Crafting level XP analysis

[BruceTheHoon]

Curiosity is the mother of Invention. That makes Boredom it's grandma.

I've ebarked upon discovering the rules and formulae behind the crafting level XP progression.

As a source of data I've used the data available on DDO wiki, copied from there at around 09:00 GMT.
Below are the results I've come up.


Step 1: Plunging into derivative waters

Strictly speaking we can not make a derivative of a discrete function, but we can do something very similar: we can look at the differences between the neighbouring points.

Using the formula (XP(level+1) - XP(level))/((level+1) - level) = XP(level+1) - XP(level)
I got the following result:


Here, with a careful look, we can already make some interesting observations.

It seems the XP progression is not a smooth function of the crafting level, but rather a composite of a few different ones.
-Levels 1-10: Function looks very linear, which would indicate an arithmetic progression of xp/crafting level for these levels.
-Levels 11-36: The function here is clearly non linear. This might complicate deducting a formula in the level range and lead to some guesswork.
-Levels 37-42: There seems to be an anomaly here, which could just be the result of incorrect data in the DDO wiki's XP tables.
-Levels 43-60: This again looks linear, but with a different slope than at levels 1-10.

To make sure of my findings so far, I went further.

Step 2: Reaching the derivative bottom

Using the same formula as in the previous step, we can make a sort of second derivative of the initial XP@level function.
The results are:


While the level ranges, that are using the same formula, could only be guessed in the previous graph, they are clearly visible in the second one.

Further conclusions can be drawn:
-Levels 1-10: Function governing XP progression in this level range is indeed linear making the initial XP@level requirement a sum of an arithmetic progression. In level range 1 through 10, the XP function is a parabola.
-Levels 11-36: The second derivative is linear. In turn, this means that the initial XP@level function will be a 3rd degree polynomal in this level range.
-Levels 37-42: The anomaly is now even more extreme and easier to spot.
-Levels 43-60: Similar to level range 1-10, the initial XP@level function in this range is going to be a parabola (but a different one).

The only thing left to do now is to determine the formulae parameters.

Step 3: Fishing outt he formulae

Since there is a different formula governing the XP progression for every different level range, this will have to be done for every level range individually.

Levels 1-10:
We have the value of the second derivative in this range, which is a constant.
It alternates between 3 and 2, so I've taken 2.5 as the correct value.
Integrating the the constant twice (which I won't do here, because lacking the appropriate symbols, it would only be confusing and a pain to do) and applying the boundary conditions to determine the free constants, the formula emerges:

XP = 5/4*Level^2 + 11*Level

Boundary conditions used are of course the given XP@level values and the calculated differences.

Levels 11-36:

This one was just slightly more difficult, since some corrections had to be made to the factors after each integration, because of some approximations in the previous step.
Nevertheless, using the same procedure, I've determined the formula governing progression at levels 11 to 36 to be:

XP = 1/12*Level^3 + 5/8*Level^2 + 2/5*Level + 85

Levels 43-60:

This one was done in completely the same manner as the formula for levels 1 to 10. The result is:

XP = 5*Level^2 + 5*Level - 1862




And people say that math is not fun! Pha!

[donfilibuster]

Can we get a graph in terms of weapons-to-be-hauled-off-chests? :/

[Marten]

-Levels 37-42: There seems to be an anomaly here, which could just be the result of incorrect data in the DDO wiki's XP tables.

Most of those numbers have been input by me. I confirmed that 1-20 were correct when I made my video crafting demo part 2 (see sig). From my hand written notes (and screen shots found here) I am certain that I put in 37 and then 44-49 and then 52-62. I did confirm that 35, 50 and 51 are correct. *I just check the number for 39 that someone else input based on a SS I have an it is wrong, I am changing it now.

I sadly do not have video or SSs of the 30s. My elemental is @ 35 so if I could get some help with essences I could grind that up to 43 and confirm those numbers, but since I am out of toons to transfer and I am using the daily TP to grind Divine as high as I can I would need help or trust someone else to do it later.

I hope that this helps you fix the anomaly.

[testing1234]

interesting
are all three different crafting lvls divine/arcane/xxx the same exp progression?

[Marten]

interesting
are all three different crafting lvls divine/arcane/xxx the same exp progression?

Yes they are. And its Arcane / Divine / Elemental for the crafting disciplines as it stand currently.

[pjw]

http://forums.ddo.com/showthread.php?t=311267

[BruceTheHoon]

Most of those numbers have been input by me.

That's a very commendable effort - much greater effort than me juggling the numbers and putting ribbons onto graphs. Much more than saying thanks and giving a +, I can't do. But at least now you'll know which numbers to double check

Meanwhile I've calculated the intersection between the functions for ranges 11-36 and 43-60. It's close to 36, so I expect the levels 36 to 42 to use the same formula as levels 43-60.
This would put their expected XP to:

37	5168 XP
38	5548 XP
39	5938 XP
40	6338 XP
41	6748 XP
42	7168 XP

EDIT: I see that the XP tables at DDO wiki have been changed and that they correspond with the extrapolated numbers.
Exceptions are level 40, which is 10 XP off, and level 37, which is calculated by the formula for levels 11 to 36.

[BruceTheHoon]

http://forums.ddo.com/showthread.php?t=311267

As far as I can tell, those are the formulae for calculating crafting success and recipe XP gains, not for determining how much XP is needed to reach a certain crafting level. While they are much more useful, they are not the same.

[pjw]

As far as I can tell, those are the formulae for calculating crafting success and recipe XP gains, not for determining how much XP is needed to reach a certain crafting level. While they are much more useful, they are not the same.

Good point! My only excuse is that its late here. Sorry about that.

The only useful thong I can add is that above level36 the xp requirements are equal to 10 times level....below 36, the analysis above.looks.good to me !

[Lyetisha]

HEY NOW!! I put in some of those numbers too!

Strange that you would put in such a complicated formula. I just did it kind of simply:

XP@Level - XP@Level up = XP Difference1
XP@Level up - XP@Level up2 = XP Difference2
XPDifference1/XP Difference2 = Percentage Increase.

First 20 levels or so the Percentage Increase seemed to be roughly 8% and was slowly decaying. At levels 31-40(ish), the Percentage Increase was around 6-5% still slowly decaying.

[BruceTheHoon]

Strange that you would put in such a complicated formula.

I was interested in exact and explicit expressions. Besides, I don't count 2nd and 3rd degree polynomials as complicated
My guess would be, that the seemingly unusual coefficient values are such, so that the transitions between the functions are as smooth as possible.

[Lyetisha]

Yah well N^n+1 to you!!! =P

[Marten]

Just added 63, 64, and 65. Even if I did not run out of time or TP I don't think I will hit 75 in Divine because several of the high level shards are not in game to grind the exp from... I think I have 3 more shards left and that may get me 3 or 4 more levels meaning I will cap at 68 or 69.

[Lyetisha]

Yah I'm running into the 15/1024 shards myself to keep leveling up. I'm at 60 Elemental. Teens for Divine and Arcane though, so maybe I'll flip over to those =P

[Marten]

Just input the numbers for 67 (20918) and 68 (21598). Not sure if I will be able to get to 69 but if I do I will post it.

Edit:
Just added 69 (22288) and 70 (22988) I am now at 100% crafting chance for all shards in the Divine field that are currently in game.