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  1. #1
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    Sample size: THREE THOUSAND

    HYPOTHESIS:

    Across a time-cumulative, large sample (numbering in the thousands at minimum), the actual accumulated crit-vs-normal crafting results will align with the crafter’s advertised crit rate.

    METHODS & MATERIALS:

    A combination of Farmer/Cook professions was determined to be the most efficient method to test a large number of crafting rolls. The cumulative sample types for the level 43 supreme master cook would consist of-
    • Cups of Winter Barley Flour
    • Balls of Dough
    • Honey-Cakes

    The intended sample size was 3000, divided across the above sample types and crafted across three days in 9 total crafting sessions. The actual total sample size was 3497 across 11 sessions (yeah, I lied; explanation at the bottom). The cook had 17% native crit chance between mastery (5%) and the superior cooking supplies (12%). The cook toon was level 43 at the time of this writing and thus could only equip that level of tool. No optional critical ingredients nor Scholar-created crafting scrolls were used. All results were logged by placing the /Standard output channel into its own tab. Results were parsed in Excel 2010 and summarily graphed in pretty colors.

    RESULTS:


    I'll let the results speak for themselves and not bother with analysis and conclusion.

    NITTY GRITTY:

    My farmer toon crafted 3000 winter barley across three days (1000 per day); costs were not counted. My cook bought with kinship discount the following materials for a 3-day sample spread:
    • 750 bottles of water
    • 750 drops of fine clover honey
    • 750 pinches of mixed spice

    After the initial 3000 cumulative rolls were completed, additional materials were purchased to convert the remainder ingredients produced by critical success from the previous crafting sessions.

    Cooking costs for three days’ worth of materials covering 3000 items, not including repairs: 4g 814s 50c
    Cooking costs for the bonus round, not including repairs: 1g 605s 88c
    Total costs for experiment, not including repairs or porting: 6g 420s 38c

    DEFINITIONS

    • RNG: The computerized random number generator behaves, theoretically, like a die. With a 17% crit rate, this is like taking a 100-sided die and rolling it. If the die lands on 1-17, you get a critical success. If the die lands on 18-100, then you get a normal result. Thus, even with a known percentage “crit rate,” the actual results are still “random.”
    • Channel (channeling): A timed act with the blue timer bar (such as certain class skills, or mapping, or in this case creating a single craft item)
    • Session: A crafting session is defined here as an uninterrupted series of “make all” channeling.
    • Roll: A “roll” here is defined as a single recipe channeling act that creates a final product(s), with the RNG applying at the end of the channel.
    • Crit rate: The crit rate indicates the probability for the crafter to produce a critical success result for every individual crafting roll. The crit rate does not apply to a total cumulative sample per se. With an 83% crit rate, it is possible to fail a dozen times in a row; the probability of that happening is low, but not impossible.
    • Ingredient: In the Cooking profession, an “ingredient” is a crafted component necessary to complete other cook recipes to produce edible food items. In this case, both “Cup of Winter Barley Flour” and “Ball of Dough” are ingredients falling under my cook’s 17% crit rate.
    • Trail Food: In the Cooking profession, Trail Food is produced from recipes that require various ingredients and a campfire. Trail Food typically gives the consumer a specific stat buff for a 20- or 30-minute length of time. In this case, Honey-cakes were chosen as the testing product.


    Both crafting window and vendor windows were open during every session; the crafting window’s selection was set to whatever item I was making at the time. Superior cooking supplies were repaired whenever they fell to around 40-45/60 without interrupting a crafting session.* The purpose for repairing in this manner was twofold: first to ensure that the cook would not go “afk” and possibly log off after a long period of alt-tabbed crafting, and second to ensure the tools wouldn’t break and inadvertently stop a session.

    *(This could be a bug; vendor interaction including buy/sell/repair is possible after a crit during a single crafting session.)

    Additional areas to be addressed:

    Streak results. I'm really not inclined to look at my logs again for these (and I wouldn't know what to do with it), but... Now, how can I attach a ZIP of logs here. Hmm.

    As a side note, I now have way too many Honey-cakes. Anyone want to buy them...?


    Edit: Mediafire link for ZIP of raw logs

    Edit2:

    Basic streak data (also added to the Lorebook article; lost table formatting here)----

    Here are some basic streak results; I don't know of any way to graph this sort of thing, especially with a data set around 3500. Be aware that I'm counting a "streak" as any identical, adjacent cell, so even a 2-string is a streak here. Keep in mind that my crafter's crit chance was 17%, so getting something like 4 crits in a row on that low probability is quite unlikely. And yet it happened thrice. Therefore, the inverse is true too--with a low failure probability (say 17% which is a 83% crit rate), a crafter can still end up failing a bunch of times in a row.

    Noncrit streaks
    Average 6.9
    Longest: 35
    Median: 5

    Crit streaks
    Average 2.15
    Longest: 4
    Median 2

    Noncrit streak lengths and number per:
    30-40: 1
    20-29: 16
    10-19: 83
    2-9: 308

    Crit streak lengths and number per:
    4: 3
    3: 7
    2: 76
    Last edited by Trilwych; Jul 31 2011 at 09:12 PM.
    [url="https://www.lotro.com/forums/showthread.php?506048-Talent-trees-class-roles-and-player-choice"]Talent trees, class roles, and player choice[/url]
    Crafting crit chance analysis: [URL="https://www.lotro.com/forums/showthread.php?410893-Sample-size-THREE-THOUSAND"]3000 sample size[/URL], [URL="https://www.lotro.com/forums/showthread.php?420198-Sample-size-ONE-THOUSAND"]1000 sample size[/URL]

  2. #2
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    Re: Sample size: THREE THOUSAND

    Excellent work.
    [CENTER][FONT=Book Antiqua][COLOR=dimgray]::: [SIZE=3][URL="http://waywatchersofcardolan.guildportal.com"][COLOR=SlateGray][SIZE=4]T[/SIZE]he [SIZE=4]W[/SIZE]aywatchers of [SIZE=4]C[/SIZE]ardolan[/COLOR][/URL] [SIZE=2]:[/SIZE] [URL="http://palantiri.guildportal.com"][COLOR=LightBlue][SIZE=4]T[/SIZE]he [SIZE=4]P[/SIZE]alantiri[/COLOR][/URL][/SIZE] :::[/COLOR][/FONT]
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  3. #3

    Re: Sample size: THREE THOUSAND

    So, what you're saying is that people were right - actual crit rates *are* lower then what your crit rate score says!

    Gimme back my 0.0712% NOW!


    :-)

    Excellent work! You should put this up in the Lorebook for permanent reference.

  4. #4
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    Re: Sample size: THREE THOUSAND

    Very well done. The only problem with this research, I presume, is that you will never want to cook again.
    Confused about the F2P/Premium/VIP account types? [URL=http://forums.lotro.com/showthread.php?377885-What-happens-if...-answers-about-the-account-types]This post may help.[/URL]

  5. #5
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    Re: Sample size: THREE THOUSAND

    Quote Originally Posted by Trilwych View Post
    Streak results. I'm really not inclined to look at my logs again for these (and I wouldn't know what to do with it), but... Now, how can I attach a ZIP of logs here. Hmm.
    You could try Google Docs, maybe?

  6. #6
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    Re: Sample size: THREE THOUSAND

    Live and in Person, it's SCIENCE! Nicely done...and looks like you need to hold a bake sale

  7. #7

    Re: Sample size: THREE THOUSAND

    Interesting. Well done.

  8. #8

    Re: Sample size: THREE THOUSAND

    Nice work! Now you just have to test ALL the other crafting professions to prove to many folks that the percentages are accurate as stated.

    I must admit, even I'm a bit surprised that it came out that close with such a small sample. With a run of only 3500 (-ish), I'd have probably assumed an error factor of around +/- 2%. Granted, your numbers don't preclude that possibility. Just means your sampling came out "lucky" in that regard. Can't really help myself, though - I don't really trust data samples like this if they don't at least number in the 10s of thousands of samples, just to squinch that possible error factor down tighter.

    Still, as I've already said, nice work.
    The navigation throughout the LotRO site is horrible. You can quote me on that.
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  9. #9

    Re: Sample size: THREE THOUSAND

    Quote Originally Posted by Ashrellion View Post
    I must admit, even I'm a bit surprised that it came out that close with such a small sample. With a run of only 3500 (-ish), I'd have probably assumed an error factor of around +/- 2%.
    3500 is actually overkill. If the probability of a crit is p = 0.17 then the standard error in this test is

    sqrt(0.17*(1 - 0.17)/3500) = 0.0063 or 0.63%.

  10. #10
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    Re: Sample size: THREE THOUSAND

    Quote Originally Posted by Arbalister View Post
    So, what you're saying is that people were right - actual crit rates *are* lower then what your crit rate score says!

    Gimme back my 0.0712% NOW!


    :-)

    Excellent work! You should put this up in the Lorebook for permanent reference.
    I knew someone would point out that difference!
    Eh, I don't have the motivation to fiddle with the Lorebook after this. If anyone else would like to volunteer the effort, go for it.


    Quote Originally Posted by Ozeagle View Post
    Very well done. The only problem with this research, I presume, is that you will never want to cook again.
    At least not these honey things. Farming itself went very quickly, though (wow, I didn't realize they had changed things that much; the last time I did any farming was with all the poor crops and having completely full bags).

    Quote Originally Posted by Roberto_the_First View Post
    You could try Google Docs, maybe?
    Maybe. I don't particularly trust Google to keep things anonymous and such, but I'll get the logs up eventually.

    Quote Originally Posted by Fortinobrand View Post
    Live and in Person, it's SCIENCE! Nicely done...and looks like you need to hold a bake sale
    At least the crit versions should sell.

    Quote Originally Posted by Ashrellion View Post
    Nice work! Now you just have to test ALL the other crafting professions to prove to many folks that the percentages are accurate as stated.

    I must admit, even I'm a bit surprised that it came out that close with such a small sample. With a run of only 3500 (-ish), I'd have probably assumed an error factor of around +/- 2%. Granted, your numbers don't preclude that possibility. Just means your sampling came out "lucky" in that regard. Can't really help myself, though - I don't really trust data samples like this if they don't at least number in the 10s of thousands of samples, just to squinch that possible error factor down tighter.

    Still, as I've already said, nice work.
    Quote Originally Posted by Banatsir View Post
    3500 is actually overkill. If the probability of a crit is p = 0.17 then the standard error in this test is

    sqrt(0.17*(1 - 0.17)/3500) = 0.0063 or 0.63%.
    Banatsir is probably right. It's been well over a decade since I took my one stats course, but I figured this sample was pretty solid for our purposes.

    I really only wanted to address the two most annoying things about the crafting crit rate whines:

    • "It felt like this!" (Note: No feelings were harmed, addressed, nor referenced at all in this experiment.)
    • "I made 12 things and that's totally a valid sample size!" (Note: Er, no. Just... no.)


    So, anyone who wants to whine about a broken crafting RNG... Your complaint is invalid until you show us with a sample size of at least 3000.

    I could see doing a similar experiment with components in other crafts since those stack nicely, but I won't be trying it anytime soon... Unless someone supplied me with the mats, seriously. The problem is that a crafter's native crit rate can't exceed 25% right now (5% proficiency + xx% tool).
    [url="https://www.lotro.com/forums/showthread.php?506048-Talent-trees-class-roles-and-player-choice"]Talent trees, class roles, and player choice[/url]
    Crafting crit chance analysis: [URL="https://www.lotro.com/forums/showthread.php?410893-Sample-size-THREE-THOUSAND"]3000 sample size[/URL], [URL="https://www.lotro.com/forums/showthread.php?420198-Sample-size-ONE-THOUSAND"]1000 sample size[/URL]

  11. #11

    Re: Sample size: THREE THOUSAND

    Quote Originally Posted by Trilwych View Post
    Banatsir is probably right. It's been well over a decade since I took my one stats course, but I figured this sample was pretty solid for our purposes.
    No argument there, couldn't remember the math myself, and it's certainly been at least that long for me, as well. Thanks, Ban!

    "I made 12 things and that's totally a valid sample size!" (Note: Er, no. Just... no.)
    Personally, I'm done being "nice" to folks who make assertions like this, especially when they then claim to have studied statistics. I see it in EVERY mmo I have EVER played. In only a very few has there actually been anything wrong with the expected vs actual results.
    The navigation throughout the LotRO site is horrible. You can quote me on that.
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  12. #12

    Re: Sample size: THREE THOUSAND

    Quote Originally Posted by Banatsir View Post
    3500 is actually overkill. If the probability of a crit is p = 0.17 then the standard error in this test is

    sqrt(0.17*(1 - 0.17)/3500) = 0.0063 or 0.63%.
    Heh, still "too large" an error factor for me, but I'm rather OCD in that regard.

    But thanks again for the math. Been WAY too long for me.
    The navigation throughout the LotRO site is horrible. You can quote me on that.
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  13. #13

    Re: Sample size: THREE THOUSAND

    +rep for the patience to verify the current crafting system. Appears to be accurate.
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  14. #14
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    Re: Sample size: THREE THOUSAND

    Quote Originally Posted by Ashrellion View Post
    I don't really trust data samples like this if they don't at least number in the 10s of thousands of samples, just to squinch that possible error factor down tighter.
    Polling companies all around the world produce results with much smaller sample sizes that 3,500.

  15. #15

    Re: Sample size: THREE THOUSAND

    83% of all statistics are made up on the spot.
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  16. #16
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    Re: Sample size: THREE THOUSAND

    + rep for an extraordinary job!

    Now if the complainers will only take the time to read and understand this . . . .

    I do hope this gets stickied when the inevitable "Turbine Fix the Crafting Crit Chance!!" post arises again.
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  17. #17
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    Thumbs up Re: Sample size: THREE THOUSAND

    Impressive work!
    Now my little hobbit cook can sleep peacefully again
    Glad you took the time to have a closer look - also + rep for your effort.
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  18. #18
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    Re: Sample size: THREE THOUSAND

    That is an impressive piece of research, well done to you for having the patience for it
    Galuhad | Narvelan
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  19. #19
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    Re: Sample size: THREE THOUSAND

    Quote Originally Posted by Slyfinger View Post
    + rep for an extraordinary job!

    Now if the complainers will only take the time to read and understand this . . . .

    I do hope this gets stickied when the inevitable "Turbine Fix the Crafting Crit Chance!!" post arises again.
    Unfortunately it won't matter in the least. There is a large group of players who are very entitled, very loud, and very under-educated who will continue to rage that they can't crit constantly. I mean come on, 75% means that you MUST crit three times out of four, and that's practically every time, so if they aren't critting every single time then the game is broken and Turbine owes them a refund payable in cookies.

  20. #20
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    Re: Sample size: THREE THOUSAND

    Very nice work!

    In 2009 I ran a similar trial... on 3650 crafting attempts across a wider range of professions (Mostly Prospector, Forrester, Jeweler, Tailor, plus a few Weaponsmith and Cook results) over 90 days. I obtained a similar result to yours, where the actual critical rate was .08% higher than the theoretical rate - ie pretty much an exact match. At the time people were mostly complaining that the random number generator was broken. There was also lots of chatter about streaks of losing. I did analyze streakiness of both success and failure at the time and it fell within statistical norms.

    I also measured the in game random number generator output in 2009 over 2500 rolls and again in 2010 over 1200 rolls and it appeared to have a pretty normal distribution of results. I had not looked in along time but I assume the same complaints are rampant.

    So congrats again on a thorough study.

  21. #21

    Re: Sample size: THREE THOUSAND

    +rep and deserved. thank you.
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  22. #22
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    Re: Sample size: THREE THOUSAND

    Quote Originally Posted by demosthenes View Post
    Very nice work!

    In 2009 I ran a similar trial... on 3650 crafting attempts across a wider range of professions (Mostly Prospector, Forrester, Jeweler, Tailor, plus a few Weaponsmith and Cook results) over 90 days. I obtained a similar result to yours, where the actual critical rate was .08% higher than the theoretical rate - ie pretty much an exact match. At the time people were mostly complaining that the random number generator was broken. There was also lots of chatter about streaks of losing. I did analyze streakiness of both success and failure at the time and it fell within statistical norms.

    I also measured the in game random number generator output in 2009 over 2500 rolls and again in 2010 over 1200 rolls and it appeared to have a pretty normal distribution of results. I had not looked in along time but I assume the same complaints are rampant.

    So congrats again on a thorough study.
    Yes, your posts helped encourage me to even try this; too bad most of that was purged--care to graph your 2009 crafting results as well? I think it'd be cool to see.

    I'm very curious how you analyzed streakiness, since I'm at a loss as to how that could be graphically represented (let's face it; most people are very visually inclined).
    [url="https://www.lotro.com/forums/showthread.php?506048-Talent-trees-class-roles-and-player-choice"]Talent trees, class roles, and player choice[/url]
    Crafting crit chance analysis: [URL="https://www.lotro.com/forums/showthread.php?410893-Sample-size-THREE-THOUSAND"]3000 sample size[/URL], [URL="https://www.lotro.com/forums/showthread.php?420198-Sample-size-ONE-THOUSAND"]1000 sample size[/URL]

  23. #23
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    Re: Sample size: THREE THOUSAND

    Quote Originally Posted by Siaer View Post
    Polling companies all around the world produce results with much smaller sample sizes that 3,500.
    Yes, but those results have margins of error several times the size of this test's. Most opinion polls run at 2-3% margin of error, and this test has 0.63%. Of course, as the margin gets smaller you need proportionately more data to decrease it by another interval, so... yeah.
    Last edited by ANewMachine; Jul 30 2011 at 12:21 PM.
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  24. #24
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    Re: Sample size: THREE THOUSAND

    +rep for this!

    As a lowly Liberal Arts major who struggled with Algebra, forget comprehending statistics ...

    Would it be of any use for me to track my crafting sessions over time? I would be more than willing to contribute data to a wider study of crits over multiple players, if doing it in small batches would add up to anything useful.

    One idea I had a while ago during the height of the ZOMGCRITSUX angst was to roll a new character and track their crafting through their life. I am - despite my mathematical failings - fairly adept with Excel, and could set up a system that would be able to show critting over the lifetime of the character with an overlay of skill, tools and the like.

    But that being somewhat optimistic a goal, I don't mind tracking crafting across my characters as I do it. Would it be at all useful?
    Last edited by ArmoiseFrogjump; Jul 30 2011 at 12:38 PM. Reason: spelling requires coffee
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  25. #25
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    Re: Sample size: THREE THOUSAND

    Quote Originally Posted by ArmoiseFrogjump View Post
    +rep for this!

    As a lowly Liberal Arts major who struggled with Algebra, forget comprehending statistics ...

    Would it be of any use for me to track my crafting sessions over time? I would be more than willing to contribute data to a wider study of crits over multiple players, if doing it in small batches would add up to anything useful.
    Yes. My trial was done over three days because it's possible for farmer/cook to do large samples in a short period, but the hypothesis should hold true for, say, 3000 cross-craft items (e.g. metalsmith + tailor) across three months, the way demosthenes did it. I think it'd be ideal to track 2k-3k within the same profession across 3 months, however, if only to address that special-snowflake profession-specific angst. (Oh ####, I should've tracked all crafting for my little scholar. Scholar would be expensive!)

    One idea I had a while ago during the height of the ZOMGCRITSUX angst was to roll a new character and track their crafting through their life. I am - despite my mathematical failings - fairly adept with Excel, and could set up a system that would be able to show critting over the lifetime of the character with an overlay of skill, tools and the like.

    But that being someone optimistic a goal, I don't mind tracking crafting across my characters as I do it. Would it be at all useful?
    It's always useful. It's important to keep notes about the general surrounding and what else you did on top of the pure logging--for example, my little cook couldn't wear the horseshoe. With the power of Excel and understanding some basics (e.g. what a "percent" actually means), you don't need to be a mathematician or engineer to output useful data. I'm certainly not either!
    [url="https://www.lotro.com/forums/showthread.php?506048-Talent-trees-class-roles-and-player-choice"]Talent trees, class roles, and player choice[/url]
    Crafting crit chance analysis: [URL="https://www.lotro.com/forums/showthread.php?410893-Sample-size-THREE-THOUSAND"]3000 sample size[/URL], [URL="https://www.lotro.com/forums/showthread.php?420198-Sample-size-ONE-THOUSAND"]1000 sample size[/URL]

 

 
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