Wouldn't it be nice to know beyond a shadow of a doubt which item is the cheapest to craft to level a profession? (given good information about the prices of the materials and the value of the results).

Curious about what the skillup % is for various shades of yellow and green?

I set out to test the shape of the skillup curve through yellow and green so that I could better determine how to powerlevel a few professions. It turns out that theoretically I can save 400g over the standard sequence for Blacksmithing on the professions forums.

I started by testing the Runed Copper Rod recipe. Over 62 sequences of leveling enchanting to 10, I gathered the following data.

skill: color: attempts (for 62 skillups): % of skillup
4: orange
5: yellow: 62 attempts: 100.00%
6: yellow: 83 attempts: 74.70%
7: yellow: 107 attempts: 57.94%
8: green: 145 attempts: 42.76%
9: green: 342 attempts: 18.13%
10: grey: assumed 0%

This data has an R^2 of 0.995 with a linear plot. The best fit graph turns out to project skillup % of 97.8%, 78.2%, 58.7%, 39.1%, 19.6%, and 0% for the points listed above. It looks like it's basically a linear function from 100% at the first yellow rank to 0% at the first grey rank.

So if a particular crafting recipe goes yellow at y and grey at g, the chance that recipe will skillup at n is (g-n)/(g-y) subject to a max of 100% and a minimum of 0%.

Validation was done with Bolt of Linen Cloth and Light Armor Kit recipes. They both had linearly decreasing shapes with the coefficients of the equations close to the predicted ones. Not enough tests were run to make that data publishable.

There were also no meaningful correlations between successive notches (ie the time to level from 6 to 7 doesn't affect the time from 7 to 8) or between successive trials (ie the time to level at the same time of day/server state)

Followups:

I'd love to have others verify the formula, especially in high end crafting, but the only viable way would be a tracking mod that merged the data.

It should be possible to incorporate this formula along with a list of when recipes go yellow and grey into tradeskill mods so that they can display the cost to get the next skillup with a given recipe, and even sort a character's recipe list by this cost.

If anyone is interested in the low level trial by trial data I have it. The distributions aren't perfect poisson variables but they looks semi reasonable.

I've created a spreadsheet to display the optimal blacksmithing path for myself. It will save me around 400g, too bad I won't have the Thorium Shield Spike recipe when I'm at 279 (saves another 150g). You can find that spreadsheet at http://files.filefront.com//;7050810;/ if you're interested or want to go to the work to create one for another profession.

All the prices came off Allakhazam over this past weekend as the median AH sale price. I was making a conservative spreadsheet so that the fact that there's a simple formula for the skillup % stands out, rather than an in depth discussion of the spreadsheet.

If you notice because of the value I assign to grinding stones, they are always used to skill up. Elemental Sharpening Stones would work similarly, It will work with negative net costs. However due to lazy spreadsheet programming if cost = value it ends up dividing by 0 on some of my summary tabs. I calculate # crafted by taking total cost and dividing by unit cost as that saves two more big tabs, but causes potential divide by 0 on my summary.


Note:
I'm only moderately skilled at Excel given some of the spreadsheets I've seen, if anyone wants to revise and adjust it to look/work better or have better sale values, feel free.

Is there a way one could find out about an engineering/jewelcrafting skillup?

I'm going to assume that you want to create a spreadsheet to calculate the optimal leveling path along with the expected materials required. If you want to verify the chance to skill % function as skill changes you're going to need to write a popular tradeskill addon or have some other way to get lots of people (be wowhead/curse/etc) to install your software to collect the needed dataset.

The steps that I'd use

1) Gather recipe data, I used thottbot (wowhead also has this data now) to determine the yellow/grey transition points. I used crafterstome to extract the materials used for each recipe. A simple script would easily parse any of the data sites, but crafterstome had the data in a textual fashion (they still do) that didn't require a script, just copy/paste and a bit of manipulation.

2) Create your spreadsheet. My original blacksmithing one could be used as a guide, but it's likely not the best way to do it as I just hacked it together as a proof of concept, not a finalized product.

3) Save money while leveling professions. This is really only a big deal if there's two or more professions that you're going to be swapping frequently to min/max. I think I saved about 500g over the standard 1-300 BS guide that I was going to follow. Since this was on an alt, it wasn't worth the time involved in making the spreadsheet. If you're only doing this once for each of the professions, just take the standardized guides off Blizzard's forums as they are "good enough".

4) If you're a mod author or feel like maintaining your own patch files, hack in an "estimated cost to skillup" into your favorite tradeskill mod. I'm not sure where the data sites get their data on yellow/grey points that are past the current maximum skill as I can't find anything in the UI that would give that information, but that information is out there (it might be in the mpq or wdb files somewhere).

I never did a real statistic, so what follows lies in the realm of the empyrical data. I levelled up to 350ish almost every crafting profession twice, this is my data source. Also, what follows doesn't apply to gathering professions (I never checked).
Of course I have no physical data, as I said what follows is empyrical. The reason why I post this is that it can be useful to compare my experience with those of others, since my feeling is that the skilling up system is not based on a linear law.

#Orange = skill value at which the recipe starts being orange
#Yellow = skill value at which the recipe starts being yellow
#Green = skill value at which the recipe starts being green


1) Orange always gives a point (of course)
2) Most of the time Yellow gives 1 point everytime up to (#Green - 5). Rarely I missed 1 point during this phase.
3) From (#Green - 5) to (#Green) there are some "lost" skill ups. I can't really say a percentage since I avoided them (not usually worth it), my feeling was something around 50% with fewer percentage for the first points and higher for the last ones.
4) Green is worth it only if you craft something you need for later crafts (like Bolts for Tailoring).

The very last point of Yellow, aka (#Green - 1), is sometimes really hard to get.


Putting this all togheter and comparing this to weapon skill up system (many alts equals lots of weapon skill ups at 70) my guess is that the law is more like the weapon skill low, which seems to be exponential to me (since the last points asks for a LOT of swings more than what a linear increase would be, this I checked personally).

Note that the behaviour seems to be a little different at low skill ratings, just to help the start (but this may be a feeling, like I have the feeling that expensive crafts are more likely to give skill ups than cheap ones). This is why the data gathered from Sservis did not disproof my theory, in my eyes.


More specifically, my idea is:

5) Orange progression is constant: always 100% to get the point
6) Yellow progression can be modeled as constant up to (#Green - 5), than is probably exponential (or maybe linear, I sadly have no data to check, but my experience of skilling from (#Green - 1) to #Green and the weapon skill up system point to an exponential law)
Note that I almost never ever lost 1 point up to (#Green - 5), and when I lost, I lost only 1. Also I never ever lost 1 point skilling up to (#Green - 10). So actually the exponential change speed quite dramatically right after (#Green - 5) while it's perfectly constant up to (#Green - 10) and somewhat really near constant in the middle of those points.
7) Green progression is probably exponential (but this point is pure speculation based on the others)

I'd like to provide data, I'll gather them in future, but it can only be after wotlk ships, so if someone is going to do some test on skill ups in gathering profession, I suggest he writes down the percentage of success for every single point while gathering data mostly from recipes with at least 10 - 15 points of yellow, since it's difficult to estabilish a behaviour over 3 points of yellow and 2 of green. Anything could fit those 3 points, not to talk how many curves can fit 2 points (sorry Sservis, your percentage are have a good data base, but you have too few points to decide what's the right fit for them).

I never did a real statistic ... I have no physical data ... my feeling is that the skilling up system is not based on a linear law

The first post in this thread pretty clearly shows that your feeling is wrong. If the formula is (g-n)/(g-y), then the chance decreases linearly as you go from yellow to gray.

Green is worth it only if you craft something you need for later crafts

I don't discount the value of heuristics like this for people who have nothing better to work with, but it seems like we're aiming for something more rigorous here. A rule of thumb like this would be a step backwards. To point out one obvious counterexample, when leveling First Aid: Heavy Linen Bandages go yellow at 50 and gray at 100. Wool Bandages (first learned at skill 80) are yellow from the beginning and go gray at 150. If we assume that the cost of making a heavy linen bandage is one third that of making a wool bandage (which is consistent with the latest AH data, linen at 1g per stack and wool at 6g), then we can use the above formula to figure out where we should make the switch:
(100-n)(100-50) or (100-n)/50 is the heavy linen bandage skillup chance
(150-n)(150-80) or (150-n)/70 is the wool bandage skillup chance

The costs are identical when ((100-n)/50)*3 = (150-n)/70. Solving, you get n=84. Even though the heavy linen bandages are green (past 75 I believe), you should continue to make them until the chance for skillup is only about 30-32%. Wool is too expensive. A similar situation exists when the transition from silk to mageweave bandages is made (again because of a large price difference between the two cloths). A spreadsheet obviously can make a more general calculation based on different price inputs.