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Tutorial: Understanding Arbitrary Item Quality

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    Tutorial: Understanding Arbitrary Item Quality

    Arbitrary Item Quality, I finally cracked it!

    Since I like the premise of the Research and Development mods. I wanted to create one similar to that, because currently the stats are way overpowered in contrast to the regular game.
    The problem for me now was. What are possible regular game values. Since it all comes down to the Arbitrary Item Quality used when generating items, I needed to find out how that value is actually determined.
    Using spawn commands you can go up to 100. But the normal Ark game doesn't get anywhere near the gear produced by quality 100. Many tests and calculations determined that the current maximum is probably 14.375. (But don't shoot me if it is higher: I haven't checked all item crates and their multipliers yet!)

    So I went on a mission, to find out how the Arbitrary Quality is determined. Thanks to Sench, I was immediately set onto the right path. So thank you for that Sench! See: Tutorial-Understanding-Item-Quality

    To determine the Arbitrary Item Quality so far, I only found 3 values which change it, namely:
    Difficulty Offset.
    Supply/Loot Crate Quality Multiplier
    Item/Item Set Entry Quality Multiplier.

    Step 1: Determine Base Arbitrary Quality (BAQ)
    Difficulty offset: (DO) (Which you can set in your gameusersettings or settings screen in game!) Can be set between 0 and 1.
    However keep in mind when set to 0. You will actually get a difficulty value of 1.
    Difficulty value = DO * 3.5 + 0.5. So setting it in your usersettings to 0 results in a DO = 0.1428571429.

    Formula:
    BAQ = 0.75 + DO * 1.75

    In my tests with the Ark Dev Kit I never could influence the results by setting the DO higher than 1.
    So if I set in Gameusersettings: Difficulty Offset to 1.25, Changed the Map Level setting 'Override Difficulty Max' = 5, The Game Mode Settings: 'Difficulty Value' = 5, 'Difficulty Value Max'= 5.
    Still all calculations happened based on a Difficulty Offset of 1. If anybody can get different results please report how you did it!

    To recap: BAQ ranges thus between 0.75 and 2.5 (And not like you would maybe expect simply by using the difficulty value of 0.5 to 4).

    Step 2: Determine the Crate Arbitrary Quality (CAQ)
    Each crate/supply crate has settings for 'Min Quality Multiplier' and 'Max Quality Multiplier'. For calculations I will name it Crate Quality Multiplier (CQM)
    e.g. SupplyCrate_Level15: Min: 1, Max: 1; SupplyCrate_Cave_QualityTier2: Min: 1.75, Max: 2.5; SupplyCrate_OceanInstant (The famous Ocean Loot drops!): Min: 3.25, Max: 4.
    Keep in mind, If you want to get proper test results, you need to set the same value for min and max. Otherwise you will not be able to verify the results as the game will pick a random value between the two.
    Furthermore you can also find an extra variable: Above One Extra Quality Multiplier; but so far I haven't been able to trigger results, not with, multiple quantities, multiple sets, ... . So far this seems to have no influence. If you do find it, please report back to us.

    Formula:
    CAQ = CQM + ((CQM - 1) * 0.2)

    e.g. CQM of 1: CAQ = 1 + ((1-1) * 0.2) = 1
    CQM of 1.75: CAQ = 1.75 + ((1.75 - 1) * 0.2) = 1.9
    CQM of 4: CAQ = 4 + ((4 - 1) * 0.2) = 4.6

    Step 3: Get the Item Quality Multiplier (IQM)
    The Item Quality Multiplier, you can find it either in the Supply Drop Blueprint itself where you determine the item sets: in the item entry: 'Min Quality' and 'Max Quality'. Or if you are working with item set overrides: in the LootSet Blueprint again at the item entries with the values for 'Min Quality' and 'Max Quality'. Again to get verifiable results, you will need to set the same value for Min and Max Quality, otherwise the Random Number Gods will take over.

    e.g. LootItemSet_SupplyDrop_Ocean has 'Min Quality' and 'Max Quality' set to 1.25

    Once you have all of these values:

    Step 4: Multiply them all and get the Arbitrary Item Quality
    Formula:
    AIQ = BAQ * CAQ * CQM

    e.g. DO = 0.9, CQM = 3.2, IQM = 1.25
    BAQ = 0.75 + 0.9 * 1.75 = 2.325
    CAQ = 3.2 + ((3.2 - 1) * 0.2) = 3.64
    IQM = 1.25

    AIQ = 2.325 * 3.64 * 1.25 = 10.57875

    eg. Max found levels so far by me:
    DO= 1, CQM=4, IQM=1.25
    BAQ = 0.75 + 1 * 1.75 = 2.5
    CAQ = 4 + ((4-1) * 0.2) = 4.6

    AIQ = 2.5 * 4.6 * 1.25 = 14.375

    Now how does AIQ influence the stats of generated items, and also the Item Rating (and does the Primitive, Ramshackle, ..., Ascendant Rating)
    Sench provided us with 2 formulas:

    Formula 1:
    Generated Stat Value = Initial Value Constant + Initial Value Constant * State Modifier Scale * Default Modifier Value + Initial Value Constant * State Modifier Scale * Randomizer Range Multiplier * X

    Formula 2: (New formula!)
    Item Rating = (X/Randomizer Range Override)^2 / Arbitrary Item Quality * Rating Value Multiplier
    X is a float value determined by the Random Number Generator between 0 and the AIQ * the Randomizer Range Override.

    Example: Riot Shield: has only 1 variable stat: Durability
    Stat settings: IVC: 2300, SMS= 0.001, DMV= 0, RRM= 0.25, RRO= 1000, RVM= 0.25

    Example 1: AIQ= 10, X (between 0 - 10000): 5000 (half of what is possible)
    Durability Stat Value = 2300 + 2300 * 0.001 * 0 + 2300 * 0.001 * 0.25 * 5000 = 2300 + 0 + 2875 = 5175
    Item Rating = (5000 / 1000)^2 / 10 * 0.65 = (5 * 5) / 10 * 0.65 = 1.625
    Thus this is a Ramshackle item (between 1.25 and 2.5: See Primal Game Data: Item Quality Definitions: Quality Random Multiplier Treshold)

    Example 2: AIQ= 10, X = 10000 (Max possible)
    Durability Stat Value = 2300 + 2300 * 0.001 * 0 + 2300 * 0.001 * 0.25 * 10000 = 2300 + 0 + 5750 = 8050
    Item Rating = (10000 / 1000)^2 / 10 * 0.65 = 10 * 10 / 10 * 0.65 = 10 * 0.65 = 6.5
    Thus this item is a Journeyman Item between 4.5 and 7.

    Example 3: DO: 1, CQM: 4, IQM = 1.25 (Max settings for an Ocean Drop)
    BAQ = 0.75 + 1 * 1.75 = 2.5
    CAQ = 4 + ((4 - 1) * 0.2) = 4.6
    IQM = 1.25
    AIQ = 2.5 * 4.6 * 1.25 = 14.375
    X = 7187.5 (half of what is possible: 14.375 * 1000 = 14375)
    Durability Stat Value= 2300 + 2300 * 0.001 * 0 + 2300 * 0.001 * 0.25 * 7187.5 = 2300 + 4132.8125 = 6432.8125
    Item Rating = (7187.5 / 1000)^2 / 14.375 * 0.65 = 7.1875 * 7.1875 / 10 * 0.65 = 3.35791015625
    Thus this is a Apprentice Item, between 2.5 and 4.5. (So higher AIQ, better durability but lower Item Rating in comparison to example 1!!!)

    Example 4: Same AIQ as example 3: 14.375
    X: 14375 (Max possible)
    Durability Stat Value= 2300 + 2300 * 0.001 * 0 + 2300 * 0.001 * 0.25 * 14375 = 2300 + 8265.625 = 10565.625
    Item Rating= (14375 / 1000)^2 / 14.375 * 0.65 = 9.34375
    Thus this item is a Mastercraft Item. between 7 and 10.

    Conclusions:
    Higher Quality Cave Crates can yield stat wise better items, but can have an Lower Quality Index.
    Even with all the best quality multipliers it is impossible for some items to get an ascendant rating, unless you start modding (or can provide me with an example based on unaltered DevKit Blueprints, if so report back please!)

    Extra work:
    Item Rating for several stat values is determined by adding them all together and dividing by the number of stats rated. AKA as the average or mean value.
    So e.g. Flak armor shirt has Armor, Durability, Hypo Thermal Insulation and Hyper Thermal Insulation. Add them all up and divide by 4.

    If you noticed when using the Max possible generated value in the item rating formula: you can reduce the Item Rating Formula to the following: IR= Arbitrary Item Quality * Rating Value Multiplier.
    The Default Rating Value Multipliers are:
    Generic Quality: 1 (Not sure if used); Armor: 1.55; MaxDurability: 0.65; WeaponDamagePercent: 1.4; WeaponClipAmmo: 1.15 (Haven't checked if this is used); Hypothermalinsulation: 0.9; Weight: 1 (Not sure if ever used); Hyperthermalinsulation: 0.9

    For each individual stat rating at the maximum of 14.375 AIQ (I haven't found anything greater as of yet, but you can do whatever you want if you start playing with the Supply Quality Crate Multipliers, and Item Quality Multipliers, DO is on a fixed range)
    Generic Quality: 14.375 (Max Stat Item Rating)(So ascendant possible) Ascendant starts at X values from 11989.5788082818 upwards: (11990 / 1000)^2 / 14.375 * 1 = 143,7601 / 14.375 * 1 = 10.00070260869565 (So a chance of 16.59130434782609% for Ascendant Quality if single stat)
    Armor: 22.28125 (Max Item Stat Rating) (So lots more of ascendant rating possible): Ascendant starts at X values from 9630.261444211729. A chance of (14375 - 9631) / 14375 = 4744 / 14375 = 33.00687690983145 %
    MaxDurability: 9.34375 (Max Item Stat Rating)(No ascendant possible)
    Weapon Damage Percent: 20.125 (Max Item Stat Rating), Ascendant X values start at: 10133.04354222222, A chance of 29.50926231497586 % for ascendant or higher
    Hypo and HyperInsulation: 12.9375 (Max Item Stat Rating) Ascendant X Values start at: 12638.12574008592, Ascendant percantage of 12.0826035472284 %

    Keep in mind that Item ratings is the average of all the stats that determine the item rating!

    Quick Summary:
    Arbitrary Item Quality = Base Arbitrary Quality * Crate Arbitrary Quality * Item Quality Multiplier
    Base Arbitrary Quality = 0.75 + Difficulty Offset * 1.75, Where difficulty offset is limited to the range of Min: 0 - Max: 1
    Crate Arbitrary Quality = Crate Quality Multiplier + ((Crate Quality Multiplier - 1 ) * 0.2)

    Random float number X in range of Min: 0 to Max: AIQ * Randomizer Range Override
    Generated Stat Value = Initial Value Constant + Initial Value Constant * State Modifier Scale * Default Modifier Value + Initial Value Constant * State Modifier Scale * Randomizer Range Multiplier * X

    Item Stat Rating = (X/Randomizer Range Override)^2 / AIQ * Rating Value Multiplier

    Global Item Rating = Average of the different Item Stat Ratings.

    Remember: Due to the Random Number Gods: items cannot ever be compared on their Color (Primitive, Mastercraft, Ascendant, ...), but only on their actual stat values. Better stated items with a lower item rating can beat higher rated items with lower stats!
    And lastly: keep in mind that rounding errors can minimally influence the final results.

    So armed with this knowledge you now can start actually balancing your own items! Have fun!

    Guinaro
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