Calculating CR is the same as it is for anyone else. You take the average offensive CR for 3 rounds, compare it to the Defensive CR for three rounds, and go from there. This is partially decided by their tactics. A normal mage would cast fly early to get out of range of most attacks. Then they'd rain death upon their enemies.
In the above mage's case, their best option is going to be casting fireball every round. That's going to jack up their offensive CR considerably, to about 16. This, in turn, will raise their average CR to about 8. But they'll have lower AC than a typical mage and be more vulnerable to attacks in general. So while it might seem stronger in terms of raw math, it won't last nearly as long in a fight.
EDIT:
It was late last night, so I didn't want to get into the nitty-gritty. But with a good night's rest, let's get into details. The first thing to remember is we're only talking about the first three rounds of combat. There's also a section, found on page 249 of the DMG, for Adjudicating Areas of Effect. This comes way before the section on calculating CR; which begins on page 275.
The default mage has a couple of things going for it. Since mage armor lasts for 8 hours, we can safely assume it's active before the fighting begins even though it's not expressly tagged as such. That'll save it a turn for buffing itself so it can just focus on blasting. Now, because of their size, spells like cone of cold and fireball hit up to 6 and 4 targets, respectively. This is important.
The mage has an Offensive CR of 10 just from striking six targets with cone of cold once in a single fight. It's an average of 64 damage per round. But if they're only buffing for one round, are they casting this? Two fireballs average 75 damage, and the DC is still 14, so the Offensive CR is still CR 10. And we know it casts fly and not greater invisibility because the latter increases it's effective AC by +2; which it needs to have the Defensive CR of 1 to average out to 6. Disadvantage on all incoming attacks is great, but it only effectively increases AC by +1 (see the Avoidance trait found on DMG 280).
Sometimes, you have to reverse engineer a monster in order to figure out how it's AC got to where it is. The orc is another great example of this because its CR is based entirely on using Aggresive and throwing javelins. If it swung its greataxe just once, its CR would be 1.
Creature stat blocks don't assume things like upcasting spells or reaction spells because they're not done on the creature's turn. The mage, for example, makes no assumptions about casting counterspell or shield. So, already, your 7th-level spellcaster doesn't fully work as an NPC; given your stated assumptions. You've given them too many options to attack with, that they can't all use even by your own admission, and not enough defenses. The above mage is expected to burn through all their 3rd-level spell slots, and if they do it in less than three rounds then they're going to break out the big guns.
If your plan is for counterspell to be an option every single turn, then your players will dislike you right quick. But it also means your 3rd-level slots shouldn't have offensive spells. That dimension door is meaningless if the spellcaster can't ever use it on an upcast fireball. Don't give them something only to deny them access to it.
I suggest giving them mage armor and mirror image. Treat it like Avoidance and give it effectively +1 AC for your Defensive CR calculation. It might not matter much in the grand scheme of things, but that's it. Two fireballs will still give them an Offensive CR of 10, so they balance out to CR 5. And if you run out of 3rd-level slots, then you use weaker spells. They're not nearly as fun or challenging as a regular mage.
80hp would give it a defensive CR of 1. Next we need the AC, which you haven't provided, however this is based off the mage statblock so I'll assume its 12. Now this is the part I see a lot of people miss when calculating spellcasters CR, the mage knows shield, and they have enough spell slots to cast it every turn for 3 rounds. Therefore their theoretical ac is 17. This increases the defensive CR to 3. If you're mages AC isn't 12, increase the defensive CR by 1 for every 2 points the AC of the mage is higher than 12.
Offensively, your mage just casts fireball 3 times, once with a lvl 4 slot and twice with level 3 slots. We assume the fireball strikes 2 targets making the damage each round: 62, 56, 56. Giving an average damage of 58. This gives an offensive CR of 9. The spell attack bonus and save DC don't affect this CR this time, so the final offensive CR is 12.
Calculate the average of the 2 CR's and you get a CR of 6. Which is the exact same CR as the normal mage statblock.
The normal mage statblock has an offensive CR of 10 and a defensive CR of 2, so whilst your mage deals less damage, it can last longer.
Edit: I just noticed the CR calculation Jounichi used. That is a wild miscalculation of offensive CR, to get it that high you'd need to be casting fireball with 7th level spell slots. The normal Mage statblock is also capable of casting fireball every round yet it has a CR of 6, so it's impossible for that creature to have an offensive CR of 16. The DMG says that being able to fly only increases a monsters theoretical ac by 2. Trading 56 points of damage for +2 ac is not the best idea, and while it may be a standard mage tactic, the offensive CR is calculated to assume the creature uses their most devastating attacks as soon as possible.
80hp would give it a defensive CR of 1. Next we need the AC, which you haven't provided, however this is based off the mage statblock so I'll assume its 12. Now this is the part I see a lot of people miss when calculating spellcasters CR, the mage knows shield, and they have enough spell slots to cast it every turn for 3 rounds. Therefore their theoretical ac is 17. This increases the defensive CR to 3. If you're mages AC isn't 12, increase the defensive CR by 1 for every 2 points the AC of the mage is higher than 12.
Offensively, your mage just casts fireball 3 times, once with a lvl 4 slot and twice with level 3 slots. We assume the fireball strikes 2 targets making the damage each round: 62, 56, 56. Giving an average damage of 58. This gives an offensive CR of 9. The spell attack bonus and save DC don't affect this CR this time, so the final offensive CR is 12.
Calculate the average of the 2 CR's and you get a CR of 6. Which is the exact same CR as the normal mage statblock.
The normal mage statblock has an offensive CR of 10 and a defensive CR of 2, so whilst your mage deals less damage, it can last longer.
Edit: I just noticed the CR calculation Jounichi used. That is a wild miscalculation of offensive CR, to get it that high you'd need to be casting fireball with 7th level spell slots. The normal Mage statblock is also capable of casting fireball every round yet it has a CR of 6, so it's impossible for that creature to have an offensive CR of 16. The DMG says that being able to fly only increases a monsters theoretical ac by 2. Trading 56 points of damage for +2 ac is not the best idea, and while it may be a standard mage tactic, the offensive CR is calculated to assume the creature uses their most devastating attacks as soon as possible.
Actually, my plan for his tactics is to use all 3rd level slots for counterspell, 4th level slot for an upcast fireball, and 2nd level for scorching ray., and 1st for shield (if his reaction hasn’t been used on counterspell). I could have calculated his CR If he had done as you suggest, but since his damage each round will have such a wild variance (4th level fireball, round 1, does average 31 damage, let’s assume it hits 3 characters and 2 make their save , 66 damage on average, then scorching ray from here on out, let’s say 2 rays hit, average 14 damage. He will use his reaction to counterspell any 3rd level stuff (the party is 5th level) and just use shield after that). So, yeah, his damage and defences are wildly different every round. Oh, and his AC is 14 or 15 (I’ll let him add his proficiency bonus to it) Thanks for answering!
Actually, my plan for his tactics is to use all 3rd level slots for counterspell, 4th level slot for an upcast fireball, and 2nd level for scorching ray., and 1st for shield (if his reaction hasn’t been used on counterspell). I could have calculated his CR If he had done as you suggest, but since his damage each round will have such a wild variance (4th level fireball, round 1, does average 31 damage, let’s assume it hits 3 characters and 2 make their save , 66 damage on average, then scorching ray from here on out, let’s say 2 rays hit, average 14 damage. He will use his reaction to counterspell any 3rd level stuff (the party is 5th level) and just use shield after that). So, yeah, his damage and defences are wildly different every round. Oh, and his AC is 14 or 15 (I’ll let him add his proficiency bonus to it) Thanks for answering!
Don't include the assumption that they'll save when calculating damage for CR, that's included in the save DC part of offensive CR. Same with attack rolls and the attack bonus.
What Lunali said, offensive CR is calculated by assuming any attack that can hit multiple opponents only hits 2 of them and that each enemy fails their save if they have to make one.
You shouldn't account for tactics when calculating CR as it just complicates matters, especially for spellcasters. If you're worried about your party steamrolling the mage, give the mage some minions such as mephits or imps.
Also don't add the proficiency bonus to the mages ac, just give him studded leather armour, that'll give him an ac of 14. Alternatively you can give them the mage armour spell to give him 15ac.
What Lunali said, offensive CR is calculated by assuming any attack that can hit multiple opponents only hits 2 of them and that each enemy fails their save if they have to make one.
You shouldn't account for tactics when calculating CR as it just complicates matters, especially for spellcasters. If you're worried about your party steamrolling the mage, give the mage some minions such as mephits or imps.
Also don't add the proficiency bonus to the mages ac, just give him studded leather armour, that'll give him an ac of 14. Alternatively you can give them the mage armour spell to give him 15ac.
That's not entirely accurate. Only breath weapons explicitly assume two targets are hit. This is because, if you follow the general rules for adjudicated areas of effect, it's possible for only one target to be hit.
Spells still hit their full expected number of targets.
What Lunali said, offensive CR is calculated by assuming any attack that can hit multiple opponents only hits 2 of them and that each enemy fails their save if they have to make one.
You shouldn't account for tactics when calculating CR as it just complicates matters, especially for spellcasters. If you're worried about your party steamrolling the mage, give the mage some minions such as mephits or imps.
Also don't add the proficiency bonus to the mages ac, just give him studded leather armour, that'll give him an ac of 14. Alternatively you can give them the mage armour spell to give him 15ac.
That's not entirely accurate. Only breath weapons explicitly assume two targets are hit. This is because, if you follow the general rules for adjudicated areas of effect, it's possible for only one target to be hit.
Spells still hit their full expected number of targets.
The adjudicating area of effects rule has nothing to do with calculating CR, it's an optional rule used to determine how many targets you hit in theatre of the mind games.
What is an expected number of targets in a game that can have such a large range in party sizes? The two targets in an area rule is used for clarity, as it's impossible to predict how many targets will actually be in a spells area of effect. The DMG gives breath weapons as an example, they don't say this only applies to breath weapons. It also makes sense to use the only two targets rule as a smart party will spread out where possible to avoid everyone being in the same radius.
I should also clarify that when I say 'only two targets for spells that are capable of targeting more than one creature' I mean for spells with areas of effect (Cube, Cone, Circle etc). Spells like Magic Missile and Scorching Ray that are multiple attack spells, it's assumed all of those attacks hit their target.
What Lunali said, offensive CR is calculated by assuming any attack that can hit multiple opponents only hits 2 of them and that each enemy fails their save if they have to make one.
You shouldn't account for tactics when calculating CR as it just complicates matters, especially for spellcasters. If you're worried about your party steamrolling the mage, give the mage some minions such as mephits or imps.
Also don't add the proficiency bonus to the mages ac, just give him studded leather armour, that'll give him an ac of 14. Alternatively you can give them the mage armour spell to give him 15ac.
That's not entirely accurate. Only breath weapons explicitly assume two targets are hit. This is because, if you follow the general rules for adjudicated areas of effect, it's possible for only one target to be hit.
Spells still hit their full expected number of targets.
The adjudicating area of effects rule has nothing to do with calculating CR, it's an optional rule used to determine how many targets you hit in theatre of the mind games.
What is an expected number of targets in a game that can have such a large range in party sizes? The two targets in an area rule is used for clarity, as it's impossible to predict how many targets will actually be in a spells area of effect. The DMG gives breath weapons as an example, they don't say this only applies to breath weapons. It also makes sense to use the only two targets rule as a smart party will spread out where possible to avoid everyone being in the same radius.
I should also clarify that when I say 'only two targets for spells that are capable of targeting more than one creature' I mean for spells with areas of effect (Cube, Cone, Circle etc). Spells like Magic Missile and Scorching Ray that are multiple attack spells, it's assumed all of those attacks hit their target.
Nowhere is the two targets specified except for breath weapons. There's no other guidance given. If you're seriously going to say "well, the rules don't say you don't apply X" then you're arguing against the actual rules as presented.
What Lunali said, offensive CR is calculated by assuming any attack that can hit multiple opponents only hits 2 of them and that each enemy fails their save if they have to make one.
You shouldn't account for tactics when calculating CR as it just complicates matters, especially for spellcasters. If you're worried about your party steamrolling the mage, give the mage some minions such as mephits or imps.
Also don't add the proficiency bonus to the mages ac, just give him studded leather armour, that'll give him an ac of 14. Alternatively you can give them the mage armour spell to give him 15ac.
That's not entirely accurate. Only breath weapons explicitly assume two targets are hit. This is because, if you follow the general rules for adjudicated areas of effect, it's possible for only one target to be hit.
Spells still hit their full expected number of targets.
The adjudicating area of effects rule has nothing to do with calculating CR, it's an optional rule used to determine how many targets you hit in theatre of the mind games.
What is an expected number of targets in a game that can have such a large range in party sizes? The two targets in an area rule is used for clarity, as it's impossible to predict how many targets will actually be in a spells area of effect. The DMG gives breath weapons as an example, they don't say this only applies to breath weapons. It also makes sense to use the only two targets rule as a smart party will spread out where possible to avoid everyone being in the same radius.
I should also clarify that when I say 'only two targets for spells that are capable of targeting more than one creature' I mean for spells with areas of effect (Cube, Cone, Circle etc). Spells like Magic Missile and Scorching Ray that are multiple attack spells, it's assumed all of those attacks hit their target.
Nowhere is the two targets specified except for breath weapons. There's no other guidance given. If you're seriously going to say "well, the rules don't say you don't apply X" then you're arguing against the actual rules as presented.
Nowhere does it say you use the adjudicating area of effect rule to determine the challenge rating either. It doesn't mention the rule I use, but I infer it based off what I have available, and the closest thing there is to saying what to do is "A breath weapon would do 45 damage against one target, or would do 90 damage if it hit two targets (and it probably will)". When I use this method to work out how other creatures challenge ratings were determined, as shown by how I calculated the Mage's CR earlier, this method works or gets within 1 CR of the creatures CR.
I won't claim that this is how WotC actually calculate their CR, WotC have said in the past that sometimes they just give creatures a CR that seems to fit best. There are many small details missing from the guide, such as whether you round up or down when you end up with a CR of 2.5. You can't even work out the answer by looking at other creatures, gnoll for example end up with a CR of 3/8, which is rounded up to 1/2, Hobgoblin's however end up with a CR of 3/4, which they round down to 1/2, there's no consistency.
I use the method I use because it is simple(ish) and it is accurate enough for me to tell other people that you should use this method.
Changes:
80 hit points
Intelligence of 18 (spell save DC and attack bonus increased to 15 and +7)
proficiency in DEX and CON saves
No 5th level spells or slots, and only 1 fourth level slot.
Spell list changed to:
1st level: burning hands, chromatic orb, shield
2nd level: gust of wind, shatter, scorching ray
3rd level: counterspell, dispel magic, fireball, lightning bolt
4th level: dimension door
I can't seem to find any rules for calculating spellcasters CR, so I hope someone on here knows how.
I'm the Valar (leader and creator) of The Lord of the Rings/The Hobbit/Anything Tolkien Cult!
Member of the Cult of Cats, High Elf of the Elven Guild, and Sauce Priest & Sauce Smith of the Supreme Court of Sauce.
If you want some casual roleplay/adventures in Middle Earth, check out The Wild's Edge Tavern, a LotR/Middle Earth tavern!
JOIN TIAMAT'S CONGA LINE!
Extended Sig
Calculating CR is the same as it is for anyone else. You take the average offensive CR for 3 rounds, compare it to the Defensive CR for three rounds, and go from there. This is partially decided by their tactics. A normal mage would cast fly early to get out of range of most attacks. Then they'd rain death upon their enemies.
In the above mage's case, their best option is going to be casting fireball every round. That's going to jack up their offensive CR considerably, to about 16. This, in turn, will raise their average CR to about 8. But they'll have lower AC than a typical mage and be more vulnerable to attacks in general. So while it might seem stronger in terms of raw math, it won't last nearly as long in a fight.
EDIT:
It was late last night, so I didn't want to get into the nitty-gritty. But with a good night's rest, let's get into details. The first thing to remember is we're only talking about the first three rounds of combat. There's also a section, found on page 249 of the DMG, for Adjudicating Areas of Effect. This comes way before the section on calculating CR; which begins on page 275.
The default mage has a couple of things going for it. Since mage armor lasts for 8 hours, we can safely assume it's active before the fighting begins even though it's not expressly tagged as such. That'll save it a turn for buffing itself so it can just focus on blasting. Now, because of their size, spells like cone of cold and fireball hit up to 6 and 4 targets, respectively. This is important.
The mage has an Offensive CR of 10 just from striking six targets with cone of cold once in a single fight. It's an average of 64 damage per round. But if they're only buffing for one round, are they casting this? Two fireballs average 75 damage, and the DC is still 14, so the Offensive CR is still CR 10. And we know it casts fly and not greater invisibility because the latter increases it's effective AC by +2; which it needs to have the Defensive CR of 1 to average out to 6. Disadvantage on all incoming attacks is great, but it only effectively increases AC by +1 (see the Avoidance trait found on DMG 280).
Sometimes, you have to reverse engineer a monster in order to figure out how it's AC got to where it is. The orc is another great example of this because its CR is based entirely on using Aggresive and throwing javelins. If it swung its greataxe just once, its CR would be 1.
Creature stat blocks don't assume things like upcasting spells or reaction spells because they're not done on the creature's turn. The mage, for example, makes no assumptions about casting counterspell or shield. So, already, your 7th-level spellcaster doesn't fully work as an NPC; given your stated assumptions. You've given them too many options to attack with, that they can't all use even by your own admission, and not enough defenses. The above mage is expected to burn through all their 3rd-level spell slots, and if they do it in less than three rounds then they're going to break out the big guns.
If your plan is for counterspell to be an option every single turn, then your players will dislike you right quick. But it also means your 3rd-level slots shouldn't have offensive spells. That dimension door is meaningless if the spellcaster can't ever use it on an upcast fireball. Don't give them something only to deny them access to it.
I suggest giving them mage armor and mirror image. Treat it like Avoidance and give it effectively +1 AC for your Defensive CR calculation. It might not matter much in the grand scheme of things, but that's it. Two fireballs will still give them an Offensive CR of 10, so they balance out to CR 5. And if you run out of 3rd-level slots, then you use weaker spells. They're not nearly as fun or challenging as a regular mage.
Or strip away fireball entirely for scorching ray, but that'll drop their CR to 1.
To reiterate, you've basically built a blaster that's not going to last long and is going to disappoint.
Okay we'll start with the defensive CR.
80hp would give it a defensive CR of 1. Next we need the AC, which you haven't provided, however this is based off the mage statblock so I'll assume its 12. Now this is the part I see a lot of people miss when calculating spellcasters CR, the mage knows shield, and they have enough spell slots to cast it every turn for 3 rounds. Therefore their theoretical ac is 17. This increases the defensive CR to 3. If you're mages AC isn't 12, increase the defensive CR by 1 for every 2 points the AC of the mage is higher than 12.
Offensively, your mage just casts fireball 3 times, once with a lvl 4 slot and twice with level 3 slots. We assume the fireball strikes 2 targets making the damage each round: 62, 56, 56. Giving an average damage of 58. This gives an offensive CR of 9. The spell attack bonus and save DC don't affect this CR this time, so the final offensive CR is 12.
Calculate the average of the 2 CR's and you get a CR of 6. Which is the exact same CR as the normal mage statblock.
The normal mage statblock has an offensive CR of 10 and a defensive CR of 2, so whilst your mage deals less damage, it can last longer.
Edit: I just noticed the CR calculation Jounichi used. That is a wild miscalculation of offensive CR, to get it that high you'd need to be casting fireball with 7th level spell slots. The normal Mage statblock is also capable of casting fireball every round yet it has a CR of 6, so it's impossible for that creature to have an offensive CR of 16. The DMG says that being able to fly only increases a monsters theoretical ac by 2. Trading 56 points of damage for +2 ac is not the best idea, and while it may be a standard mage tactic, the offensive CR is calculated to assume the creature uses their most devastating attacks as soon as possible.
Actually, my plan for his tactics is to use all 3rd level slots for counterspell, 4th level slot for an upcast fireball, and 2nd level for scorching ray., and 1st for shield (if his reaction hasn’t been used on counterspell). I could have calculated his CR If he had done as you suggest, but since his damage each round will have such a wild variance (4th level fireball, round 1, does average 31 damage, let’s assume it hits 3 characters and 2 make their save , 66 damage on average, then scorching ray from here on out, let’s say 2 rays hit, average 14 damage. He will use his reaction to counterspell any 3rd level stuff (the party is 5th level) and just use shield after that). So, yeah, his damage and defences are wildly different every round. Oh, and his AC is 14 or 15 (I’ll let him add his proficiency bonus to it) Thanks for answering!
I'm the Valar (leader and creator) of The Lord of the Rings/The Hobbit/Anything Tolkien Cult!
Member of the Cult of Cats, High Elf of the Elven Guild, and Sauce Priest & Sauce Smith of the Supreme Court of Sauce.
If you want some casual roleplay/adventures in Middle Earth, check out The Wild's Edge Tavern, a LotR/Middle Earth tavern!
JOIN TIAMAT'S CONGA LINE!
Extended Sig
Don't include the assumption that they'll save when calculating damage for CR, that's included in the save DC part of offensive CR. Same with attack rolls and the attack bonus.
What Lunali said, offensive CR is calculated by assuming any attack that can hit multiple opponents only hits 2 of them and that each enemy fails their save if they have to make one.
You shouldn't account for tactics when calculating CR as it just complicates matters, especially for spellcasters. If you're worried about your party steamrolling the mage, give the mage some minions such as mephits or imps.
Also don't add the proficiency bonus to the mages ac, just give him studded leather armour, that'll give him an ac of 14. Alternatively you can give them the mage armour spell to give him 15ac.
That's not entirely accurate. Only breath weapons explicitly assume two targets are hit. This is because, if you follow the general rules for adjudicated areas of effect, it's possible for only one target to be hit.
Spells still hit their full expected number of targets.
The adjudicating area of effects rule has nothing to do with calculating CR, it's an optional rule used to determine how many targets you hit in theatre of the mind games.
What is an expected number of targets in a game that can have such a large range in party sizes? The two targets in an area rule is used for clarity, as it's impossible to predict how many targets will actually be in a spells area of effect. The DMG gives breath weapons as an example, they don't say this only applies to breath weapons. It also makes sense to use the only two targets rule as a smart party will spread out where possible to avoid everyone being in the same radius.
I should also clarify that when I say 'only two targets for spells that are capable of targeting more than one creature' I mean for spells with areas of effect (Cube, Cone, Circle etc). Spells like Magic Missile and Scorching Ray that are multiple attack spells, it's assumed all of those attacks hit their target.
Nowhere is the two targets specified except for breath weapons. There's no other guidance given. If you're seriously going to say "well, the rules don't say you don't apply X" then you're arguing against the actual rules as presented.
Nowhere does it say you use the adjudicating area of effect rule to determine the challenge rating either. It doesn't mention the rule I use, but I infer it based off what I have available, and the closest thing there is to saying what to do is "A breath weapon would do 45 damage against one target, or would do 90 damage if it hit two targets (and it probably will)". When I use this method to work out how other creatures challenge ratings were determined, as shown by how I calculated the Mage's CR earlier, this method works or gets within 1 CR of the creatures CR.
I won't claim that this is how WotC actually calculate their CR, WotC have said in the past that sometimes they just give creatures a CR that seems to fit best. There are many small details missing from the guide, such as whether you round up or down when you end up with a CR of 2.5. You can't even work out the answer by looking at other creatures, gnoll for example end up with a CR of 3/8, which is rounded up to 1/2, Hobgoblin's however end up with a CR of 3/4, which they round down to 1/2, there's no consistency.
I use the method I use because it is simple(ish) and it is accurate enough for me to tell other people that you should use this method.