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Thread: The stat system

  1. #1

    The stat system

    Last Updated: 28 february 2014 - Update 15.2.1
    Work in progress, correctness not validated

    This thread is purely meant to reflect the current state of the stat and stat-related systems. Discussion about how good or bad this system is NOT welcome. Please stick purely to keeping this up-to-date and theory crafting, or asking for clarification

    I'm making this thread to have a place with a good overview on the stat system, which in turn can be used by players to optimize their builds.

    Terminology

    Primary Stats
    The primary stats are Might, Agility, Will, Vitality and Fate. These stats do not have any effect directly, but instead contribute to several other stats.
    The primary stats that grant Tactical and or Physical mastery (Might, Agility, Will) are called Primary Class Stats.

    Contribution Cap (from rating)
    A contribution cap is a limit on how much the rating of a stat can affect the resulting percentage. It does not state a limit on what the percentage can eventually be. For example, Critical Rating has a contribution cap of 25% to critical chance, this means that above a certain amount of rating, Critical Rating will no longer contribute to Critical Chance. But critical chance can still be increased by other sources like traits.

    To be extended...

    Contributions - Primary Stats

    Might
    For all classes except Champions and Beornings:
    +3 Block
    +2 Parry

    For Guardians, Captains and Champions:
    +8 Physical Mastery
    +8 Tactical Mastery

    For Champions:
    +5 Parry

    For Beornings:
    +8 Physical Mastery
    +6 Tactical Mastery
    +3 Parry

    For Wardens:
    +8 Physical Mastery
    +5 Tactical Mastery
    Agility
    For all classes:
    +1 Critical Rating

    For all classes except Beornings:
    +2 Parry
    +3 Evade

    For Hunters and Burglars:
    +8 Physical Mastery

    For Beornings:
    +2 Evade
    +6 Physical Mastery

    For Wardens:
    +8 Physical Mastery
    +5 Tactical Mastery
    Will
    For all classes:
    +1 Tactical Mitigation
    +2 Resistance

    For Minstrels, Rune-keepers
    and Lore-masters:
    +8 Tactical Mastery
    +8 Physical Mastery

    For Burglars, Beornings and Champions:
    +5 Tactical Mastery

    For Guardians
    +8 Tactical Mastery

    For Beornings:
    +1 Evade
    Vitality
    For all classes:
    +2 Resistance
    +7.2 OCMR

    For Guardians, Wardens and Beornings:
    +5 Maximum Morale
    For all other classes:
    +3 Maximum Morale
    Fate
    For all classes:
    +1 Tactical Mitigation
    +2.5 Critical Rating
    +1.5 ICMR

    For all classes except Beornings:
    +1.71 ICPR
    +24 OCPR

    For Beornings:
    +4 Tactical Mastery

    Contributions - Secondary Stats
    Only secondary stats that affect multiple things are listed here.

    Critical Rating
    - Critical Chance (max. 25%)
    - Devastate Chance (max. 10%)
    - Critical and Devastate Magnitude (infinite rating required to hit cap: 100%)

    Physical Mastery
    - Melee Damage
    - Ranged Damage

    Tactical Mastery
    - Tactical Damage
    - Outgoing Healing

    Block, Parry, Evade
    - Full Block, Parry, Evade Chance
    - Partial Block, Parry, Evade Chance
    - Partial Block, Parry, Evade Mitigation

    Armour
    Note: the character penal lists Common mitigation as the default Physical Mitigation, with other types shown on the tooltip.
    - Common Mitigation Rating [100% contribution]
    - Physical Mitigation Rating (Orc-craft/Fell-wrought/Beleriand/Ancient dwarf-make/Westernesse) [20% contribution]
    - Tactical Mitigation Rating (Fire/Frost/Lightning/Light/Shadow/Acid) [20% contribution]

    General Formula: Rating to Percentage

    P = Y + 1/(1 + C/(R/L - X))

    And it's inverse:
    R = ( C(P - Y)/(1 - (P - Y)) + X ) * L

    P = Stat in decimals (multiply by 100 to get it as percentage)
    X = Translation on the input (R/L)
    Y = Translation on the output (P)
    C = Constant (determines how steep the curve is)
    R = Rating
    L = Level of the target

    Translations are used for segmentation.
    Last edited by Vulcwen; May 27 2015 at 08:55 AM. Reason: update the last-updated date
    ~Dwarrowdelf (Bomb Squad)~
    Freeps: Vulcwen (R8 LM), Vulciel (lvl 100 RK), and some lower level alts.. Creep: Shadowweb (R6 spider)
    My ideas on how LM should be: [url=https://www.lotro.com/forums/showthread.php?543323-LM-revamp-reconsidered]LM Revamp reconsidered[/url]

  2. #2
    Critical Chance and Incoming Healing

    Contribution Cap
    Critical Chance: 25% (16842 Critical Rating at lvl 100)
    Incoming Healing: 25% (16842 Incoming Healing Rating at lvl 100)

    Formula Constants

    Y = 0 | X = 0 | C = 396.667
    Y = 0.15 | X = 70 | C = 794.2
    Y = 0.2 | X = 111.8 | C = 1075.8


    Devastate Chance and Partial Avoidance Chance

    Contribution Cap
    10% (14778 rating at lvl 100)

    Formula Constants

    Y = 0 | X = 0 | C = 1330


    Critical and Devastate Magnitude

    Contribution Cap
    100% (infinite Critical Rating)

    Interesting info
    At the critical chance cap, at level 100 (16842 rating), you get 36% critical magnitude.

    Formula Constants

    Y = 0 | X = 0 | C = 300


    Graph (Level 100) from measured data:
    http://i.imgur.com/2xOPBzg.jpg?1


    Avoidance Chance and Partial Avoidance Mitigation

    Contribution Cap
    25% (39670 rating at lvl 100)

    Interesting Info
    20% = 15161 rating at lvl 100
    This is the point the extra diminishing returns kicks in.
    Also interesting is that you can get to 15% with only 7001 rating, which is less than half of what it takes to get to 20%.

    Formula Constants

    Y = 0 | X = 0 | C = 396.7
    Y = 0.15 | X = 70.01 | C = 991.5
    Y = 0.17 | X = 90.25 | C = 1984
    Y = 0.2 | X = 151.61 | C = 3968



    Physical and Tactical Mastery (Damage)

    Contribution cap
    200% (80k rating at lvl 100)

    Interesting info
    At level 100:
    80% = 30000 Mastery
    100% = 37500 Mastery
    120% = 50000 Mastery
    140% = 57500 Mastery
    160% = 65000 Mastery

    Formula Constants

    Y = 0 | X = 0 | C = 300
    Y = 0.2 | X = 75 | C = 300
    Y = 0.4 | X = 150 | C = 300
    Y = 0.6 | X = 225 | C = 300
    Y = 0.8 | X = 300 | C = 300
    Y = 1.2 | X = 500 | C = 300
    Y = 1.4 | X = 575 | C = 300
    Y = 1.6 | X = 650 | C = 300
    Y = 1.8 | X = 725 | C = 300


    Outgoing Healing (Tactical Mastery)

    Contribution Cap
    70% (66583 rating at lvl 100)

    Interesting Info
    You can hit 50% at 36833 rating.

    Formula Constants

    Y = 0 | X = 0 | C = 1190/3
    Y = 0.3 | X = 170 | C = 1190 * (2/3)
    Y = 0.5 | X = 1105/3 | C = 1190



    Mitigation Rating

    Contribution cap
    Contribution caps depend on armour type:
    Light: 40% (12500 rating at lvl 100)
    Medium: 50% (18750 rating at lvl 100)
    Heavy: 60% (16658 rating at lvl 100)

    Formula
    The formula also depends on armour type: Heavy armour classes get more mitigation for each point of mitigation rating.

    Light and Medium

    Constants:
    Y = 0 | X = 0 | C = 150
    Y = 0.2| X = 37.5 | C = 350


    Heavy

    Constants:
    Y = 0 | X = 0 | C = 150
    Y = 0.1| X = 16.667 | C = 150


    Critical Defence

    Contribution Cap
    100% (infinite Critical Defence rating)

    Interesting info
    At level 100:
    50% = 10000 Critical Defence
    60% = 15000 Critical Defence
    70% = 23333 Critical Defence
    80% = 40000 Critical Defence

    Formula Constants

    Y = 0 | X = 0 | C = 100
    Last edited by Vulcwen; Jun 15 2015 at 05:41 AM. Reason: little fix
    ~Dwarrowdelf (Bomb Squad)~
    Freeps: Vulcwen (R8 LM), Vulciel (lvl 100 RK), and some lower level alts.. Creep: Shadowweb (R6 spider)
    My ideas on how LM should be: [url=https://www.lotro.com/forums/showthread.php?543323-LM-revamp-reconsidered]LM Revamp reconsidered[/url]

  3. #3
    Item stats system

    Note: This system is not validated for all items, but it's expected to work correctly for items higher than level 66, and a lot of items below that as well.

    How are items defined
    Each item has an Item Level (iLevel), and a Stat Slice (S) distribution. The total of slices depends on the Quality of an item.

    An example is:
    Greater Resolute Bracelet of Fate
    2.8 *S Will, 2.4 * S Vitality, 1.2 * S Fate and 0.6 * S Critical Rating.
    Calculating this with the formula and values below (iLevel 176):

    Will: 2.8 * (176 * 0.5 - 10.5) = 77,5 * 2.8 = 217
    Vitality: 2.4 * (176 * 0.5 - 10.5) = 77,5 * 2.4 = 186
    Fate: 1.2 * (176 * 0.5 - 10.5) = 77,5 * 1.2 = 93
    Critical Rating: 0.6 * (176 * 4) = 0.6 * 704 = 422,4 => 422

    Helm's Deep's standardized gear (Incomparable) always has 2.8 slices of a primary stat and 2.4 slices of another primary stat, with one of those being vitality.
    Rare has 0.4 slices of these 2 primary stats less, and Uncommon 0.8 slices less.

    Slice Totals - Items
    - Uncommon: 5 slices
    - Rare: 6 slices
    - Incomparable: 7 slices
    - Epic: 8 slices

    Armour value does not count for this, nor does the critical defence on shields.

    Slice Totals - Essences
    - Uncommon: 1.4 slices (lower item level than Rare)
    - Rare: 1.4 slices
    - Incomparable: 1.6 slices
    - Epic: 1.8 slices

    Note: On socketed gear, an empty slot is worth 1.4 slices, even though you can put up to 1.8 slices in it.

    Slice values
    Slice values follow the following general formula:
    S = a * iLevel + b

    And the resulting stat is than: result = floor(S * slicecount + c)
    With c being a constant to determine the rounding result.

    This is still a work-in-progress and it'll take a while to get it correct. I need to collect more data.


    Stat Name (iLevel range) a b Slice at iLevel 192 Value of a Rare essence (iLevel 192)
    Primary (>=60) 0.5 -10.5 85.5 119
    Primary (50-59) 0.3 1.5 - -
    Critical Rating 4 0 768 1075
    Physical/Tactical Mastery 4 0 768 1075
    Block/Parry/Evade 4 0 768 1075
    Physical/Tactical Mitigation 9 0.5 1728.5 2420
    Critical Defence 10 10 1930 2702
    Finesse 11.9523 48.029 2342.909 3280
    Resistance 6 8 1160 1624
    Maximum Morale (>=50) 3.508 -126.9 546.636 765
    Maximum Power (>=50) 2.984 -101.2 471.728 660
    Incoming Healing* 8 0 1536 2150,4
    ICPR** (>=50) 0.3 33.3 90.9 127.26
    more yet to add...

    *) Rounded on 1 decimal
    **) Rounded on 2 decimals
    FAQ

    TBD...
    Last edited by Vulcwen; Sep 08 2014 at 08:00 AM. Reason: added resist
    ~Dwarrowdelf (Bomb Squad)~
    Freeps: Vulcwen (R8 LM), Vulciel (lvl 100 RK), and some lower level alts.. Creep: Shadowweb (R6 spider)
    My ideas on how LM should be: [url=https://www.lotro.com/forums/showthread.php?543323-LM-revamp-reconsidered]LM Revamp reconsidered[/url]

  4. #4
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    Very nice article!

    Some more slice data:

    Resistance: 6; 18
    ICMR: 0.612244898; 0 (<= 49) (0.612244898 = 30/49)
    ICMR: 0.9; -14.1 (>=50)
    ICPR: 0.7142857143; 10 (<=49) (0.7142857143 = (45-10)/49)
    ICPR: 0.3; 30.3 (>=50)
    Power,Morale: 0.9; 1 (<=49)

    Armour uses a similar formula, but it's very complex. Some mechanic I understand, but I just use factor and constant and many, many of those for many quality and types of armour.

    Edit: my source are game items. indirect from Lotro-wiki is not reliable because sometimes it has old information.
    Last edited by Giseldah; Sep 14 2014 at 04:45 AM.

  5. #5
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    I just looked up the number of armour entries I have: 266. And this number will get higher.. because still some unknown exist because of the progression (factor) nerf for ilvl>=185.

    Currently new Gondor uncommon/yellow drop armour items mistakenly have the values from rare/purple armour. However, this does not apply to uncommon/yellow Nahdin socket armour.
    So.. you can have a lvl100 yellow gloves and yellow lvl100 Nahdin gloves with different armour values. The Nahdin gloves will have the lesser values. Fun xD

    One more thing concerning slices, in my theory, Turbine can use a couple of ways to enter stat data. One is the hard-coded way from the ancient (lower level) system and the other is newer by formula. The old way is used at lower levels, but newer entries there get partly at least the newer way by formula. So it's inconsistent. Stats seem to get reliable from ilvl 60. Armour values from ilvl 80.

    Edit:
    To illustrate the armour change for itemlevel 185 and above:



    The graph shows itemlevel->armour values for teal/incomparable quality gloves for classes light, medium & heavy.

    The change became first noticeable when golden Onodrim armour from Fangorn (iLvl 188) had reduced armour values from U14.

    Edit2: With new items and higher itemlevels comes more data available. With current data it looks like the old segments are until itemlevel 182 and new is starting at 183.
    Progression in new segment was compared with before reduced to:
    - Heavy: 79%
    - Medium: 73.5%,
    - Light: 70%
    - Shields: 43%
    - Cloaks: 72%
    Last edited by Giseldah; Apr 12 2015 at 07:53 AM.

  6. #6
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    Lightbulb Stats Posts that calculate into great detail and show when you are "seriously smart* about your beloved char

    *faint* Can I please hire a brain.
    [SIZE=3][COLOR=#faebd7][B]Susameldal ~ Raidling ~ Crickhollow[/B][/COLOR]
    [URL="http://raidlings.net"][COLOR=#faebd7][B]The Council of the Wise Alliance[/B][/COLOR][/URL][/SIZE]

  7. #7
    Since some people probably don't know which essences to get to make their build viable for T2 content now could you make Recommended stats for all classes? (including different builds for tank, healer, support)

  8. #8
    I updated the Beorning data from what I remembered from beta. I don't have a Beorning atm, so if anyone can confirm if it's true, or post the errors, I'd appreciate that.

    A summary:
    Might: 8 PM, 8 TM, 3 Parry
    Agility: 1 Crit, 3 Evade, 6 PM
    Will: 1 TMit, 2 Resist, 8 TM, 1 Evade
    Vitality: 5 Morale, 2 Resist, 7.2 OCMR
    Fate: 1 TMit, 5 TM, 1.5 ICMR, 2.5 Crit

    I'm mainly not really sure about the TM/evade contribution of will.
    Last edited by Vulcwen; Nov 20 2014 at 08:42 PM.
    ~Dwarrowdelf (Bomb Squad)~
    Freeps: Vulcwen (R8 LM), Vulciel (lvl 100 RK), and some lower level alts.. Creep: Shadowweb (R6 spider)
    My ideas on how LM should be: [url=https://www.lotro.com/forums/showthread.php?543323-LM-revamp-reconsidered]LM Revamp reconsidered[/url]

  9. #9
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    Beorning stats as of u15 live:

    Might: 8 PM, 6 TM, 3 Parry
    Agility: 1 Crit, 2 Evade, 6 PM
    Will: 1 Evade, 1 TMit, 2 Resist, 5 TM
    Vit: 5 Morale, 2 Resist, 7.2 OCMR
    Fate: 1 TMit, 2.5 Crit, 1.5 ICMR, 4 TM
    Last edited by Coeprandua; Nov 20 2014 at 07:42 PM.

  10. #10
    Quote Originally Posted by Coeprandua View Post
    Beorning stats as of u15 live:

    Might: 8 PM, 6 TM, 3 Parry
    Agility: 1 Crit, 2 Evade, 6 PM
    Will: 1 Evade, 1 TMit, 2 Resist, 5 TM
    Vit: 5 Morale, 2 Resist, 7.2 OCMR
    Fate: 1 TMit, 2.5 Crit, 1.5 ICMR, 4 TM
    Thanks, updated it with the right stuff :P
    ~Dwarrowdelf (Bomb Squad)~
    Freeps: Vulcwen (R8 LM), Vulciel (lvl 100 RK), and some lower level alts.. Creep: Shadowweb (R6 spider)
    My ideas on how LM should be: [url=https://www.lotro.com/forums/showthread.php?543323-LM-revamp-reconsidered]LM Revamp reconsidered[/url]

  11. #11
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    Quote Originally Posted by Ksenija View Post
    Since some people probably don't know which essences to get to make their build viable for T2 content now could you make Recommended stats for all classes? (including different builds for tank, healer, support)
    This would help a lot. if someone could do it, would be great.

  12. #12
    How did you arrive at 1.71 ICPR per point of fate? This doesn't match the measured value on any of my level 100 characters:
    FATE
    304
    475
    646
    650
    802
    821
    973
    1060
    1109
    ICPR
    756
    1052
    1344
    1351
    1611
    1643
    1903
    2052
    2136
    Contribution
    2.49
    2.21
    2.08
    2.08
    2.01
    2.00
    1.96
    1.94
    1.94

    The values for ICPR were taken from the tooltip for fate, so the icpr isn't skewed from other sources. I should note, that years ago, ICPR from fate used to be 30 * sqrt(fate) but this has clearly been changed since that formula doesn't produce the observed numbers.

  13. #13
    Quote Originally Posted by mjmallon View Post
    How did you arrive at 1.71 ICPR per point of fate? This doesn't match the measured value on any of my level 100 characters:
    FATE
    304
    475
    646
    650
    802
    821
    973
    1060
    1109
    ICPR
    756
    1052
    1344
    1351
    1611
    1643
    1903
    2052
    2136
    Contribution
    2.49
    2.21
    2.08
    2.08
    2.01
    2.00
    1.96
    1.94
    1.94

    The values for ICPR were taken from the tooltip for fate, so the icpr isn't skewed from other sources. I should note, that years ago, ICPR from fate used to be 30 * sqrt(fate) but this has clearly been changed since that formula doesn't produce the observed numbers.
    Using your data:
    delta fate: 1109 - 304 = 805
    delta ICPR: 2136 - 756 = 1380
    1380/805 = 1.71428

    So, 1 fate = 1.71 ICPR


    EDIT (28 feb 2015):
    Added devastating chance, avoidance and outgoing healing information.
    Last edited by Vulcwen; Feb 28 2015 at 11:42 AM.
    ~Dwarrowdelf (Bomb Squad)~
    Freeps: Vulcwen (R8 LM), Vulciel (lvl 100 RK), and some lower level alts.. Creep: Shadowweb (R6 spider)
    My ideas on how LM should be: [url=https://www.lotro.com/forums/showthread.php?543323-LM-revamp-reconsidered]LM Revamp reconsidered[/url]

  14. #14
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    Stats on relics use the same linear formulas: factor * level + constant

    This is one is the most often used with factor 8.08 and constant 0. (or x0.5 of it = 4.04, x2.5 = 20.2 etc)



    Similar:

    Might/Agility/Vitality/Will/Fate
    factor: 0.5
    constant: -10.25
    (In this case true relics can have higher levels then normal. For example true extraordinary have lvl70 stats instead of 65.)

    Morale
    factor: 6.6667
    constant: -203.6667

    Power
    factor: 6.6667
    constant: -223.6667

    Physical/Tactical Mitigation (1x,1.3333x)
    factor: 2.29
    constant: -1.35

    ICMR
    factor: 2.6
    constant: -52

    ICPR
    factor: 2.4
    constant: -45

    Btw, this data is not valid for crafted relics.

  15. #15
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    Quote Originally Posted by Giseldah View Post
    Power,Morale: 0.9; 1 (<=49)
    Nearby, but looks incorrect now. Not sure about Power (likely incorrect also), but Morale for ilvl<=49 is:

    1x slice level 1 = 2
    1x slice level 49 = 45

    factor:
    (45-2)/(49-1) ->
    43/48 = 0.8958333333

    constant:
    2-43/48 ->
    96/48-43/48 ->
    53/48 = 1.1041666667

    complies with 60 datapoints

  16. #16
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    Quote Originally Posted by Giseldah View Post
    Nearby, but looks incorrect now. Not sure about Power (likely incorrect also), but Morale for ilvl<=49 is:

    1x slice level 1 = 2
    1x slice level 49 = 45

    factor:
    (45-2)/(49-1) ->
    43/48 = 0.8958333333

    constant:
    2-43/48 ->
    96/48-43/48 ->
    53/48 = 1.1041666667

    complies with 60 datapoints
    As a result whe can also more refine the upper segment because both meet in lvl49:

    morale (ilvl>=49):

    factor = 3.5079
    constant = -126.8871

    &

    power (ilvl>=49):

    factor = 2.9842
    constant = -101.2258
    Last edited by Giseldah; May 24 2015 at 03:03 AM.

  17. #17
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    Quote Originally Posted by Vulcwen View Post
    Contribution Cap
    Critical Chance: 25% (16842 Critical Rating at lvl 100)
    Incoming Healing: 25% (16842 Incoming Healing Rating at lvl 100)
    When I look at my critical chance, it seems to cap at 30%, although I play hunter, and currently have a base crit chance of 30% and won't go any higher, unless I proc the +20% crit chance from my jewelry.
    Just giving this off as an fyi, I don't know if it is for any other classes due to the fact that I only play one toon :P

  18. #18
    Quote Originally Posted by Unknowned View Post
    When I look at my critical chance, it seems to cap at 30%, although I play hunter, and currently have a base crit chance of 30% and won't go any higher, unless I proc the +20% crit chance from my jewelry.
    Just giving this off as an fyi, I don't know if it is for any other classes due to the fact that I only play one toon :P
    I have updated the OP to clarify what I mean with "contribution cap".
    Basically it's that the cap doesn't state what critical chance can eventually be, just how much you can get from rating. You can get more (no limit) with traits/whatever that give a direct % bonus to critical chance.
    ~Dwarrowdelf (Bomb Squad)~
    Freeps: Vulcwen (R8 LM), Vulciel (lvl 100 RK), and some lower level alts.. Creep: Shadowweb (R6 spider)
    My ideas on how LM should be: [url=https://www.lotro.com/forums/showthread.php?543323-LM-revamp-reconsidered]LM Revamp reconsidered[/url]

  19. #19
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    slice formulas:
    Morale = 3.507873833 * iLvl - 126.8825 (+-0.0025)
    Power = 2.984251941 * iLvl - 101.2285 (+-0.0015)
    Finesse = 11.951935937 * iLvl + 48.052 (+-0.004)

    factors correct up to 9 decimals and variance for constants are between ()

    edit:
    factors are at least 5-6 decimals correct. possibly 9.
    Last edited by Giseldah; Jun 02 2015 at 06:58 AM.

  20. #20
    I've found a discrepancy between the parameters quoted for Incoming Healing Rating and my character sheet.

    Specifically, for Incoming Healing, the third set of constants

    Y = 0.2 | X = 111.8 | C = 1075.8

    should simply be ignored. The second set of constants fits the data perfectly up to the cap.

    There is one other slight inaccuracy:

    Y = 0 | X = 0 | C = 396.667 = 1190/3
    Y = 0.15 | X = 70 | C = 2*1190/3 (not 794.2)

    The old formula with three segments leads to almost a 1% error for ratings near the cap.

    This means that the cap on incoming healing rating is actually 15815, not 16842.


    Here are the data:

    Rating
    2458
    4915
    6531
    6733
    7373
    8349
    8989
    9191
    10807
    10960
    11446
    11600
    11648
    11802
    12442
    13264
    13418
    14058
    14260
    Contrib (from Sheet)
    0.058
    0.11
    0.141
    0.145
    0.155
    0.167
    0.174
    0.177
    0.196
    0.198
    0.203
    0.205
    0.205
    0.207
    0.214
    0.223
    0.225
    0.232
    0.234
    Old Formula
    0.058
    0.11
    0.141
    0.145
    0.155
    0.167
    0.174
    0.177
    0.196
    0.197
    0.202
    0.204
    0.204
    0.206
    0.212
    0.219
    0.22
    0.226
    0.228
    Corrected Formula
    0.058
    0.11
    0.141
    0.145
    0.155
    0.167
    0.174
    0.177
    0.196
    0.198
    0.203
    0.205
    0.205
    0.207
    0.214
    0.223
    0.225
    0.232
    0.234

  21. #21
    Join Date
    Jul 2011
    Posts
    921
    Quote Originally Posted by LagunaD2 View Post
    I've found a discrepancy between the parameters quoted for Incoming Healing Rating and my character sheet.

    Specifically, for Incoming Healing, the third set of constants

    Y = 0.2 | X = 111.8 | C = 1075.8

    should simply be ignored. The second set of constants fits the data perfectly up to the cap.

    There is one other slight inaccuracy:

    Y = 0 | X = 0 | C = 396.667 = 1190/3
    Y = 0.15 | X = 70 | C = 2*1190/3 (not 794.2)

    The old formula with three segments leads to almost a 1% error for ratings near the cap.

    This means that the cap on incoming healing rating is actually 15815, not 16842.


    Here are the data:

    Rating
    2458
    4915
    6531
    6733
    7373
    8349
    8989
    9191
    10807
    10960
    11446
    11600
    11648
    11802
    12442
    13264
    13418
    14058
    14260
    Contrib (from Sheet)
    0.058
    0.11
    0.141
    0.145
    0.155
    0.167
    0.174
    0.177
    0.196
    0.198
    0.203
    0.205
    0.205
    0.207
    0.214
    0.223
    0.225
    0.232
    0.234
    Old Formula
    0.058
    0.11
    0.141
    0.145
    0.155
    0.167
    0.174
    0.177
    0.196
    0.197
    0.202
    0.204
    0.204
    0.206
    0.212
    0.219
    0.22
    0.226
    0.228
    Corrected Formula
    0.058
    0.11
    0.141
    0.145
    0.155
    0.167
    0.174
    0.177
    0.196
    0.198
    0.203
    0.205
    0.205
    0.207
    0.214
    0.223
    0.225
    0.232
    0.234
    Yes, Incoming Healing doesn't follow the graph of Critical Rating.

    You can also check here: https://lotro-wiki.com/index.php/Rat...ngs_Graph_Data

    Part of the data in wiki comes from my own investigations. I do a full research whenever I find a discrepancy with game data. (I don't do a full analysis of everything with every update *gasp*)

  22. #22
    Join Date
    Jul 2011
    Posts
    921
    Quote Originally Posted by Giseldah View Post
    slice formulas:
    Morale = 3.507873833 * iLvl - 126.8825 (+-0.0025)
    Power = 2.984251941 * iLvl - 101.2285 (+-0.0015)
    Finesse = 11.951935937 * iLvl + 48.052 (+-0.004)

    factors correct up to 9 decimals and variance for constants are between ()

    edit:
    factors are at least 5-6 decimals correct. possibly 9.
    I could collect more data and found that my previous data was unreliable above item level 1000000.
    I collected new and more beneath 1000000 and result is this:

    Morale = 3.5078741609 * iLvl - 126.88497
    Power = 2.9842521321 * iLvl - 101.2285
    Finesse = 11.951937108 * iLvl + 48.04765

    Data point search sheet for scanning 1000s of item levels for suitable candidates:


    Procedure:
    1) Search a data point.
    2) Collect data from Lotro
    3) If confirms with formula go to [1]
    4) Adjust formula to fit with all collected data and go to [1]

    Searching data points involves finding points both above (green cells) and under (red cells) .5 values, while ever decreasing the distance. Once you have to adjust/refine the formula then in a way pretty much all collected points become irrelevant and you have to start anew.

    If you analyse the resulting formulas then you notice that with morale and power the item level points 49 and 176 are close to having very nice numbers.

    Morale:
    49: 45.000863884
    176: 490.500882318

    Power
    49: 44.999854473
    176: 423.999875250

    Item level 49 is the end level of the previous (lower) segment. Item level 176 is the incomparable level for lvl95 items.

    If you calculate factors:
    Morale: (490.5-45)/(176-49) = 3,507874015748
    Power: (424-45)/(176-49) = 2,9842519685

    In the end it's close, but it doesn't fit all data completely.
    It's not unusual in Lotro that devs take some simple numbers and modify them slightly to disguise the inner workings.
    Last edited by Giseldah; Jun 09 2016 at 03:43 AM.

  23. #23
    Join Date
    Jun 2010
    Location
    Alabama
    Posts
    6,373
    Quote Originally Posted by Giseldah View Post
    I could collect more data and found that my previous data was unreliable above item level 1000000.
    I collected new and more beneath 1000000 and result is this:

    Morale = 3.5078741609 * iLvl - 126.88497
    Power = 2.9842521321 * iLvl - 101.2285
    Finesse = 11.951937108 * iLvl + 48.04765

    Data point search sheet for scanning 1000s of item levels for suitable candidates:


    Procedure:
    1) Search a data point.
    2) Collect data from Lotro
    3) If confirms with formula go to [1]
    4) Adjust formula to fit with all collected data and go to [1]

    Searching data points involves finding points both above (green cells) and under (red cells) .5 values, while ever decreasing the distance. Once you have to adjust/refine the formula then in a way pretty much all collected points become irrelevant and you have to start anew.

    If you analyse the resulting formulas then you notice that with morale and power the item level points 49 and 176 are close to having very nice numbers.

    Morale:
    49: 45.000863884
    176: 490.500882318

    Power
    49: 44.999854473
    176: 423.999875250

    Item level 49 is the end level of the previous (lower) segment. Item level 176 is the incomparable level for lvl95 items.

    If you calculate factors:
    Morale: (490.5-45)/(176-49) = 3,507874015748
    Power: (424-45)/(176-49) = 2,9842519685

    In the end it's close, but it doesn't fit all data completely.
    It's not unusual in Lotro that devs take some simple numbers and modify them slightly to disguise the inner workings.
    What would help here is knowing the internal representation. If they are using 32 bit IEEE floating point, you should never use more than 5 or 6 significant digits. Even then you'll have to take the time to propagate the rounding/truncation errors inherent in the calculations and check to see if your algorithm's order is sensitive to how the operations are done. If they're using 64 bit IEEE floating point operations, you can get away with keeping more digits. You'll still have rounding/truncation errors to propagate correctly. Finally, you will need to consider floating point to string conversion errors for the visible outputs.
    "No sadder words of tongue or pen are the words: 'Might have been'." -- John Greenleaf Whittier
    "Do or do not. There is no try." -- Yoda
    On planet Earth, there is a try.
    Indeed, in a world and life full of change, the only constant is human nature (A is A, after all :P).
    We old vets need to keep in mind those who come after us.

  24. #24
    Join Date
    Jul 2011
    Posts
    921
    Quote Originally Posted by cdq1958 View Post
    What would help here is knowing the internal representation. If they are using 32 bit IEEE floating point, you should never use more than 5 or 6 significant digits. Even then you'll have to take the time to propagate the rounding/truncation errors inherent in the calculations and check to see if your algorithm's order is sensitive to how the operations are done. If they're using 64 bit IEEE floating point operations, you can get away with keeping more digits. You'll still have rounding/truncation errors to propagate correctly. Finally, you will need to consider floating point to string conversion errors for the visible outputs.
    It's like shooting a bullet through a pipe, which is ever getting slightly more narrow, ending in the diameter of the bullet. Will it come out? No. You might think that a bullet is going completely straight, but in fact it follows a wobbly trajectory. The inside of the pipe is not completely straight either, due to the imperfect production method. Eventually, it will get stuck.
    What I'm doing is trying to get the bullet as far as possible. At the end it's a hopeless case.

    I'll leave it for the moment. Examining low level (<50) primary/main stats now which are quite intriguing. I've made some adjustments to former formulas in my spreadsheet.

  25. #25
    Join Date
    Jul 2011
    Posts
    921
    Main/primary stats:

    Formula: Stat = slice count * (factor * iLvl + constant) + add



    Verified for slice counts:
    iLvl 1-60: 0.4, 1, 1.4, 1.6, 2.4, 2.8, 3, 3.2
    iLvl 10-60: 2
    iLvl 45-60: 3.6
    iLvl 50-60: 4

    Lower levels: only for scalable (instance) items, crafted items, mathom items. Not for very old items, created long time ago (pre-Moria?).

 

 

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