the MM user.
In second round, the GB user has a 50% of having advantage, or a 50% of repeating the round 1 scenario. This is where my math will likely fail me, as I struggle to calculate hit chances based on keeping the better of two rolls, so forgive me for googling a table and trusting that. In the advantage timeline, to hit our target roll of 11 with advantage, we've gone up from a 50% chance to a 75% chance, 9.75% of which is hitting 20 (lets call it 10% to save hassle). That gives us a 25% of 0 damage, a 65% of 4-24 damage (14 avg), and a 10% chance of 8-48 damage crit (28 avg crit). Together, that's an average of (14*.65)+(28*.1)=10.5. But recall, we only had a 50% of living in this timeline vs. missing in round 1 and repeating the 7.7 calculation above, so really our Round 2 average damage is (7.7+10.5)/2=9.1 in round 2?
I'd love to say that round 3 is just round 2 again... but I guess we would have to fork missing on Round 2 (50% if you never had advantage +25% if you had advantage)/2=37.5% leading to a 50% hit rate no-advantage calculation in Round 3, vs. a 62.5% chance of being in a Round 2 with a 75% hit rate calculation. Ughhh... am I messing up yet? We know that our average damage on 50/50 rounds is 7.7, and it looks like we do 10.5 on 25/75 rounds, so (7.7*.375)+(10.5*.625)=9.45 avg damage in round 3?
So all together, the MM user did 10.5 avg damage per round, totaling 31.5 avg damage over 3 rounds.
The GB user did as little as 0 damage per round (indeed, there's a... 7% chance that we did?), but avg of (7.7+9.1+9.45)/3=8.75 avg damage per round, totaling 26.25 damage over 3 rounds. Or I suppose they could have done as much as 144 damage with three crits (.01% chance of that, plus another staggeringly low chance that they rolled nothing but 6's across 32 d6?).
I have very little confidence in my math above... but unless someone can do it better, it looks to me like a caster's average damage is higher both round-to-round and over 3 rounds casting Magic Missile than they are Guiding Bolt.
Magic Missile is more damage on average, when one accounts for actually needing to land a hit. Other than that, sure.
That is not correct. In general, Guiding bolt does more damage than magic missile, if you include the advantage into your combat calculation. Consider for example a simple situation of 1 on 1 fight, where you hit 50% of the time and repeatedly choose only one spell. Note, 50% is fairly LOW chance to hit, usually your prof + spell stat => AC.
Given that situation, every round magic missile does: 3d4+3, which averages out to 10.5, every round.
Guiding bolt, does (if it hits) 4d6 in the first round, averaging out to 14. Times 1/2 (for missing half the time) PLUS another 14/20 (chance of a crit, which always hits) = 7.7 damage the first round, before including the advantage.
After the first round it gets advantage, so the formula becomes 14 * .75 (as it has advantage) + 14 /10 (rough chance of a crit now) = 11.9 damage on average each round after the first.
In a 1 on 1 situation Guiding Bolt vs Magic Missile, Guiding bolt does 2.8 less damage the first round, but does 1.4 more each successive round. 4th round or later it beats Magic Missile.
If you have a Rogue, it does more damage in the 2nd round of combat. You see, that is the silly situation where you are using Guiding Bolt for your own advantage. If you do it right, the Rogue takes the advantage, and gets the sneak attack on top of the increased chance to hit and the increased chance of a critical. Or not a Rogue - a Paladin that is SMITING but only when he crits.
Magic Missile does have certain other advantages. Mainly because the advantage of Force damage over Radiant, but no Monster Manual creature is immune to Radiant (6 published are immune), only 4 MM are resistant (9 other published are resistant) and 9 are vulnerable (2 from the MM). If you are not fighting Celesitals or Aeorians consistently, then Guiding Bolt is a FAR better spell than Magic Missile.
Everyone likes to talk about the ability to spread it out among multiple monsters, but that only helps when you are facing a horde of weaklings. I mean really, when do you know that only 3.5 damage or even 7 (two missiles) will be enough? The rest of the time you concentrate your fire to kill creatures.
Guiding Bolt is a statistical better spell than Magic Missile, unless you are an evil SOB attacking Celestials and Aeorians.
Again, I'm bad at math, so I fully concede I could be doing this wrong. It would be easier to compare if we could agree on a target to measure against.... so let's just assume 2nd level characters (attack stat is +3, Prof is +2, 3 slots to burn) against an AC 16 target? That gives the Guiding Bolt user a 50% base chance to hit like you say.
Using all three spell slots, the Magic Missile user will do no less than 6 damage per round, nor any more than 15 damage per round (10.5 avg), but will do it each round. So no less than 18 total, no more than 45 total, avg. 31.5.
In the first round, the Guiding Bolt user will have a 50% chance of doing 0 damage, a 45% chance of doing 4-24 damage (14 avg), and a 5% chance of doing 8-48 damage crit (28 avg crit). Together, that's an average of (14*.45)+(28*.05)=7.7 in the first round, 2.8 less than the MM user.
In second round, the GB user has a 50% of having advantage, or a 50% of repeating the round 1 scenario. This is where my math will likely fail me, as I struggle to calculate hit chances based on keeping the better of two rolls, so forgive me for googling a table and trusting that. In the advantage timeline, to hit our target roll of 11 with advantage, we've gone up from a 50% chance to a 75% chance, 9.75% of which is hitting 20 (lets call it 10% to save hassle). That gives us a 25% of 0 damage, a 65% of 4-24 damage (14 avg), and a 10% chance of 8-48 damage crit (28 avg crit). Together, that's an average of (14*.65)+(28*.1)=10.5. But recall, we only had a 50% of living in this timeline vs. missing in round 1 and repeating the 7.7 calculation above, so really our Round 2 average damage is (7.7+10.5)/2=9.1 in round 2?
I'd love to say that round 3 is just round 2 again... but I guess we would have to fork missing on Round 2 (50% if you never had advantage +25% if you had advantage)/2=37.5% leading to a 50% hit rate no-advantage calculation in Round 3, vs. a 62.5% chance of being in a Round 2 with a 75% hit rate calculation. Ughhh... am I messing up yet? We know that our average damage on 50/50 rounds is 7.7, and it looks like we do 10.5 on 25/75 rounds, so (7.7*.375)+(10.5*.625)=9.45 avg damage in round 3?
So all together, the MM user did 10.5 avg damage per round, totaling 31.5 avg damage over 3 rounds.
The GB user did as little as 0 damage per round (indeed, there's a... 7% chance that we did?), but avg of (7.7+9.1+9.45)/3=8.75 avg damage per round, totaling 26.25 damage over 3 rounds. Or I suppose they could have done as much as 144 damage with three crits (.01% chance of that, plus another staggeringly low chance that they rolled nothing but 6's across 32 d6?).
I have very little confidence in my math above... but unless someone can do it better, it looks to me like a caster's average damage is higher both round-to-round and over 3 rounds casting Magic Missile than they are Guiding Bolt.
Actually, I'm fairly certain that most people use AC 13 (35% chance to miss, 60% to hit, 5% to critical) as the average target AC against enemies at 1st-level (by averaging CR 1 monsters' AC from the Monster Manual or something like that), but regardless, you are correct that Magic Missile will do more *damage* on average than Guiding Bolt, although it's not quite as large a gap as what you said.
The main (correct) reason that Guiding Bolt would be considered preferable would be that it has a pretty nice secondary effect, while Magic Missile has none. 65% of the time, you will hit (or crit) with Guiding Bolt, and if you do, then you get a nice effect along with your damage.
It's sort of like comparing Firebolt and Ray of Frost; Firebolt does 1 extra damage on average if you hit, while Ray of Frost gets a semi-decent effect if you hit. I prefer Ray of Frost because frankly the damage is pretty pitiful either way.
Magic Missile will net you a little more damage on average, Guiding Bolt will get you a nice effect if you hit. This is what you would compare between them.
It's sort of like comparing Firebolt and Ray of Frost; Firebolt does 1 extra damage on average if you hit, while Ray of Frost gets a semi-decent effect if you hit. I prefer Ray of Frost because frankly the damage is pretty pitiful either way.
Magic Missile will net you a little more damage on average, Guiding Bolt will get you a nice effect if you hit. This is what you would compare between them.
I personally think that the benefit of Magic Missile is not the slightly greater damage, it is the ability to dependably deal damage. Guiding Bolt can miss, but is much better when it hits. Higher risk, higher reward.
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Yeah, I'm not too sure what Chicken_Champ is talking about. First, he doesn't seem to know that Shield ALWAYS is activated after the attack roll is seen. Secondly, healing in general is pretty trash in 5e, and is absolutely not what any Cleric besides a Life Cleric should be specializing it. I'd recommend having 1 healing spell just to get an unconcious ally off the ground, but doing that every round is really not good in 5e. Thirdly, Guiding Bolt is widely thought to be one of the best 1st-level Cleric spells, and one of the better 1st-level spells in general. Also, he seems to be implying that Sorcerers care less about their spell slots, which makes absolutely no sense.
Yeah, I was working off of memory and had kind of merged Shield with the wording of Lucky where "You can choose to spend one of your luck points after you roll the die, but before the outcome is determined." Around the table, when the DM attacks me and I choose to cast Shield, they usually ask me to make that call without knowing what they rolled behind the screen... I'd kind of just assumed that DM should do the same for players, but the text of the spell doesn't really require that, you're right.
Sorcerers care less about spell slots compared to other casters, because Sorcerers have a greater flexibility to recover spell slots than other casters. That's all I meant by that.
Healing is trash compared to damage from a math perspective (better to mitigate damage by dropping targets than to mitigate damage by healing). But 1) that true-ism sort of relies on assuming a multi-enemy encounter, where the parties' damage is lowering the enemy teams DPR, while GB usually gets trotted out in single-enemy boss battles where the team's damage isn't reducing the enemy's, and 2) it overlooks that whether it's efficeient or not, healing is needed, especially at low levels. The "tank" may have 20ish hit points at low levels while the squishy characters only have 10ish, but that doesn't mean that they aren't going to go down fast from a lucky hit or two, or that the enemy isn't going to eat an attack of opportunity from them to rush past and chomp the cannon. Whether it's efficient or not, in that situation the character that can heal others needs to heal the unconscious or low-hp target, not take a chance on a GB, no matter the fact that on paper damage is theoretically "better." And the cleric is likely the only character that has that capacity, regardless of how awesome their other options for that spell slot might be.
As for "widely thought"... well, as we've seen, depends on which crowd you ask. I've never heard much praise for it, either on the forums or in person.
For what I think is the third time: target an appropriate stat. I have repeatedly said to use a saving throw based spell against a high ac target, and to use an attack roll against targets that resist your spell saves. The reason i disregard accuracy for average damage is because I'm not going to use a spell or ability that has a low chance of working. A character has multiple options, it is common sense to use the best tool for the job.
EDIT: strike this. Apparently I read too quickly. Though you still probably have a saving throw based cantrip at low levels.
Like I was trying to say, you don't have an infinitude of options in combat; Sorcerers get 1 spell per level of Sorc. Also, as I said before, Magic Missile does more assuming 13 AC. THIRTEEN IS NOT "HIGH AC." Also, most of the time, a spell attack roll has a slightly HIGHER chance of hitting than most enemies failing a save, so even if they have the oh-so-high 13 AC, you still probably have a better chance hitting them than of them failing their save.
Quite frankly, with a level-1 Divine Soul Sorcerer, our damage options in combat will pretty much be:
Our choice (made in advance) of Firebolt or Ray of Frost -- Attack Roll
Toll the Dead -- WIS Save
Our choice (made in advance) of Guiding Bolt or Magic Missile which we are debating here -- Attack Roll or guaranteed
Light Crossbow -- Attack Roll
Unarmed Strike -- probably 0 damage, unless we boosted STR for some reason
As you can see, WE DON'T HAVE ANY SAVING THROW SPELLS FOR DAMAGE EXCEPT TOLL THE DEAD. What if they have WIS save proficiency? What if 1d12 (assuming they've already taken some damage) isn't enough damage? What if they're a Paladin, with 20 AC and +5 as their lowest save? Your strategy of "use a saving throw based spell against a high ac target, and to use an attack roll against targets that resist your spell saves" DOES NOT WORK on a fundamental level. Your plan has a GAPING FLAW right at the center of it. We don't get to stroll up to combat with 6 spells prepared (that would be a pitiful amount, but it is THREE TIMES what we actually do get). Even if we were at a higher level, we STILL wouldn't have enough options, due to the low number of spells known a Sorc gets. You have to go for as much mileage as you can get on each and every one, which is why we need to compare the pros and cons of each, including chances of success.
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I've never had an enemy shield on me to ruin a magic missile.
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Yep, I did misread the VoA bit. Considering an Order Cleric can cast Guiding Bolt, I assumed that was the case, my bad.
I think you are also making an assumption of my position, however. I do consider the ability to crit to be a big benefit, but I at no point meant to infer that the ability to crit alone was worth picking a spell for. My comment on critical hits was much more of the nature of "If a critical hit happens, it can give you a victory instead of a TPK". That isn't something that Magic Missile can do due to its static damage output. Even with max damage on a cast of magic missile, it won't reach the same single round output that an attack roll spell can achieve.
Crit fishing is also a player preference, so it is much more variable table-to-table. I have seen plenty of players go for it. I can understand if its not something you are used to, but Elven Accuracy is a feat -- and it applies to all spell attack rolls that have advantage. You very much can make a spell caster that is a crit-fisher, and in many cases it is one of the most effective version of crit fishers.
The average damage of attack rolls depends on the specific AC of the target, which is why I don't factor them in. You can just as easily be fighting a monster with very low ac but high HP as you could be fighting a monster with high AC and midling to low HP. It is a variable that effects damage per round on an encounter-to-encounter basis and thus shouldn't be used to determine averages. Some DM's particularly favor one sort of enemy over others. Some tables may only ever see creatures with 18+ ac, others might never see one with an AC over 16. It is a meaningless level of granularity that assumes too much.
Good for you? Considering magic missile prompts multiple concentration checks (so sayeth the jcrawford), it is something that most characters with access to the Shield spell should want to do. If your DM's aren't taking advantage of actions available to some creatures, then that is to your benefit, but your personal experience is anecdotal at best. Shield DOES negate Magic Missile.
yes it does, but not nearly as often as bad rolls or high ACs negate guiding bolt.
EDIT: Shield can make guiding bolt miss too.
Any time an unfathomably powerful entity sweeps in and offers godlike rewards in return for just a few teensy favors, it’s a scam. Unless it’s me. I’d never lie to you, reader dearest.
Tasha
Yes it can make Guiding Bolt miss. But Guiding bolt has a chance to not miss even when shield is in effect (either by a high enough roll or by a crit). Magic missile is entirely negated. The point of bringing up shield was to rebut using to-hit in calculating average damage. I suggest you review the conversation i've been having with a couple others on this point, in this thread.
Oh I've reviewed it. I just think you're way off base. You're arguing very situational facts....situational to the point I find them to be mostly irrelevant. 9 rounds out of 10, magic missile is going to out perform guiding bolt.
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Tasha
I like to assume the best about people, but I guarantee you that your DM, if they are going to pop Shield at all, is going to do so after having seen your attack roll. You are not going to hit with Guiding Bolt against a Shield-ed opponent. :)
I do grant that getting into weighting the likely to-hit% on top of the average damage gets too mathy to generally be worth discussing. But that's because generally we're weighing two options that will be at least similarly impacted by to-hit... do I optimize my Hexblade for Eldritch Blast, or for using his Hex weapon? Either way, I have to hit AC, so if I disregard it from the equation, it's kind of balanced. But in the specific scenario of comparing an AC-targeting spell vs. an auto-hit spell, it is an important part of the conversation, and not one that can be glossed over.
I will concede that Guiding Bolt gets a worse rap than other spells like Chromatic Orb, probably because it's most often discussed in the context of being a Cleric spell. Right or wrong, most groups will give their Clerics side-eye when they spend rounds and precious spell slots doing attack spells instead of healing or support, since that isn't really their party role... and I think all of us have seen that side-eye evolve into open grumbling from the group or self-loathing from the Cleric when the spell misses (which anecdotally it always does!). It always sucks to miss and "waste" a spell slot, but it EXTRA sucks for a Cleric to spend a round missing and wasting a could-have-been-a-Cure Wounds slot during a boss battle!
This thread popped up in the context of a Sorcerer, and of all the caster classes, Sorcerers probably care the least about "wasting" a spell slot by missing because of their Font of Magic. So credit where it's due, while a Cleric usually has MUCH better uses for their round than attacking (and certainly better uses for their spell slot than missing!), a Sorcerer is supposed to be slinging attack spells and Guiding Bolt may be an attractive one to throw instead of Chromatic Orb or something for whatever reason (but Divine Souls get access to Cleric spells, so usually I see them getting played like weird alt-Clerics, not like Sorcerers at all).
So... yeah it's not all bad. I give Guiding Bolt a D- as a Cleric spell, but I suppose for a Divine Soul Sorcerer that doesn't have anything better to do than attack, it's probably on par with other options. Heck, Divine Souls have Favored by the Gods, so if anyone in the history of D&D is ever going to land a Guiding Bolt, I suppose the Divine Soul is going to be the one to do it!
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I feel your pain. I had the opposite experience. My GB (twinned) hit most of the time and it was very exciting and much appreciated by my party members - especially the cleric who preferred to cast Inflict Wounds but for some reason the dice were never in her favor unless she had advantage. Everyone's experience is different. If my rolls for GB constantly missed, I would hate it. I have the same feelings when it comes to Chromatic Orb. I hate that spell because my rolls almost always missed. I'm convinced that spell is cursed :-)
That is not correct. In general, Guiding bolt does more damage than magic missile, if you include the advantage into your combat calculation. Consider for example a simple situation of 1 on 1 fight, where you hit 50% of the time and repeatedly choose only one spell. Note, 50% is fairly LOW chance to hit, usually your prof + spell stat => AC.
Given that situation, every round magic missile does: 3d4+3, which averages out to 10.5, every round.
Guiding bolt, does (if it hits) 4d6 in the first round, averaging out to 14. Times 1/2 (for missing half the time) PLUS another 14/20 (chance of a crit, which always hits) = 7.7 damage the first round, before including the advantage.
After the first round it gets advantage, so the formula becomes 14 * .75 (as it has advantage) + 14 /10 (rough chance of a crit now) = 11.9 damage on average each round after the first.
In a 1 on 1 situation Guiding Bolt vs Magic Missile, Guiding bolt does 2.8 less damage the first round, but does 1.4 more each successive round. 4th round or later it beats Magic Missile.
If you have a Rogue, it does more damage in the 2nd round of combat. You see, that is the silly situation where you are using Guiding Bolt for your own advantage. If you do it right, the Rogue takes the advantage, and gets the sneak attack on top of the increased chance to hit and the increased chance of a critical. Or not a Rogue - a Paladin that is SMITING but only when he crits.
Magic Missile does have certain other advantages. Mainly because the advantage of Force damage over Radiant, but no Monster Manual creature is immune to Radiant (6 published are immune), only 4 MM are resistant (9 other published are resistant) and 9 are vulnerable (2 from the MM). If you are not fighting Celesitals or Aeorians consistently, then Guiding Bolt is a FAR better spell than Magic Missile.
Everyone likes to talk about the ability to spread it out among multiple monsters, but that only helps when you are facing a horde of weaklings. I mean really, when do you know that only 3.5 damage or even 7 (two missiles) will be enough? The rest of the time you concentrate your fire to kill creatures.
Guiding Bolt is a statistical better spell than Magic Missile, unless you are an evil SOB attacking Celestials and Aeorians.
You have to use hit chance to calculate average damage. It's mostly impossible to get a truly accurate result there, because it's not feasible to figure out what the average AC for an enemy is (we could get the average AC of every monster in the Monster Manual, but that doesn't take into account the frequency at which each might appear), which is why we make assumptions like "probably a 50% hit chance," which is the assumption the balance of the game makes. Factors like Shield are deliberately excluded because they complicate things unnecessarily, and their actual impact on the numbers is tiny. "Just assume it hits" in a game where the possibility of failure is constant is just flat-out incorrect.
The reason hit chance doesn't usually come up in discussions of expected damage is that the things being compares almost invariably have the same hit chance (greatsword vs. greataxe, 2H vs. two-weapon fighting, etc.). The fact that, in this case, the hit rates are not the same, makes hit chance extremely important. If you ignore it, you will be misled.
You do have to use hit chance, but only having a 50% chance seems small. At first level, you probably have a +5 to hit, and I doubt most enemies have 15 AC.
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Ah yes, because there is no chance that shield could have been popped earlier in the round and DMs never make a simple math mistake in the middle of battle. For a caster with Guiding bolt this essentially boils down to a target with 20ish ac now (compared to around 15, assuming mage armor) but the magic missile user is SOL.
I think the auto-hit nature of Magic Missile is an important benefit/factor in considering it, i just don't weigh probability into the effectiveness of spells beyond considering if a spell targets a bad attribute for the task at hand. I think most players who have multiple options will choose to NOT use an attack roll against a high AC target and will choose an appropriate saving throw based spell. It is just one more reason why using to-hit or saving throw percentages is less useful -- in a vacuum it matters, but a CHARACTER has multiple options and will choose the best of them for a given situation.
I also VEHEMENTLY disagree with the peculiar social stigma of clerics playing anything other than a healbot, but that is not the topic of this thread.
You seem to have missed why i included shield. It was because assuming that a player will choose to make a spell attack roll against a high ac target is directly analogous to assuming a player will choose to cast magic missile against a character with the shield spell. It is assuming the player will take a course of action with the least chance of success.
It was also pointing out that we are "just assuming it hits" for magic missile when there is a specific counter for it that is easy to access. I have never met an arcane caster my dm made (nor made an arcane caster npc) that DIDN'T have shield as a spell. I can understand that not every table has the same experiences, but in my experience casters generally are present post lvl5 unless the quest is specifically about monsterous beasts.
No spell is perfect for all situations. Magic Missile is capable of being a multi target spell, but it performs terribly in this capacity compared to specifically designed aoe spells. Reading the description allows us to compare the applications of different effects. We should compare what the spells themselves DO.
Yeah, I'm not too sure what Chicken_Champ is talking about. First, he doesn't seem to know that Shield ALWAYS is activated after the attack roll is seen. Secondly, healing in general is pretty trash in 5e, and is absolutely not what any Cleric besides a Life Cleric should be specializing it. I'd recommend having 1 healing spell just to get an unconcious ally off the ground, but doing that every round is really not good in 5e. Thirdly, Guiding Bolt is widely thought to be one of the best 1st-level Cleric spells, and one of the better 1st-level spells in general. Also, he seems to be implying that Sorcerers care less about their spell slots, which makes absolutely no sense.
Now, I disagree with Barathol_Creed in that considering chances of success is one of the first things you should be looking at when determining effectiveness. For example, if you just assume everything will succeed, then why don't you spend every dollar you have on lottery tickets? If you win, you'll get more bang for your buck than with anything else. This is the exact same principle, but on a smaller scale. Would you take a 10% chance to win $5, or an 80% chance to win $1? You're saying that since 5 is more than 1, you'd go for that bet. However, if you actually look at it, the $1 bet is more profitable. Also, it's actually really easy to calculate damage with chance of success in mind. Also, you say that we have multiple options, but we don't have all the options in the world; that's why we're considering taking one or the other. For a 1st-level damage spell, the character in question will only have one, and we are determining which one. Frankly, the "multiple options" would be either whatever we pick with this, a Cantrip or a Light Crossbow. This is a Sorcerer character; one of their main weaknesses is the LACK of having a lot of spell options on their sheet.
On the other hand, Barathol_Creed is totally right about Clerics. Maybe a Life Cleric would try to be a "healbot," but for any other subclass, that's pretty much the least effective role they could pick. Healing Word is pretty decent because of its range and casting time, but the other healing spells all suck until you get to Heal and Mass Heal (which are both actually amazing). Frankly, your "healer" should be the shopkeeper who sells you the potions. Clerics have great offensive spells, like Spirit Guardians (absolutely amazing), Spiritual Weapon (simply fantastic), and Bless, all at low levels. These are what the Cleric should be casting, not a Cure Wounds on the Fighter who took 4 damage.
Again, I'm bad at math, so I fully concede I could be doing this wrong. It would be easier to compare if we could agree on a target to measure against.... so let's just assume 2nd level characters (attack stat is +3, Prof is +2, 3 slots to burn) against an AC 16 target? That gives the Guiding Bolt user a 50% base chance to hit like you say.
Using all three spell slots, the Magic Missile user will do no less than 6 damage per round, nor any more than 15 damage per round (10.5 avg), but will do it each round. So no less than 18 total, no more than 45 total, avg. 31.5.
In the first round, the Guiding Bolt user will have a 50% chance of doing 0 damage, a 45% chance of doing 4-24 damage (14 avg), and a 5% chance of doing 8-48 damage crit (28 avg crit). Together, that's an average of (14*.45)+(28*.05)=7.7 in the first round, 2.8 less than the MM user.
In second round, the GB user has a 50% of having advantage, or a 50% of repeating the round 1 scenario. This is where my math will likely fail me, as I struggle to calculate hit chances based on keeping the better of two rolls, so forgive me for googling a table and trusting that. In the advantage timeline, to hit our target roll of 11 with advantage, we've gone up from a 50% chance to a 75% chance, 9.75% of which is hitting 20 (lets call it 10% to save hassle). That gives us a 25% of 0 damage, a 65% of 4-24 damage (14 avg), and a 10% chance of 8-48 damage crit (28 avg crit). Together, that's an average of (14*.65)+(28*.1)=10.5. But recall, we only had a 50% of living in this timeline vs. missing in round 1 and repeating the 7.7 calculation above, so really our Round 2 average damage is (7.7+10.5)/2=9.1 in round 2?
I'd love to say that round 3 is just round 2 again... but I guess we would have to fork missing on Round 2 (50% if you never had advantage +25% if you had advantage)/2=37.5% leading to a 50% hit rate no-advantage calculation in Round 3, vs. a 62.5% chance of being in a Round 2 with a 75% hit rate calculation. Ughhh... am I messing up yet? We know that our average damage on 50/50 rounds is 7.7, and it looks like we do 10.5 on 25/75 rounds, so (7.7*.375)+(10.5*.625)=9.45 avg damage in round 3?
So all together, the MM user did 10.5 avg damage per round, totaling 31.5 avg damage over 3 rounds.
The GB user did as little as 0 damage per round (indeed, there's a... 7% chance that we did?), but avg of (7.7+9.1+9.45)/3=8.75 avg damage per round, totaling 26.25 damage over 3 rounds. Or I suppose they could have done as much as 144 damage with three crits (.01% chance of that, plus another staggeringly low chance that they rolled nothing but 6's across 32 d6?).
I have very little confidence in my math above... but unless someone can do it better, it looks to me like a caster's average damage is higher both round-to-round and over 3 rounds casting Magic Missile than they are Guiding Bolt.
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Actually, I'm fairly certain that most people use AC 13 (35% chance to miss, 60% to hit, 5% to critical) as the average target AC against enemies at 1st-level (by averaging CR 1 monsters' AC from the Monster Manual or something like that), but regardless, you are correct that Magic Missile will do more *damage* on average than Guiding Bolt, although it's not quite as large a gap as what you said.
The main (correct) reason that Guiding Bolt would be considered preferable would be that it has a pretty nice secondary effect, while Magic Missile has none. 65% of the time, you will hit (or crit) with Guiding Bolt, and if you do, then you get a nice effect along with your damage.
It's sort of like comparing Firebolt and Ray of Frost; Firebolt does 1 extra damage on average if you hit, while Ray of Frost gets a semi-decent effect if you hit. I prefer Ray of Frost because frankly the damage is pretty pitiful either way.
Magic Missile will net you a little more damage on average, Guiding Bolt will get you a nice effect if you hit. This is what you would compare between them.
I personally think that the benefit of Magic Missile is not the slightly greater damage, it is the ability to dependably deal damage. Guiding Bolt can miss, but is much better when it hits. Higher risk, higher reward.
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Yeah, I was working off of memory and had kind of merged Shield with the wording of Lucky where "You can choose to spend one of your luck points after you roll the die, but before the outcome is determined." Around the table, when the DM attacks me and I choose to cast Shield, they usually ask me to make that call without knowing what they rolled behind the screen... I'd kind of just assumed that DM should do the same for players, but the text of the spell doesn't really require that, you're right.
Sorcerers care less about spell slots compared to other casters, because Sorcerers have a greater flexibility to recover spell slots than other casters. That's all I meant by that.
Healing is trash compared to damage from a math perspective (better to mitigate damage by dropping targets than to mitigate damage by healing). But 1) that true-ism sort of relies on assuming a multi-enemy encounter, where the parties' damage is lowering the enemy teams DPR, while GB usually gets trotted out in single-enemy boss battles where the team's damage isn't reducing the enemy's, and 2) it overlooks that whether it's efficeient or not, healing is needed, especially at low levels. The "tank" may have 20ish hit points at low levels while the squishy characters only have 10ish, but that doesn't mean that they aren't going to go down fast from a lucky hit or two, or that the enemy isn't going to eat an attack of opportunity from them to rush past and chomp the cannon. Whether it's efficient or not, in that situation the character that can heal others needs to heal the unconscious or low-hp target, not take a chance on a GB, no matter the fact that on paper damage is theoretically "better." And the cleric is likely the only character that has that capacity, regardless of how awesome their other options for that spell slot might be.
As for "widely thought"... well, as we've seen, depends on which crowd you ask. I've never heard much praise for it, either on the forums or in person.
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For what I think is the third time: target an appropriate stat. I have repeatedly said to use a saving throw based spell against a high ac target, and to use an attack roll against targets that resist your spell saves. The reason i disregard accuracy for average damage is because I'm not going to use a spell or ability that has a low chance of working. A character has multiple options, it is common sense to use the best tool for the job.
EDIT: strike this. Apparently I read too quickly. Though you still probably have a saving throw based cantrip at low levels.
Like I was trying to say, you don't have an infinitude of options in combat; Sorcerers get 1 spell per level of Sorc. Also, as I said before, Magic Missile does more assuming 13 AC. THIRTEEN IS NOT "HIGH AC." Also, most of the time, a spell attack roll has a slightly HIGHER chance of hitting than most enemies failing a save, so even if they have the oh-so-high 13 AC, you still probably have a better chance hitting them than of them failing their save.
Quite frankly, with a level-1 Divine Soul Sorcerer, our damage options in combat will pretty much be:
As you can see, WE DON'T HAVE ANY SAVING THROW SPELLS FOR DAMAGE EXCEPT TOLL THE DEAD. What if they have WIS save proficiency? What if 1d12 (assuming they've already taken some damage) isn't enough damage? What if they're a Paladin, with 20 AC and +5 as their lowest save? Your strategy of "use a saving throw based spell against a high ac target, and to use an attack roll against targets that resist your spell saves" DOES NOT WORK on a fundamental level. Your plan has a GAPING FLAW right at the center of it. We don't get to stroll up to combat with 6 spells prepared (that would be a pitiful amount, but it is THREE TIMES what we actually do get). Even if we were at a higher level, we STILL wouldn't have enough options, due to the low number of spells known a Sorc gets. You have to go for as much mileage as you can get on each and every one, which is why we need to compare the pros and cons of each, including chances of success.