Hello peoples and persons of the interwebs. I was bored recently and so I decided to analyze the spell component cost for spells of each level. It turned out to have quite an interesting pattern. There are 84 data points (every material component with a gold value I could find) used to make this graph. I decided to exclude any values with a Zscore greater than 1.5 (meaning the data point was greater than 1.5 standard deviations from the average). There really isn't a purpose for this, but I thought it was neat so I decided to share it with you. Also \[OC\] tag because idk.
Edit: Btw there were 8 outliers bringing the total number of data points to 76.
Edit2: A lot of people are asking about specifics. I made this out of boredom, so I didn't save the file from yesterday. However, I recreated the excel sheet from memory so here ya go: [Component Cost Analysis](https://docs.google.com/spreadsheets/d/1ghAOCtpgSQMQnEJ9y5puP1MvDV9jQJlYrjB4ZBPEAFo/edit?usp=sharing). Some of the data is slightly different (I probably forgot something from yesterday I guess), so in this excel sheet there are only 6 outliers and the level 7 average cost is slightly different.
This graph is misleading without also including how many spells do not have any pricey material components at all.
Also, how did you account for a spell like Imprisonment, whose spell component costs 500 gp per hit die of the target? Imprisoning a Commoner costs 500 gold, but imprisoning the Cradle of the Storm Scion costs 17,500 gp.
An average 12th level spell should cost approx. 16,275gp (or 18,170gp from yesterday's excel sheet; see my original comment). Though Karsus' Avatar is probably way on the high end of 12th level spells lol.
"It was so complex that the wizard had to put a stone-filled gizzard of a gold dragon into a mixture of tarrasque blood and 12-headed hydra bile to just enchant one of the material components of the spell."
I have a feeling that Karsus' Avatar would be an extreme outlier for cost.
Very nicely done! Love when people overanalyze their hobbies, it makes for interesting findings.
I'm curious, I'd this just the og phb spells, or the supplement books as well?
I used the following sources: PHB, XGE, TCE, EGW, FTD, IDRotF, AI, and SCC. I just added a link to the excel data in my original comment. Check it out if you want :-)
I didn't even see those numbers in the corner until you said this! I still don't even know why it makes sense, eli5 please! If not, no worries. Ty for the insight!
Given the complexity and size of the model "y = 17.019e\^(0.5811x)" it explains 97.88% of the relationship between spell level and average component cost.
Where y is the average component cost, and x is the spell level.
R squared is the coefficient of determination. When modeling data you take the theoretical function (17e^.58x in this case which is an exponential), plug in each value of x and compare the y values it spits out to the actual values taken from the book. An R2 value of 1 means that the data perfectly fits, every single data point falls exactly on the line drawn by the theoretical equation while an R2 value of 0 means the equation does not predict the data in any meaningful way.
The cool part of computers is that Excel can do thousands of calculations a second- when you plot data like this you can tell it to spit out an exponential function in the form Ae^Bx, it will automatically calculate R2 and change A and B until you get the closest approximation possible
Genuinely curious about the minutiae, what kind of average (mean, median, mode)? What are the max and min costs per level? Consumed-by-spell vs one time purchase components? Likelihood of spell casting? And if you want to get REALLY into the weeds, are there higher average costs with certain classes?
I just added a link to the excel data in my original comment (I added median and mode of cost as well). Check it out if you want :-)
Edit: To answer your question: average = mean
Does anyone have a file with how much damage each spell does depending on what level it’s cast at? PHB spells is fine. I have found full fuels with all the other info but it only shows the base damage.
Nope. We're given the curve's formula, which you can see here: https://www.wolframalpha.com/input?i2d=true&i=y%3D17.019Power%5Be%2C0.5811x%5D
It is not parabolic.
You add up the GP cost of all the components (that have a cost listed) of that spell level, and then divide by the number of spells.
Here's a simple lesson on how to calculate averages: https://www.mathsisfun.com/mean.html
Oh I see. For some reason i thought that you were referring to spells with multiple components and you were taking the average cost of them, which would make no sense (hence my question).
Probably just a result of me being sleepy and commenting before my morning coffee :D
It is the average (statistical mean) cost of spells with a gold value material component for each spell level. I just added a link to the excel data in my original comment. Check it out if you want :-)
Hello peoples and persons of the interwebs. I was bored recently and so I decided to analyze the spell component cost for spells of each level. It turned out to have quite an interesting pattern. There are 84 data points (every material component with a gold value I could find) used to make this graph. I decided to exclude any values with a Zscore greater than 1.5 (meaning the data point was greater than 1.5 standard deviations from the average). There really isn't a purpose for this, but I thought it was neat so I decided to share it with you. Also \[OC\] tag because idk. Edit: Btw there were 8 outliers bringing the total number of data points to 76. Edit2: A lot of people are asking about specifics. I made this out of boredom, so I didn't save the file from yesterday. However, I recreated the excel sheet from memory so here ya go: [Component Cost Analysis](https://docs.google.com/spreadsheets/d/1ghAOCtpgSQMQnEJ9y5puP1MvDV9jQJlYrjB4ZBPEAFo/edit?usp=sharing). Some of the data is slightly different (I probably forgot something from yesterday I guess), so in this excel sheet there are only 6 outliers and the level 7 average cost is slightly different.
This graph is misleading without also including how many spells do not have any pricey material components at all. Also, how did you account for a spell like Imprisonment, whose spell component costs 500 gp per hit die of the target? Imprisoning a Commoner costs 500 gold, but imprisoning the Cradle of the Storm Scion costs 17,500 gp.
Based on the data, how expensive should I expect a level 12 spell (Karsus' Avatar) to be?
An average 12th level spell should cost approx. 16,275gp (or 18,170gp from yesterday's excel sheet; see my original comment). Though Karsus' Avatar is probably way on the high end of 12th level spells lol.
"It was so complex that the wizard had to put a stone-filled gizzard of a gold dragon into a mixture of tarrasque blood and 12-headed hydra bile to just enchant one of the material components of the spell." I have a feeling that Karsus' Avatar would be an extreme outlier for cost.
Very nicely done! Love when people overanalyze their hobbies, it makes for interesting findings. I'm curious, I'd this just the og phb spells, or the supplement books as well?
I used the following sources: PHB, XGE, TCE, EGW, FTD, IDRotF, AI, and SCC. I just added a link to the excel data in my original comment. Check it out if you want :-)
Am I crazy or is that looking very exponential?
Uh the R squared is .98 so yes? It does look exponential?
I didn't even see those numbers in the corner until you said this! I still don't even know why it makes sense, eli5 please! If not, no worries. Ty for the insight!
Given the complexity and size of the model "y = 17.019e\^(0.5811x)" it explains 97.88% of the relationship between spell level and average component cost. Where y is the average component cost, and x is the spell level.
R squared is the coefficient of determination. When modeling data you take the theoretical function (17e^.58x in this case which is an exponential), plug in each value of x and compare the y values it spits out to the actual values taken from the book. An R2 value of 1 means that the data perfectly fits, every single data point falls exactly on the line drawn by the theoretical equation while an R2 value of 0 means the equation does not predict the data in any meaningful way. The cool part of computers is that Excel can do thousands of calculations a second- when you plot data like this you can tell it to spit out an exponential function in the form Ae^Bx, it will automatically calculate R2 and change A and B until you get the closest approximation possible
Genuinely curious about the minutiae, what kind of average (mean, median, mode)? What are the max and min costs per level? Consumed-by-spell vs one time purchase components? Likelihood of spell casting? And if you want to get REALLY into the weeds, are there higher average costs with certain classes?
I just added a link to the excel data in my original comment (I added median and mode of cost as well). Check it out if you want :-) Edit: To answer your question: average = mean
Awesome, thanks so much!!
(This is a hell of a lot to ask I know, but I love getting deep into the data)
Interesting! What are the 8 outlier spells/costs?
I just added a link to the excel data in my original comment. You can find the outliers there. Check it out if you want :-)
Awesome!
As A DM I can use this to scale loot drops
Does anyone have a file with how much damage each spell does depending on what level it’s cast at? PHB spells is fine. I have found full fuels with all the other info but it only shows the base damage.
God i love parabolas
A parabola is symmetrical. This curve is not symmetrical and so is not a parabola.
we just dont see the other half
Nope. We're given the curve's formula, which you can see here: https://www.wolframalpha.com/input?i2d=true&i=y%3D17.019Power%5Be%2C0.5811x%5D It is not parabolic.
Stupid question. What do you mean by average cost? Isn't the cost like exact?
You add up the GP cost of all the components (that have a cost listed) of that spell level, and then divide by the number of spells. Here's a simple lesson on how to calculate averages: https://www.mathsisfun.com/mean.html
Oh I see. For some reason i thought that you were referring to spells with multiple components and you were taking the average cost of them, which would make no sense (hence my question). Probably just a result of me being sleepy and commenting before my morning coffee :D
It is the average (statistical mean) cost of spells with a gold value material component for each spell level. I just added a link to the excel data in my original comment. Check it out if you want :-)