Crafting formulas

[Aura]

I plan to reverse engineer the formulas for how Exp, Progress Gain, durability loss, etc work based on your stats like level, synth level, craftsmanship, etc. Here's some preliminary data I've collected, along with some observations that people might find useful. The amount of data here is almost nothing, frankly, but it was still enough to draw some conclusions.

Lv. Synth Lv. Difficulty    Control Craftsmanship  Dura. Decrease  Qual. Increase  Progress Increase | Final Quality  + Exp % Total Exp  Base Exp
10    1          9          85        83              10              65              25             |    130         212    112          36
10    1          9          85        83              10              65              25             |    130         212    112          36
10    1          9          85        83              10              65              25             |    195         264    131          36
10    9          42         85        83              10              65              20             |    260         231    953          288
10    13         27         85        83              10              55              13             |    110         90     919          484
10    5          33         85        83              10              65              24             |    325         282    538          141
10    13         81         85        83              10              55              13             |    107         60     774          484
10    14         27         85        83              10              52              11             |    208         155    1269         498
11    14         27         85        83              10              55              13             |    165         125    1120         498
11    14         27         85        83              10              55              13             |    165         125    1120         498
11    14         27         85        83              10              55              13             |    110         84     916          498

Based on this data, we can make some observations.

1. |Base Exp| is affected by either the relationship between |Lv.| and |Synth Level|, or |Final Quality|. The data in rows 8-11 suggests that |Base Exp| is affected by the levels and not the quality, but a comparison of rows 5 and 8 suggests the opposite.
2. |+ Exp%| is affected by |Final Quality|. You can see this by comparing the final 3 rows.
3. |Your Level| - |Synth Level| probably doesn't affect |+ Exp%|. This is because you can still get very high % Increases with items you are high above the level of, even with lower quality. This suggests that perhaps |Final Quality| / |Max Quality| might be involved in the formula (I didn't write down the value of |Max Quality| for any of these.
   
4. |Dura. Decrease| is probably based only on Control, and nothing else.
5. |Qual. Increase| and |Progress Increase| both depend on |Your Level| - |Synth Level|. You can see this by comparing row 5 against row 8.
6. |Difficulty| might factor into the |+ Exp%| calculation, based on a comparison of row 5 against row 8.

More to come in time.

 

[Aangeliceus]

How many synths did you use to compose this data?

 

[Elvier]

Let us know if you need data and how we need to record it.

 

[Aura]

How many synths did you use to compose this data?

Each row is 1 synth, so not many. I have more data in my spreadsheet, this was just a small amount of it. Once I get enough to draw more conclusions (and with more confidence), I'll post more.

Let us know if you need data and how we need to record it.

If you want to contribute data, just post it in the same format as above. The final column |Base Exp|, is computed as =ROUND(|TotalExp|/(1+|Bonus Exp%|/100)). This is the amount of exp you should get in theory with a 0% exp bonus.

 

[Aura]

Update: |Base Exp| is based on |Synth Lv. | and no other factors. Should have an exact formula later today when I'm in front of my computer instead of my phone.

Edit: It's non-linear, so I guess I need more data first. Maybe tonight

 

[Aura]

Just gonna keep posting here as a record to myself so I don't lose track of important information. so my latest findings are:

1. Certain things change for synths where your level is >10 levels over the synth level. One example of this is the Base Exp, but this means other things could change too, so care needs to be taken in analyzing data to account for this.
2. It's possible (although I'm doubtful), that # of steps that you take to finish the synth could affect the Bonus Exp %. Currently I'm chalking this up to a mis-recorded entry in my data, but I can't rule it out yet. Should be easy to test using the GSM ability that makes a turn pass with no decrease in durability or increase in progress.
3. I've seen a synth with 0 quality have +45% Bonus Exp, and I've also seen a (different) synth with 0 quality get +0% Bonus Exp. Figuring out what causes this is probably the easiest way to proceed and get a starting point for more complicated aspects of the formula. It might be # of steps (i.e. point #2 here), or it might be something else, like the synth difficulty.
4. I'm pretty sure durability loss per action is always 10, and nothing can change this.
5. When you do a Quick Synthesis, the amount of exp you get appears to be exactly 1/2 of its Base Exp. This will almost certainly prove to be the easiest way to get the Base Exp for different synth levels.
6. I'm having difficulty explaining the following 2 data entries:

Level   Synth Lv.  Lv. Diff.  Synth Difficulty    Max Quality    Craftsmanship    Control   Qual. Increase    Progress Increase    Final Quality    + Exp %    Total Exp    Base Exp
12        6          6              18               474              83             85          65                24                   325           326         740         174
12        6          6              18               474              56             68          59                17                    59           122         385         173

Base Exp is automatically computed from the other columns, as ROUND(|TotalExp|/(1+|Exp Bonus%|/100)), but the numbers come out differently. There is obviously some rounding somewhere to account for this, but it's unclear where it might be. If we assume that one of the computed values is wrong and that it's either 173 or 174 for both, then going the other direction and computing the Total Exp will not match up. In any case, it's not clear what's going on here.

 

[Aura]

Earlier when I logged in I did a synth with and intentionally got 0 quality, and I got +45% bonus exp. Repeated the same synth and immediately got +0% Bonus Exp. I think the +45% Bonus Exp came from my resting bonus, and it got used up after my first synth.

Later, with no resting bonus, I managed to max out a synth at 100% of it's quality (e.g. 100% HQ rate), and I got a straight +300% Bonus Exp. This leads me to believe that the formula for Bonus Exp is something like the following:

|Bonus Exp| = |Bonus Exp From Quality| + |Bonus Exp From Resting|

|Bonus Exp From Quality| ranges from 0 to 300 and depends on HQ%, and |Bonus Exp From Resting| ranges from 0 to 50, depending on how much rested exp you have left.

This should make it easier to figure out the formula for |Bonus Exp From Quality|, just only test using no rested exp. But it also means the rest of my results are invalidated since I wasn't doing that.

 

[Aura]

So here's an interesting discovery. The Lv. 5 GSM ability Basic Touch has the following stats:

Increases Quality
Efficiency: 100% Success Rate: 70%

The Lv. 18 GSM ability Standard Touch has the following stats:

Increases Quality
Efficiency: 125% Success Rate: 80%

At first glance, Standard Touch seems like a better ability, but it's worse in almost every scenario. Here's why. You need to work out the expected amount of Quality / CP. This is the only important number. The more quality you're getting for a single point of CP, the better.

First, need to mention that using Basic Touch on a Good is worth 125% Quality, and using Basic Touch on an Excellent is worth 400% Quality. With that in mind, here's the table:

              Normal     Good     Excellent
Basic           N        1.5N        4N
Standard      1.25N     1.875N       6N

Here N is just whatever the +Quality formula is going to return based on your current Craftsmanship value and other variables. You can get these numbers through experimentation, or by using the aforementioned multipliers.

Taking into consideration the Success Rates, averaged over an infinitely long period of time, we would expect each ability to return the following amount of Quality per attempt:

              Normal     Good     Excellent
Basic          .7N       1.05N        2.8N
Standard        N        1.5N         4.8N

Finally, if we divide each one by the amount of TP required for the ability, we get the following expected Quality / TP

              Normal     Good     Excellent
Basic         .039N     .058N      .156N
Standard      .031N     .047N      .15N

Since Basic always has a better return than Standard, there are only three situations where you should ever use standard:

1. You're almost out of Durability, and you have to burn as much CP as possible in 1 action
2. You have enough CP for 1 Standard, but not enough for 2 Basics.
3. You have such a surplus of CP that you know (even from the beginning of the synth) that there's no way for you to use it all if all you do is Basic Touch. Then you shoudl use Standard Touch on your Goods and Excellents.

I guarantee you that the first time you use Basic Touch on an Excellent and fail you're going to kick yourself for passing up not only a higher return but also a higher success rate, but the numbers show that you did the right thing

I'm not sure what gear progression is like as your levels get higher, but if it ever gets to the point where you have way more CP than you know what to do with, then this information will be less useful, since you can just use Standard Touch every time. Regardless, as you settle into various gear configurations, you will become pretty comfortable with how much CP you have left over at the end of each synth. The goal is try to schedule your Basics and Standards such that you always end up as close to 0 CP as possible, and if you are going to be using Standard Touch on some synth, try to do it on a Good / Excellent if possible.

 

[Aura]

Just discovered that using HQ materials reduces your exp bonus. This means I also have to do all testing with no HQ materials.

The bonus exp seems to be based off of how much you increase the HQ% from its starting point. So if it starts off at 5% because of HQ materials, and you get it to 100%, you only increased it by 95%, so you'll get less bonus exp than if you had started from 0% and got it to 100%

 

[Aura]

Wiped all my data and started over from scratch last night due to learning that HQ materials and rested exp can invalidate a test result. Good news is that now I have basic graphs of the HQ% function and the Bonus Exp% function. These are particularly interesting because even just by looking at them, with no formula, you can get a basic idea of how to maximize your risk / reward ratio. I'll post graphs tonight.

 

[Aangeliceus]

Thanks for all of the great information, looks like I'll have a nice road map of what to do with crafting.

 

[Aura]

Here's a rough graph of what the exp bonus curves and the HQ% curves look like, as a function of Quality.



I think a few of my entries got screwed up which is why it doesn't look as smooth as it should and there's that bump in the Bonus Exp% graph.

The x axis here means "% of the quality bar that is filled up". So if you fill the quality bar halfway, you'll use an x-value of 0.5.

Looking at this graph, we can see that you shouldn't waste a lot of effort trying to HQ something unless you can get the quality of the item up to at least about 65%, because then your HQ rate explodes after 65% quality. (I believe 65% quality corresponds to roughly 20% HQ rate).

So basically, 20% HQ to about 80% HQ is a sweet spot. It's difficult to get from 0 to 20, and difficult to get from 80 to 100, but very easy to shoot up from 20% to 80%.

Exp on the other hand, is kind of the opposite. If your'e levelling up, play it safe on your quality bar because you can get up to 225% Bonus Exp with only about 50% quality, which is very doable (or at least close to it is doable).

Hopefully I'll have some actual formulas at some point.

 

[Shadowedge]

So here's an interesting discovery. The Lv. 5 GSM ability Basic Touch has the following stats:

Increases Quality
Efficiency: 100% Success Rate: 70%

The Lv. 18 GSM ability Standard Touch has the following stats:

Increases Quality
Efficiency: 125% Success Rate: 80%

At first glance, Standard Touch seems like a better ability, but it's worse in almost every scenario. Here's why. You need to work out the expected amount of Quality / CP. This is the only important number. The more quality you're getting for a single point of CP, the better.

Also, the level 37 culinarian ability, Steady Hand II, adds 30% to success rate for the next 5 steps. These %'s seem to be cumulative, too. i.e. 70% + 30% = 100%. I noticed the same thing with Steady Hand (+20% success) and Standard Touch (80% +20% = 100%). In well over 200 attempts, I have never failed a Standard Touch with Steady Hand active.

This will of course factor more into which of those two abilities is better. If you have enough CP to keep Steady Hand active, Standard Touch could be much better in the long run. Even though the CP/Quality ratio is worse, it will never fail. However, if you have Steady Hand II, you could potentially get a much higher quality boost by spamming Basic Touch.

Things get even more complex once you get Great Strides (doubles the effect of the next touch again).

 

[Aura]

Also, the level 37 culinarian ability, Steady Hand II, adds 30% to success rate for the next 5 steps. These %'s seem to be cumulative, too. i.e. 70% + 30% = 100%. I noticed the same thing with Steady Hand (+20% success) and Standard Touch (80% +20% = 100%). In well over 200 attempts, I have never failed a Standard Touch with Steady Hand active.

This will of course factor more into which of those two abilities is better. If you have enough CP to keep Steady Hand active, Standard Touch could be much better in the long run. Even though the CP/Quality ratio is worse, it will never fail. However, if you have Steady Hand II, you could potentially get a much higher quality boost by spamming Basic Touch.

Things get even more complex once you get Great Strides (doubles the effect of the next touch again).

I'm pretty sure (but not 100%) that I've failed with Steady Hand + Standard Touch. I'll keep an eye out next time though.

You're right that optimizing ability usage is a difficult problem. I've been thinking about it in the back of my mind, I think there's probably a way to figure out an optimal ability sequence with a simple algorithm. If I can program that into an excel function then we should be able to have a spreadsheet just tell you which action to perform next for optimal theoretical results. That's a ways off though.