Is it better to use Geerlok, or WIS +10 item? Surprising answer! (Long post w/math)

[scarbrowed]

OK, now that we have all the formulae, I could not resist answering this age old question. The question is who to use as a test case. I thought about my own experience skilling up baking. When I was trying to get past the 190's I could only afford WIS gear up to about 200 or so. So my test case is:

A mid 30's druid with WIS 200 normally, but only WIS 190 with geerlok equipped. I'm making HMP's, and the market for HMP's has crashed, so I only care about skillups.

Here's where it get's long. How do we calculate the odds? First, lets try without the geerlok. We need to calculate the odds of success and failure, then the chances of a skillup with each.

According to the formula from the FAQ, the chance of success is: (191 - (226*.75)) + 51.5 = 73% = 0.73 as a fraction.

Now the chance of skillup has 2 checks. The first check formula is N = ((200-15)* 10)/ (2*1) = 925. So the first check succeeds 92.5% or .925.

The second check is ran(200) >= 190. Since ran(200) on most systems is really 0-199, there are 10 numbers out of 200 that work, so the odds are 1/20=.05. So the overall chance of a skillup on success is .05*.925=.04625.

(Having fun yet? Skip to the BOLD text at the bottom if you hate math.)

The chance for failure is 1.00-0.73= 0.27. The first check for failure is:
N = ((200-15)*10)/(2*2) = 462.5. So the first check is 46.25% or 0.4625.

The second check will always be .05 for all the below calculations, since skill is over 190. So the over all chance of skillup on failure is .023.

To put it together, the chance of skillup without geerlok is .73*.05 + .27 * .023 = 0.04.

OK, with geerlok, the WIS drops to 190, and the effective skill goes to 200.

The chance of success is now: (200 - (226*.75)) + 51.5 = 82.55% = .8255.

The first skillup check is now: N=((190-15)*10)/(2*1) = 875 => .875 chance to pass first check. The second check is still .05, so the over all chance is now 0.04375.

For failure, N= ((190-15) * 10)/(2*2) = 437.5 => First check is .4375. So the overall chance on failure is now .475 * .05 = .021875.

Putting it all together the overall chance of skilling up with geerlok is now: .8255 * .04375 + .1745 * .021875 = .039933.


RESULTS: The odds are so close, that in this case it doesn't really matter. So using the geerlok is probably the way to go.

Of course, I just cancelled my hosting account, so I have no way to automate this formula. Except maybe figuring out Excel, which I'm not looking forward to.

Edit: I did this by hand the first time, and rounding errors changed the results.

Further Edit: Baking does not have a secondary skill, so I forgot the -15 in the formula. Adding it switches the answer again.

[scarbrowed]

I have it in an excel spreadsheet

I now have the formulae above in an Excel spreadsheet. It's ugly, but I think it works. If you have a main stat of 255, and it drops to 245, when tailoring Wyvern masks, you have a 4% better chance of skillup w/out the geerlok.

If anyone cares, I'll happily email the spreadsheet around. If not, I'll putter in my own little world. Have fun all!

[Tingteng]

So you're saying without geerlok I have a .000077 better chance at a skillup?

woot bye bye geerlok

[elty]

In general, unless you can increase your stat by more than 8.5% by equipping something other than geerlok, you should always use a geerlok after skill 210 (or more likely 205) to get maximum skill up rate. (by complicated calculation)

for example, your wis without geerlok is 200. If you cannot find a wis item give 17 more wis, then you better use your geerlok

[Nizanko]

If your skill is 190 or above, the only reason to use a geerlok is to ensure that you succeed on the combine. If that's the case, and you're working on items that are already at the 95% max success rate, then there's no point in using the geerlok.

At lower skill, using a geerlok is probably much better than using the wis item.

[scarbrowed]

Actually, Nizanko, now that we know skillups are more likely on success, even at high skill levels, you should probably use the geerlok.

To back up elty with an example, I'm working on tailoring with a current skill of 220. I can manage a WIS of 255, but only 247 w/out a geerlok. When making any Velious armor, I'm 4% more likely to skillup using the geerlok. And over 10% more likely to succeed on the recipe.

[Nizanko]

I think that's what I said

[Lickity]

Scar, I am very interested in the spreadsheet if you are willing to e-mail it to me. I tried to send you mail directly, but your address wasn't in your profile, mine is doctorlimes@hotmail.com, I appreciate it =)

[eriadoc]

/em scratches head

This is clear as mud, since I don't have a degree in quantum mathematics. So I'll just ask outright ... 290 INT, 229 baking skill without geerlock. 265 INT with geerlock. Sounds like I need to ditch the geerlock, but not sure. Thanks for any help.

[Ariaya]

Re: /em scratches head

Originally posted by eriadoc
This is clear as mud, since I don't have a degree in quantum mathematics. So I'll just ask outright ... 290 INT, 229 baking skill without geerlock. 265 INT with geerlock. Sounds like I need to ditch the geerlock, but not sure. Thanks for any help.

According to my math ...
At 290 INT / 229 skill -> Skillup chance = 5.81%
At 265 INT / 229 skill + geerlock -> Skillup chance = 5.64%

Ditch the Geerlock

[edit: These calculations were assuming that you were making Planer Fruit Pies for skillups (trivial 282) ... the chance of skilling up increases if you use something closer to your level .. but it seems to still be better if you don't use the geerlock]

[Bregalad]

Maybe I got some mistake here, but here are formulas I ended up in Excel with:
Part I. Success chances, given skill and trivial. I work under ussumption that that success chance is always between 5% and 95% for items that triv above raw skill level.

Cell A2: raw skill
Cell B2: item trivial
Cell C2: skill hardness (2 for baking)
Cell D2: % Success without Geerlok = max(min((A2 - (B2 * 0.75) +51.5),95),5)
Cell E2: % Success with Geerlok = max(min(((A2 * 1.05) - (B2 * 0.75) +51.5),95),5)

At 191 skill, 226 trivial, I get 73 in D2 and 82.55 in E2.

Part II. Skillup chance, for base stat, and adjusted stat.
Cell F2: Stat. Don't forget to subtract 15 for skills that need it.

First check portion of the formula:
N = (Stat * 10)/(2*F). if rand(1000) < N, 1st check succeeds, so I figured, chance of check 1 succeeding is min(1,N/1000) The min is needed because for adjusted stat values above 200, at high success rates, N can run WAY above 1000: For example, at 355INT (340 adjusted) and 95% success chance in hardness 2 skill, N becomes a whopping 1619. But in reality, 1619 or 1001 makes no difference - once past 1000, only 2nd check counts.
Factoring 1000 into N calculation, N = (Stat * 10)/(2000 * F)
F is a 2 at fail, 1 at success. Meaning actual value of F is (2 - chance to succeed), or (200 - success%) / 100
Thus, final formula for first check is:
min(1,(Stat * 10)/(20*(200 - success%)))

Second check portion of the formula is easy: (200 - min(190, skill))/200

Ok, final formulas:
Cell G2, skillup chance without geerlok =MIN(1,(F2*10)/(C2*10*(200-D2))) * (200 - MIN(190, A2))/200
Cell H2, skillup chance with geerlok =MIN(1,(F2*10)/(C2*10*(200-E2))) * (200 - MIN(190, A2 * 1.05))/200
Note that I apply the geerlok effect to 2nd check as well.

In original poster's case, I get:
Skillup chance at 191 skill on 226 triv item at 200 wis (185 adjusted) without geerlok: ~0.03642
Skillup chance at 190wis (175 adjusted) with geerlok: ~0.03725
That is, about 0.1% difference. For some, an extra skillup per 1000 combines is a blessing.
-----------------

Plugging in numbers for eriadoc:
At 290INT (275 adjusted), you have 5% chance to skillup regardless of geerlok.
At 265INT (250 adjusted), with geerlok you still got the very same 5% chance.

However, at 226 raw skill and 282 trivial, you have 69% success chance without geerlok and 80.45% chance with it. So if you want to minimize failure rates, you are better off with geerlok.