I'm trying to do a deep dive analysis of Phantasmal Killer for the Illusionist guide I'm writing.. As a sort of ballpark check, can you tell me how many rounds you believe PK should be expected to last in order to be worth a fourth level slot?
One thing you can do with PK that you can't do with the spells you mentioned is drop it on a target while your target is surrounded by your party's fighters. They can beat on the bad guy while you're inflicting damage over time and making it harder for the bad guy to hit back.
As for the math of it, if n is the number of saves failed and p is the probability of failing a particular save, then the expected value of n is equal to the integral from 2 to 10 of ((p to the x)(x-1)) please check my math.
That means that if the save is failed on a 12 or lower on a d20 (ie. 60% chance of failure), then you can expect the save to be failed three times.
If you assume a CR 7 victim and you use the following spreadsheet Monster Spreadsheet, then your victim has a Wis save of +2 on average. Assuming you are 7th level (the earliest you can cast PK), then you'll have a proficiency bonus of +3. Having nothing else to go by, I'm just going to have to guess that, at 7th level, you'll have an Int of 17. This is based on 15 being the highest stat available using the standard array and assumes you take a +2 to Int for your ability score adjustments. Of course, this doesn't include any racial bonus, so your Int could be higher and likely will be. Int of 17 will give you a +3 to your spell DC.
Your Prof Bonus + Your Int Bonus - Monster's Will Save = +4.
So, we should be able to safely assume your spells have a DC of at least 12 or, using the first equation in this post, p = 60%.
Using the numbers above the spell will fail 40% of the time. However we want the spell to work which is 60%.
Probability is multiplied not additive (at least in this case). Much like a die roll. If you want to roll a 12 on 2D6 you need a 6 then another 6. Thus 1/6 x 1/6 = 1/36 chance.
Of course these numbers change drastically with save DC and targets bonus. Let's say they have a +0 to save meaning they fail on 14 or less.
Round 1 70%
Round 2 49%
Round 3 34%
Round 4 24%
Round 5 17%
As you can see only two points difference in this case makes the spell more likely to last 5 rounds than previously lasting 3 rounds.
So anything you can do to increase spell DC greatly improves repeated save spells. Likewise boosting your own saves helps.
Now what would be a wicked combo is something that reduces stats, negatives or disadvantage on saves, combined with a continuing effect save. For example if you can get the enemy to 3 levels of exhaustion they have disadvantage on saves. I thing disadvantage works out to roughly -4 or -5. One of the UA wizard spells also caused disadvantage on wisdom saves (?), but it's concentration as well.
As you can see only two points difference in this case makes the spell more likely to last 5 rounds than previously lasting 3 rounds.
So anything you can do to increase spell DC greatly improves repeated save spells. Likewise boosting your own saves helps.
Now what would be a wicked combo is something that reduces stats, negatives or disadvantage on saves, combined with a continuing effect save. For example if you can get the enemy to 3 levels of exhaustion they have disadvantage on saves. I thing disadvantage works out to roughly -4 or -5. One of the UA wizard spells also caused disadvantage on wisdom saves (?), but it's concentration as well.
Absolutely, and, in the Guide for Illusionists that I'm in the process writing, I've included a table which examines how the expeceted number of rounds change based on changes in the probability. I suggest exactly that - that affecting the probability of failure is a great prelude to dropping this spell. My example is to work with your party's cleric to drop Contagion or Bestow Curse.
I'm trying to do a deep dive analysis of Phantasmal Killer for the Illusionist guide I'm writing.. As a sort of ballpark check, can you tell me how many rounds you believe PK should be expected to last in order to be worth a fourth level slot?
Its not very good. If you want a Disable take 3rd level Fear or Hypno Pattern that don't give you end of round saves.
If you want reliable and high damage over time take Storm Sphere.
Get this at 7th level. Gonna guess you'll have a DC of 15. Expect the enemy to have a +1-+2 to save. You do the math.
One thing you can do with PK that you can't do with the spells you mentioned is drop it on a target while your target is surrounded by your party's fighters. They can beat on the bad guy while you're inflicting damage over time and making it harder for the bad guy to hit back.
As for the math of it, if n is the number of saves failed and p is the probability of failing a particular save, then the expected value of n is equal to the integral from 2 to 10 of ((p to the x)(x-1)) please check my math.
That means that if the save is failed on a 12 or lower on a d20 (ie. 60% chance of failure), then you can expect the save to be failed three times.
If you assume a CR 7 victim and you use the following spreadsheet Monster Spreadsheet, then your victim has a Wis save of +2 on average. Assuming you are 7th level (the earliest you can cast PK), then you'll have a proficiency bonus of +3. Having nothing else to go by, I'm just going to have to guess that, at 7th level, you'll have an Int of 17. This is based on 15 being the highest stat available using the standard array and assumes you take a +2 to Int for your ability score adjustments. Of course, this doesn't include any racial bonus, so your Int could be higher and likely will be. Int of 17 will give you a +3 to your spell DC.
Your Prof Bonus + Your Int Bonus - Monster's Will Save = +4.
So, we should be able to safely assume your spells have a DC of at least 12 or, using the first equation in this post, p = 60%.
I disagree with the above calculation.
If the save fails on a 12 or less then:
You have a 60% of the spell working the first round.
On the second round they get another save, the chance of failing two saves is .60 x .60 = 36%
Third round of effect is only 22%
Fourth round is 13%
I -believe- that the sweet spot is where the expected value is greater than 100%.
My apologies as it has been a long time since I used Calculus or Probability. I encourage you to check my math.
We can expect the spell to fail on the first attempt 60% of the time.
We can expect it to fail by the second attempt 60% + 36% = 96% of the time.
We can expect it to fail by the third attempt >= 100% of the time.
Therefore, we can expect three failed saves.
Using the numbers above the spell will fail 40% of the time. However we want the spell to work which is 60%.
Probability is multiplied not additive (at least in this case). Much like a die roll. If you want to roll a 12 on 2D6 you need a 6 then another 6. Thus 1/6 x 1/6 = 1/36 chance.
Of course these numbers change drastically with save DC and targets bonus. Let's say they have a +0 to save meaning they fail on 14 or less.
Round 1 70%
Round 2 49%
Round 3 34%
Round 4 24%
Round 5 17%
As you can see only two points difference in this case makes the spell more likely to last 5 rounds than previously lasting 3 rounds.
So anything you can do to increase spell DC greatly improves repeated save spells. Likewise boosting your own saves helps.
Now what would be a wicked combo is something that reduces stats, negatives or disadvantage on saves, combined with a continuing effect save. For example if you can get the enemy to 3 levels of exhaustion they have disadvantage on saves. I thing disadvantage works out to roughly -4 or -5. One of the UA wizard spells also caused disadvantage on wisdom saves (?), but it's concentration as well.
Absolutely, and, in the Guide for Illusionists that I'm in the process writing, I've included a table which examines how the expeceted number of rounds change based on changes in the probability. I suggest exactly that - that affecting the probability of failure is a great prelude to dropping this spell. My example is to work with your party's cleric to drop Contagion or Bestow Curse.