skillup formula

[Ngreth Thergn]

I will try and remember to change the cap, but tairne is probably correct.

If I forget and have nto changed this in a while, post in DenMom's corner.

[Yakk]

Skillup math in DoN, with max/stats, at 190+ skill:

Stat caps:
The base stat cap is 365 now.

Max int/wis is 415
Max str/dex is 450
Max cha/agi is 365
Max sta is 405

Skillup chances per combine:
Y=2, no alternate stat: jewelcrafting?, brewing
5% chance of skillup with max stat, success or failure
Y=3, no alternate stat:
5% chance of skillup, sucess
3.33% chance of success, failure
Y=4, no alternate stat: pottery
5% chance of skillup, success
2.5% chance of skillup, failure

Y=2, dex/str alternate stat: jewelcrafting?
5% chance of skillup, success or failure
4.6% chance of skillup on failure, no wunshi
Y=3, dex/str alternate stat: tailoring
5% chance of skillup, success
3.75% chance of skillup, failure
3% chance of skillup, failure, no wunshi
Y=4, dex/str alternate stat: smithing
5% chance of skillup, success
2.8% chance of success, failure
4.6% chance of skillup on success, no wunshi
2.3% chance of skillup on failure, no wunshi

Y=2, str alternate, shaman using Ancestral Aid:
5% chance
Y=3:
5% chance on success
4.5% chance on failure
Y=4: smithing
5% chance on success
3.4% chance on failure

(The formulas used:
chance of skillup = 5% * modifier.
SuccessModifier = EffStat*10/Y / 1000, or 1: whichever is less
FailureModifier = EffStat*10/Y/2 / 1000, or 1: whichever is less
EffStat, no alternate stat = 400
EffStat, dex/str alternate = 450
EffStat, shaman AA, str alt = 540
)

Enjoy!

Edit: added in ancestral aid

[nightjackal77]

You forgot the Stat cap modifier for Tribute...you can get to a 550 str with it and shaman AA

[Yakk]

Good point!

However, grabbing the success rate formula:

skill - (trivial*.75)) + 51.5

250 skill, with a 5% geerlock, on a 300 trivial recipie:
88% success rate

Which means only 12% of your skillup combines should be failures, if you have a good recipie to work with.

So your rate of skillups per combine will be at least:
5% * .88 + .12 * 2.8%
=
4.7%

In other words, if your average success rate is over 75%, you will need on average between 1000 and 1100 combines to gain 50 skill points.

As noted above, past a certain point (400 in a stat), every tradeskill has a 5% skillup rate on successes.

For failures, every 10 points of stat increases your skillup rate by:
Y=2: 0.01250%
Y=3: 0.00833%
Y=4: 0.00625%

In terms of total number of combines to gain 50 skill points, every 10 stats saves you:
(average of 90% success rate)
Y=2: about 1 combine
Y=3: less than 1 combine
Y=4: about half a combine

That's the difference you'd see in a 1000 skillup run with an average 90% success rate.

If there was an average 50% success rate:
Y=2: about 5 combines
Y=3: about 4 combines
Y=4: about 3 combines

This should hold true for stats greater than 400.

Going from 400 str to 540 str would thus save you about 42 out of roughly 1000 smithing combines. (540-400)/10 * 3 = 42

A more precice model doesn't seem worth it at this point. =)

[Ngreth Thergn]

I changed it so that the calculations have no cap on the Stat.
The form itself is still limiting you to 3 digits so... you can make your wild check at what you would get with a 999 stat, even if you can't get to that yet

[Yakk]

My math above estimating the number of additional combines is sadly wrong.

The number of combines when your skillup chance is near 5% is:

50 / (1/20 - e)
where (0.05 - e) is your skillup chance.

Ie, if skillup chance is 5%, it takes
50 / 0.05
attempts to gain 50 skill points, or 1000 combines.


Simpiflying, this gives:
1000 / (1 - 20e)
or, with e between 0 and 0.05:
1000 * (1 + 20 e + 400 e^2 + 8000 e^3 + ...)
(because 1/(1-x) = 1+x+x*x+x*x*x+x*x*x*x*x+... etc, for x between 0 and 1)

with e small relative to 0.05, 1+20*e is a decent first approximation.

Let f = e * 100 (in other words, if e = 0.000125 or 0.0125%, then f = 0.0125)
Then it takes
1000 + 200 * f
combines to gain 50 skill points.

If you succeed half the time on average, and each 10 points of stat gives 0.01250% greater chance of skilling up, then each 10 points of stat saves you about 2.5 combines in your 1000 combine run.

The result is half of what I got earlier. Not that anyone probably cares. =)

To make the conclusion clear:
Every 10 points of stat over 400 saves you at most 3 out of 1000 combines, and about half that on smithing.

[miakiss]

Is there any consensus on the Y numbers associated with the various skills?

The reason I ask is that I have just been skilling up in both pottery (to 248 so far) and jewelcraft (to 270) and despite jewelcraft having a conjectured Y of 2, and pottery of 4, the pottery skill-ups came faster (about 1 in 20) than the jewelcraft ones (about 1 in 30).

At first I thought I had got confused about the formula and had them switched around, but apparently not.

All combines were done at max success chance (with no AAs) and stat of 280.

Of course it could easily just be the luck of the RNG...

[emandes]

At the edge to blow up tradeskilling

Taking in account what Absor stated about the future of tradeskilling I do think he is not playing our game at all.

I have smithing at 225 mit 15% mod wsh maxed 340 str maxed 430 when I do smithing. Started OoW smithing when I have ended with evb (triv 222) and I did succeed approx. 100 combines of magnetic armour and 20 combines of inlays for augments.

The material for these combines where given to me by my guild i.e. 60 chars playing from time to time in mpg succeeded in farming these components.
Absor - do you think your future plans on diminishing the number of skillups on these combines will keep players in EQ? I am playing a pala 70 for 4 h a day (minus 3 days of raiding) and my pala is ubar in solo camping components that drop from lvl 60+ mobs - I don't like to farm my non raid time of game for things like windstone or shadowscream components. An average game time of 34 h a week should be the measure for all the time you have to spend in tradeskills. I do think that 1 h for camping components for a skillup in the range 200 to 250 and 2 h for the range of 250 to 300 should be enough effort the average eq player should have to invest.

Its annoying to sit there clicking on the combine bar 60 times trying to skillup from 208 in pottery via unfired planar stein (wsh 340) and having no skillup at all. When I was lucky, I just had to check out quiet a number of NPCs to get the needed components but with decreasing server population there is no successfull NPC grinding anymore.

If you still stick to these numbers of combines to have a skillup - enhance the tradeskill container again - add an option to it: "continue combines till components are used up" so that we can do this boring part of the game during afk (biorun or lunch break)

I do have a suggestion:
1.) Don't screw up the loot propability for items that have a reasonable usage in game e.g. magnetic armor and the upgrade item lightning core (the whole guild just had 4 to drop since oow was released). The same is reported with DoN - the magic dragon scales only drop in group missions with the droprate screwed up after 2 weeks (being now 1 every 6 h versus 1 per h)
2.) Implement the defined skillup propability as soon as possible and assign it to magnetic, bazu, feran, don, elemental armor recipes.
3.) Implement recipes like minotorous brew (triv 248) in brewing in every tradeskill to allow a cashdriven path to at least 250 in skill with a skillup propability of 5% and the continue combine option (for afk usage)
4.) Each combine should contribute to a sort of experience bar in different manor (resulting from the formular actually used) and the experience bar being displayed in the tradeskill container. A fails contributes with at least 1% a success with 2% and by random numbers this can reach 10% for fails and 20% for success. I.e. at least 50 success combines would definitely result in a skillup. If the formular results in a skillup by chance the experience bar is reseted to zero. This would allow the tradeskiller to calculate combines and would make tradeskilling more realistic and "inline" with all the other experience oriented parts of eq.

[Sklak]

New formula guess

Haven't seen anything official yet, sorry if real info available somewhere.

This is just speculation based on public announced info by Absor that total # combines from 0-300 would go down by about 15%, while combines from 250-300 up by about 20%. Plugging with those numbers and the old formula results in a very simple change that would match the figures:

Given existing formula for skillup on success (ignoring failures for simplicity):
Old Probability of skillup as a percentage = Higher of (200 - skill) / 2, or 5%

Guessing new formula will be:
New Probability of skillup as a % = Higher of (200-skill) / 2.5, or 4%

Results in 4% minimum skillup chance coming into effect at 240+ skill, vs. old formula where 5% skillup chance started from 190 skill.

This simple change results in 13.6% reduction in combines required to reach 300 (ignoring failures for simple calculation), however, increases combines from 250-300 by 25%.

(With guess that Absor mistakenly thought 5% skillup to 4% skillup change = 20% increase in combines, when it is really a 25% increase....)


Another possibility is that the minimum skillup chance was set at the odd 4.167% which is what is required for a 20% increase in combines required above 250. Using 4.167% instead of 4% as minimum results in about 15.7% overall reduction in combines from 0-300. While possible, I'd wager the code was set at 4% skillup minimum...

Again, purely speculation, but this is a very simple model change that fits the info provided.

Side effect if this formula guess is correct -- gettting to 220 skill (e.g. for Aid Grimel) will be vastly easier (# combines required reduced by more than 50%).

[Sukrasisx]

Given existing formula for skillup on success (ignoring failures for simplicity):
Old Probability of skillup as a percentage = Higher of (200 - skill) / 2, or 5%

Guessing new formula will be:
New Probability of skillup as a % = Higher of (200-skill) / 2.5, or 4%

That can't be right. (200-skill)/2.5 would drop to 4% at skill = 190, i.e., the same point when the old formula hits 5%. You seemed to think it wouldn't bottom out until skill 240?

Anyway, the old formula used a first step that didn't depend on current skill, then a second check that did. The second check was reported to be "ran(200) >= min(skill, 190)". This means the latter check would fail skill/200 of the time, but never fail more than 95% of the time. The first check just means that the actual chance of passing both checks is reduced by some constant (on average). Now, they could change that constant by fiddling with the first check as well. More on that later.

The expected number of combines for a skillup when you have probability P per combine, is 1/P. So you can take the sum of 1/P for all skills 0-299, or all skills 250-299, to see the expected total number of combines to get to 300 from either 0 or 250, respectively, looking only at the cases where you get past the first non-skill-dependent check. I did that for the old formula, and then tried tweaking the numbers "200" and "190" to see if I could get a new formula with the +20% and -15% average total combines we've been told to expect. I couldn't find any numbers that worked, unless the first check also changes. For example, if the first check is made twice as hard (or, if you like, they add a third check that passes exactly half the time), then "ran(300) >= min(skill, 285)" is in the right ballpark. (It's actually 30% harder from 250-300, but comes pretty close to the 15% savings from 0-300.)

The problem is, we don't really have any idea if they've made the formula fancier in other ways, such as having a cap on passing the second check, as in, ran(xxx) >= min(yyy, max(zzz, skill)). There are lots of fairly simple changes to the formula that could yield the +20% / -15% figures, and without more data it's hard to speculate. Or rather, it's far too easy to speculate, and hard to have any basis for the speculation!

[Sklak]

Ah yes, messed up basic algebra there in translating spreadsheet back to text... what I was actually trying to do was equivalent to If Random (250) > min (skill, 240), though with a small techical error :/


However, keeping things simple, a better fit, designed to match the 20% increase in combines from 250-300 (4.167% chance instead of 5% chance):

Skillup formula (new) = IF Random (240) >= MIN (skill, 230)

Exactly 20% increase in combines above 250, and about 13% reduction in total combines from 0 to 300, by simply adding 40 to both parameters in the old formula.

Or using 242/232 gives 21% increase in 250+ combines, 14% reduction in total as slightly better fit. But as you said, very easy to speculate

[Sukrasisx]

Judging from some of what Tanker said in another thread, it sounds as though SOE is using different formulas depending on where in the 0-300 range you are. (He spoke of using the old formula if skill < 150.) So it could be very hard indeed to guess what they've done. But even easier to speculate!!

[Prelgor]

I have no fear of speculating. Either I'll be right, and seen as visionary, or wrong, and likely just forgotten.

Let's assume we have a function break at 150, and assume the function is continuous with what the old formula gave us (i.e. 25% to pass the second check). Assume we keep the same functional form Probability of Skillup=(A-Skill)/B. Assume that we bottom out at a 4% skillup chance. Assume that 250 is the breakpoint (easier than the old formula below 250, harder above 250). I solve this to get A=275 and B=500, so a skillup requires [275-min(255,Skill)] be greater than a random number 1-500. These assumptions are admittedly questionable, but they should give us ballpark numbers.

This model gives about what was described. Total combines for 250-300 go up ~23% and total combines 0-300 go down ~17%.

However, a striking gross feature is that combines in the range 150-250, and especially 180-205, are dramatically reduced. A post by Eggszecutor (in another thread) gave a skillup rate of ~6.5% around skill 190-ish, while this model predicts around 16-17% skillup rate. The primary stat in Eggs' test was very high, and he was attempting trivials near his skill, so it is not credible that he failed the first check almost a third of the time. Either Eggszecutor's results were skewed (wacky RNG, another manifestation of the skillup bug) or this functional form cannot be correct. This model requires, and indeed I thought we were led to expect, a dramatic improvement in skillup rate around 190-ish.

[Elfdruidess]

Is there any consensus on the Y numbers associated with the various skills?

The reason I ask is that I have just been skilling up in both pottery (to 248 so far) and jewelcraft (to 270) and despite jewelcraft having a conjectured Y of 2, and pottery of 4, the pottery skill-ups came faster (about 1 in 20) than the jewelcraft ones (about 1 in 30).

These were the latest estimates I can find from doing a search on this site. Correct me if a newer set is available. They are from Suani, last edited on 19 May 2004 (to change JC from 3 to 4).

Baking 3
Brewing 3
Fletching 4
Jewelcraft 4
Pottery 4
Smithing 2
Tailoring 2

My drive from 250 to 300 just before the patch of Apr 12 finds nothing to disagree with this set of Y values. I agree with Suani that JC is the hardest to determine. It's definitely more than 3 but not quite 4.

[Footsore]

From Absor's post on 03-18-2005:

In the near future (not this next update), we will be introducing a new feature to the tradeskill system that will allow us to add a new flag to some of the recipes that require more difficult to find items. We haven't given it a name yet, but this new flag will allow us to set a minimum chance to gain a skill increase on specific recipes. Basically, if we assign a minimum skill increase chance of 50% to a recipe, then there will be no less than a 50% chance of gaining a skill increase on that recipe.

Any idea if this made it in this last patch? There's been a couple patches since his post, no?