Rating to percentage formula

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Introduction

Many character stats generate ratings. Examples of these ratings are Critical Hit, Physical Mastery, Resistance and Mitigations. Ratings are converted to percentages for having a chance at something (scoring a critical hit or parrying an opponent's attack, etc.) or as an enhancement factor (increasing your weapons damage or decreasing the amount of damage received).

Curved graph

LF lincurv.png

The formulas which the game is using for these conversions, do not result in a linear graph. Instead of a straight rating to percentage calculation, by multiplication of a factor, it's using curved graphs like in the figure above. This has the following properties which are considered an advantage:

  • low stats are "boosted". good for starting players.
  • advanced players with good gear are at the top of the curve and get relatively less from any more advancements. they need to work hard to reach the maximum (if this is possible).

Player level

LF RL70.png

The input parameter for these graphs is not only the rating(R). To provide a continuing challenge to the player, another parameter is involved: character level(L). Together they form the input combination R/L. This means that whenever a player levels up:

  • L in R/L increases. Consequently, R/L decreases and then because of that the output of the formula decreases: lower percentage.
  • a player needs to increase his rating to keep the same percentage, thus providing the challenge of getting better gear with better stats.

The figure above shows the required rating for a constant R/L of 70 while levelling up.

Formulas

The following formulas assume an opponent on the same level as yourself (the same is assumed with the percentages in your character panel).

Basic

LF basicform.png

The first equation(1) above represents the formula in it's most basic form, which is responsible for a curved graph. You can see a constant K in there which functions the same way like a coefficient in linear functions. From (1) which has the least operations we can derive (2) with the least variables and also can calculate equations for the other variables: if you know 2 variables then you can calculate the 3rd.

Lotro Basic

LF lotroform.png

Like explained in Player level, Lotro is using the input R/L for the formula and the result is a percentage(p). So lets substitute these(2)in the basic formula(1). With this we get (3) and then (4). The resulting percentage(p) is between 0 and 1, so for example 0.15 means 15%. Note:

  • Due to the nature of these formulas, the resulting percentage here can never reach a full 1(100%).
  • Because of this, ratings which only use this single basic formula are limited to result below 100%.
  • A rating of 0 or a level of 0 are defined to result in a percentage of 0.
LF lotroderived.png

Like before we can reshape the equation to formulas calculating, in this case, K(7) or R/L(8). By substitution of P=100*p in (1-p)/p or p/(1-p), you can get (100-P)/P and P/(100-P).

Lotro Segment

LF segmented.png

Probably started from raising the level cap above 50, which I guess happened with the Moria expansion, a way was introduced to get a stronger curve in the graphs. A second segment was put on top of the first old curve, using the same formula but with a displacement vector. The K of this segment was 2 times higher than the one before, resulting in a lower slope. This technique of composing a graph using curve segments as building blocks is still in use today.

LF segmform.png

With adding a displacement possibility, we arrive at the most useful end shape of the formula.

LF segmderived.png

And these derived formulas may be handy.

Rating calculations

How to calculate a percentage out of a rating?

If you want to calculate a percentage (like it appears in your character panel) then you need some information.

  • Rating(R)
  • Level(L)
  • Graph segment information. Per segment you need at the least 2 out of these 3 (the third can be calculated):
    • height of the segment (y-axis). let's call it dp or dP (dp*100).
    • width of the segment (x-axis). let's call this dRL.
    • curve constant K

Calculating a percentage out of a rating example

LF calcsample.png

Suppose you have this information:

  • The rating is 13500 and your level is 94.
  • You have these segments:
    • 1) dP1 = 15%, K1 = 1190/3
    • 2) dP2 = 5%, K2 = 2380/3
    • 3) dP3 = 5%, K3 = 4760/3

From this you can:

  • Calculate your R/L which is the input parameter: 13500/94~=143.617
  • Calculate all missing segment information which is needed for the segment formulas:
    • 1) with dRL1=(dP1/(100-dP1))*K1 you get dRL1=(15/85)*(1190/3)=(3/17)*(1190/3)=1190/17=70, first segment starts at (0,0): X01=0 and Y01=0
    • 2) with dRL2=(dP2/(100-dP2))*K2 you get dRL2=(5/95)*(2380/3)=(1/19)*(2380/3)= 2380/57, second segment starts after where first ends (dRL1,dp1): X02=70 and Y02=0.15
    • 3) with dRL3=(dP3/(100-dP3))*K3 you get dRL3=(5/95)*(4760/3)=(1/19)*(4760/3)= 4760/57, third segment starts after where second ends (dRL1+dRL2,dp1+dp2): X03=70+2380/57~=111.754 and Y03=0.15+0.05=0.2
  • Check in which segment your R/L(143.617) is: segment1? no (until X02=70) segment2? no (until X03=111.754) so it must be in segment3.
  • Fill in the formula with the found segment: p = 0.2+1/(1+(4760/3)/(143.617-111.754)) = 0.2197 -> P ~= 22.0%

How to calculate the needed rating for a percentage cap?

It's possible to calculate a rating based on your level and knowing the percentage cap. You'll need this:

  • Cap percentage
  • Graph segment information. Per segment you need at the least 2 out of these 3 (the third can be calculated):
    • height of the segment (y-axis). let's call it dp or dP (dp*100).
    • width of the segment (x-axis). let's call this dRL.
    • curve constant K

Calculating the needed rating to reach a certain (capped) percentage example

LF calcsample.png

Suppose you have this information:

  • The cap percentage is 22% and your level is 94.
  • You have these segments:
    • 1) dP1 = 15%, K1 = 1190/3, dRL=70, X0=0, Y0=0
    • 2) dP2 = 5%, K2 = 2380/3, dRL=2380/57, X0=70, Y0=0.15
    • 3) dP3 = 5%, K3 = 4760/3, dRL=4760/57, X0=70+2380/57, Y0=0.2

From this you can:

  • Find the segment with the target percentage. 22% is in segment 3 (starting from Y0=0.2)
  • We can use the derived formula R/L = X0+((p-Y0)/(1-(p-Y0)))*K
  • Fill in this formula with the found segment: R/L = (70+2380/57)+((0.22-0.2)/(1-(0.22-0.2)))*(4760/3) and simplify:
    • R/L = (70*57+2380)/57 + (0.02/(1-0.02))*(4760/3)
    • R/L = 6370/57 + (1/(50-1))*(4760/3)
    • R/L = 6370/57 + 4760/147
    • R/L = (6370*147)/(57*147) + (4760*57)/(147*57)
    • R/L = 1207710/8379 = 19170/133
  • We now have the equation R/L = 19170/133 which can be transformed to this rating calculation formula: R = (19170/133) * L
  • R = (19170/133) * L will give you the correct needed rating at any level(L). For L=94: (19170/133) * 94 ~= 13549

Ratings Graph Data

Ratings Graph Data (Curved)

This table shows:

  • the known segment information for every rating with curved graphs (current U18).
  • information about caps, both intermediate and end, which are always at segment boundaries.
  • required ratings at end level (105) for reaching caps/segment boundaries versus on level opponents.
  • required ratings at end level (105) for reaching caps/segments boundaries in Tier 2 raids/instances versus level+3 mobs (bit unknown territory, should be fine for mitigation ratings).
Percentage Rating Seg # dP K dRL Cumulative P Cap up to Level Cumulative Req. Rating Lvl105 Cumulative Req. T2 vs Lvl108 mobs Last Checked
Critical Hit Critical Rating 1 15 1190/3 70 15 50 7350 U12.2
2 5 794.8 794.8/19 20 84 11743 U12.2
3 5 1075.2 1075.2/19 25 17685 U12.2
Devastating Hit Critical Rating 1 10 1330 1330/9 10 15517
Critical & Devastating Hit Magnitude Critical Rating 1 - 300 - <100
Finesse Finesse 1 - 1190/3 - <100 U18b3
Tactical Outgoing Healing Tactical Mastery 1 30 1190/3 170 30 50 17850
2 20 2380/3 595/3 50 38675
3 20 1190 297.5 70 69913
Resistance Resistance 1 30 1190/3 170 30 50 17850 28080 U18b3
2 20 2380/3 595/3 50 38675 49500 U18b3
Critical Defence Critical Defence 1 - 100 - <100
Incoming Healing Incoming Healing 1 15 1190/3 70 15 7350 U18b3
2 10 2380/3 2380/27 25 16606 U18b3
Block, Parry & Evade Block, Parry & Evade 1 13 499.95 43329/580 13 7845 12389 U18b1
Partially Block, Partially Parry & Partially Evade Block, Parry & Evade 1 15 396.66 59499/850 15 50 7350 11880 U18b1
2 2 991.66 49583/2450 17 84 9475 14066 U18b1
3 3 1050 3150/97 20 95 12885 17573 U18b1
4 15 1200 3600/17 35 35120 40444 U18b1
Partial Block Mitigation, Partial Parry Mitigation & Partial Evade Mitigation Block, Parry & Evade 1 50 396.66 396.66 60* 41650 47160 U18b1
Physical Mitigation, Orc-craft Mitigation, Fell-wrought Mitigation & Tactical Mitigation: Physical Mitigation, Orc-craft Mitigation, Fell-wrought Mitigation & Tactical Mitigation
Light Armour 1 20 150 37.5 20 1 3938 11340
2 20 350 87.5 40 13125 20790
Medium Armour 1 20 149.9175 59967/1600 20 1 3936 11338 U18b1
2 30 253.003 759009/7000 50 15321 23049 U18b1
Heavy Armour 1 10 5697/38 633/38 10 1 1750 9090 U18b1
2 50 5697/38 5697/38 60 17491 25281 U18b1

(*) 50% + 10% base mitigation

Ratings Graph Data (Linear)

This table shows:

  • the known level segment information for every rating with linear graphs (current U18).
  • required ratings at end of level segments (Lvl Seg End) for reaching caps

Linear graph formula: Percentage = Factor * Rating/1000 + Constant

Percentage Rating Lvl Seg Start Lvl Seg End Factor Constant Cap Perc. Req. Cap Rating at Seg End Last Checked
Physical Melee-, Physical Ranged- & Tactical Offence Damage Physical Mastery & Tactical Mastery 1 20 14.6 - 40 2740 U18b3
21 30 24.2-0.48*Lvl - 40 4082 U18b3
31 40 17-0.24*Lvl - 40 5406 U18b3
41 50 13.4-0.15*Lvl - 40 6780 U18b3
51 60 11.4-0.11*Lvl - 200 41667 U18b3
61 70 10.2-0.09*Lvl - 200 51283 U18b3
71 80 7.4-0.05*Lvl - 200 58824 U18b3
81 90 6.6-0.04*Lvl - 200 66667 U18b3
91 100 5.7-0.03*Lvl - 200 74075 U18b3
101 105 2.7 - 400 148149 U18b3


Graph of the Factor (by Character Level) used for Physical Mastery & Tactical Mastery: GR offcons.png

Rating Graphs

Critical Rating

GR crit105.jpg

Finesse Rating

GR finesse105.jpg

Mastery (Physical/Tactical) Ratings

GR mast105.jpg

Resistance Rating

GR resist105.jpg

Critical Defence Rating

GR crdef105.jpg

Incoming Healing Rating

GR inheal105.jpg

Avoidance (Block/Parry/Evade) Ratings

GR avoid105.jpg

Mitigation (Physical/Tactical) Ratings

GR mit105.jpg

Note: The effect of Mitigation penetration, as exists in T2/T3 instances and skirmishes, is not shown in this graph. See the Ratings Graph Data (Curved) table above for the correct T2 rating values.

See also