So, I obviously don't post here frequently, but I do lurk quite a bit. I've recently done a few studies on various crafting mechanics and figured I'd share my results, since they may be of interest to some of you. I have most of these in an Excel spreadsheet, but haven't bothered to upload it on Google, so bare with me if I don't share the raw data. Most of these results are fairly easy to confirm for yourself.
First, I performed a bunch of different crafts with varying class and recipe levels in order to figure out the relationship between Control and Quality Gained. To do this, I started a recipe, used Steady Hands and performed a Basic Touch (100% efficiency) a number of times at different levels of Control, ignoring an result not on Normal condition. I also repeated the process with Inner Focus active to determine the mechanism of that buff.
The results indicate that Control and the basic quality gain are a nice, simple linear function (with R-squared of 0.9997, for those that care) of:
Code:
"Base Quality Gain" = 0.36 * (Control) + 34
This "Base Quality Gain" is of course multiplied by the Touch efficiency and other boosts, such as Condition modifiers.
Another finding from this test is that your crafter level and the difficulty of the recipe have no effect on the amount of quality gained. In other words, a successful Touch will add the same quality on a level 10 recipe as a level 50. -Later testing shows this to be inaccurate. Each level that a craft is above your job seems to cause a 5% reduction in quality gains. See following posts for details. - Rehwyn
Second, Inner Focus is a 20% boost to Control per prior successful Touch. After five successful touches, your Control is twice what it was at the start. After ten successful touches, it's triple. However, because of the relationship between Control and Quality (see above), it is not a 20% boost to Base Quality Gain per prior Touch. Without going into the details, Inner Touch adds less additional quality with low base Control (5.3% greater Quality per prior Touch with 34 starting Control) and gradually increases, reactiong 9.8% greater with 90 starting Control and (based on the above formula) 15.2% greater Quality per prior touch at 300 Control. Eventually, it'd get close to 20% greater per touch, but that would require Control far higher than possible.
Here's a chart of how much the Base Quality Gain is improved per prior Touch, based on the above formula.
Code:
Base Ctrl Qual Increase per IF#
50 6.92%
100 10.29%
150 12.27%
200 13.58%
250 14.52%
300 15.21%
350 15.75%
In other words, if you had 200 Control when you started and have used five Touches since Inner Focus, your next Touch will add 67.9% (5 * 13.58%) more Quality than if you had not used Inner Focus. Even without Byregot's Blessing, Inner Focus becomes CP efficient rather quickly with any decent amount of Control.
The Inner Focus test was relatively simple, because you can actually see the change in Control if you open your character tab. Still, I related the results I got to the previous formula and confirmed the Control value in the character sheet was accurate.
On a related note, it is for this exact same reason that Innovation will not cause a 50% increase in Quality, since it is a 50% Control boost instead. What I'd like to test is how Innovation and Inner Focus affect each other, but I unfortunately do not have 50 goldsmith to test it. If they are multiplicative of each other, at the end of Hasty/TotT spam, throwing it in like Innovation > (Hasty/Basic) Touch > Great Strides > Byregot's Blessing would be even more ridiculous for the mere cost of 18 CP and 0 Durability.
Third, I tried to derive the formula for Quality to HQ Chance, but it proved a bit beyond my means. To test this, I took Current Quality and divided it by the recipe's Max Quality, giving a % Quality. I recorded this value and the HQ % Chance at a variety of different levels. The results somewhat match a logistic function with an inflection point around 75% Quality, but running a logistic regression in excel is a pain and the graph didn't quite match by visual inspection later on anyways.
The important conclusion from that test, as I'm sure people have noticed by now, was that the HQ chance is very flat until about 70% Quality, where it is about 25% HQ chance. After this, it shoots up to around 75% HQ chance at 80% Quality and then more gradually approaches 100% HQ chance. Based on this, you can look at the max quality of a recipe and estimate approximately how much quality you have to gain before your HQ chance becomes decent.
Lastly, there was some question on how much CP Rumination returns. It's actually very simple, based on my observations:
Code:
IF# CP Return
1 15
2 24
3 32
4 39
5 45
6 50
7 54
8 57
9 59
10 60
While I did not personally test all of these, you'll notice that it starts at 15, then increases by 9, then again by 8, then by 7, 6, 5, 4, etc. I'd assume that at 11+ prior Touches, Rumination would continue to return 60 CP and not increase any further.
While the above information doesn't exactly show a new method or steps of crafting, I hope this information was helpful and not too boring. Let me know if anything seems off and I'll see if I can look into it more.