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EQTraders - Apparent Skill-Up Chance Formula (2014-08-04)

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  • EQTraders - Apparent Skill-Up Chance Formula (2014-08-04)

    I only just today realized that I never went over the actual formula in the other two posts I made.

    If the Calculator on this website is correct, and it seems to mesh pretty well with my personal experiences so far in-game as I've planned out component acquisitions based on it, then the current skill-up chance formula appears to be as follows, as formatted to work in Excel:

    MIN(1,((([CharacterStat]+[TradeStatAdjustment])*10)/([TradeDifficulty]*([SucceedOrFail]))/1000)*(((200-MIN(175,[CharacterSkill]))/200)-0.0008*(MAX(0,MIN(299,[CharacterSkill])-175)))

    I'll break it down here:

    [CharacterStat] = Your character's highest of INT/WIS/SecondaryStat
    [TradeStatAdjustment] = The 0 or -15 adjustment from the Tradeskill Difficulty/Adjustment table (copied below for convenience)
    [TradeDifficulty] = The difficulty level from the Tradeskill Difficulty/Adjustment table (copied below for convenience)
    [SucceedOrFail] = 1 if successful combine, 2 if failure
    [CharacterSkill] = Your character's current UNMODIFIED skill points in the tradeskill (modifiers affect your chance of a successful combine, which can affect your skill-up chances via the SucceedOrFail value, but they do not directly affect your chance of a skill-up)

    1. MIN(1,((([CharacterStat]+[TradeStatAdjustment])*10)/([TradeDifficulty]*([SucceedOrFail]))/1000)

    This is the Stat Check portion of the formula, where your character's max of INT/WIS/Secondary comes into effect to see if your character is smart enough to have gained a skill-up from the combine.

    The MIN(1,...) part of it simply limits the chances of a skill-up based on stats to 100%. There's no such thing as a 160% chance of skilling up.

    Say you have a Shaman learning Alchemy, and they have a WIS of 400. Alchemy has a Difficulty of 4, and a StatAdjustment of -15. You failed this combine.

    The formula becomes:

    - MIN(1,(((400-15)*10)/(4*2))/1000)
    - MIN(1,((385*10)/8)/1000)
    - MIN(1,(3850/8)/1000)
    - MIN(1,481.25/1000)
    - MIN(1,.48125)

    You have a 48.125% chance of making a skill-up on a failed combine with the parameters above. If you'd succeeded the combine, you could do the calculations again with a SucceedOrFail of 1 instead of 2, and you'd have twice the chances of skilling up, or 96.25%.

    2. (((200-MIN(175,[CharacterSkill]))/200)-0.0008*(MAX(0,MIN(299,[CharacterSkill])-175)))

    This is the Skill Check portion of the formula, where the higher the skill points, the more combines it takes to get another skill-up.

    You start with a 100% chance to skill up from 0 to 1, assuming you passed the Stat Check first. Up to 175 points, you lose half a percent in the odds to gain a skill up with each combine as your skill rises.

    So once you get to 175, your odds of gaining a skill-up with a given combine are 100%-(175*0.5%), or 12.5%. It would take an average of 8 combines to get a skill-up at 175.

    Every point thereafter, the odds of a skill-up go down by .08% instead of .5%. Thankfully. So at 176, you have (12.5% - .08%) = 12.42% odds of a skill-up, and so forth.

    When trying to get that last point from 299 to 300, your odds of a skill-up are (assuming you passed the Stat Check): 12.5%-(.08%*(299-175)) = 12.5%-9.92% = 2.58%. It'll take an average of 38.75969 combines to get that last point.

    That's what the two portions of the formula are doing, is calculating your odds up to point 175, then calculating your odds for each point after 175.

    Let's run the calculations for a skill of 299, which we figured out manually above:

    - (((200-MIN(175,299))/200)-0.0008*(MAX(0,MIN(299,299)-175)))
    - (((200-175)/200)-0.0008*(MAX(0,299-175)))
    - ((25/200)-0.0008*MAX(0,124))
    - 0.125-0.0008*124
    - 0.125-.0992
    - .0258 (2.58%)

    If we run it again for a skill of, say, 100:

    - (((200-MIN(175,100))/200)-0.0008*(MAX(0,MIN(299,100)-175)))
    - (((200-100)/200)-0.0008*(MAX(0,100-175)))
    - ((100/200)-0.0008*(MAX(0,-75)))
    - (0.5-0.0008*0))
    - 0.5 (50%)

    You have a 50/50 chance of skilling up on a combine if you're currently at skill 100. Again, assuming you passed the Stat Check.

    3. Both together.

    You have to pass both checks to get a skill-up, so the odds are multiplied together. If you have a 50% chance of passing the Stat Check, and a 50% chance of passing the Skill Check, you have a combined 25% chance of getting a skill-up on that combine.

    For our 299 to 300 skill-up above, our poor Shaman isn't quite so fortunate as to have a 2.58% chance with each combine. Since her Stat Check odds are 96.25% and 48.125% depending on whether she succeeds or fails the combine, her actual odds of skilling up from 299 to 300 are 96.25%*2.58% = 2.48325% on a successful combine, and 48.125%*2.58% = 1.241625% on a failed combine. That's 1/.0248325 = 40.27 successful combines, or 80.54 unsuccessful combines.

    If she's trying to skill up on very high trivial recipes where she only succeeds 10% of the combines, she's looking at 10% * 40.27 + 90% * 80.54, for a total average number of necessary combines of 76.513. Hopefully they aren't enormously expensive. And hopefully the Random Number Generator rolls fair.

    Conclusion

    This doesn't touch on the odds of successful combines. That's a different formula that I haven't looked for or at yet, as I was primarily interested in the skill-ups.

    And, once again for convenience, here's the table of difficulties and stat adjustments as I've gleaned them from the Calculator on this site:

    Code:
    Tradeskill  Difficulty Adjustment Successes Failures
    Alchemy              4         15       415      815
    Baking               3         15       315      615
    Brewing              3         15       315      615
    Fletching            4  (0 - DEX)       400      800
    Jewelling            4         15       415      815
    Poisonmaking         2  (0 - DEX)       200      400
    Pottery              4         15       415      815
    Smithing             2  (0 - STR)       200      400
    Research             1         15       115      215
    Tailoring            2         15       215      415
    Tinkering            2         15       215      415
    Fishing              8         15       815     1615
    Bandaging            2         15       215      415
    Begging             28         15      2815     5615
    Using the formula and values above, you can calculate the odds of skilling-up at any point value for any tradeskill based on your own character's stats. The Stat Check portion is really a static value that doesn't change unless your character's stat changes. The Skill Check portion will be different for each Difficulty/Adjustment pair.

    Also, once you've figured out the odds of skilling up at each point value, you can divide 1 by that number to get the average number of combines before you get the next point. That's how I put together the total minimum (ideal) number of combines per tradeskill for the other post.

    I can look into cleaning up and posting a copy of the Excel spreadsheet I've been using, in case anyone else gets it into their head to play with the numbers so much.
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