Rating to percentage formula

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Introduction

Main character stats like Might, Agility, etc. are like containers. They contain contributions to the stats that really influence your character's performance. These stats can be like Morale, having a direct effect, or various ratings.
Ratings are indirect, in the sense that they provide the base for the calculation of a number of characteristics. Examples of these ratings are Critical Rating, Physical Mastery Rating, Resistance Rating, etc.
Ratings are in turn converted by a formula to percentages (and this can be multiple percentages from a single rating). These percentages then are having the direct effect for having for example 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).

For the game developers, it also has some other advantages:

  • by changing the bending in the curve, they can influence the height of the average result.
  • by the amount of bending in the curve, they can concentrate the result, so that most people's stats are kind of the same.

Percentage Caps

Cappedpercentage.png

Percentages from ratings are in most cases "capped". This means that a rating percentage (P) has a maximum (Pcap). However, the amount of rating (R) that you can have, is never restricted. It's just not usefull to have more than the required rating to reach the cap (Rcap).
Putting a "hard" maximum on a percentage programmatically (Hard-Pcap) is not the only way to limit a percentage. The calculation formula itself has the property to limit the resulting percentage. This mathematical cap (Soft-Pcap) is unreachable by any rating: the curve will always stay under that limit.

Player level

SegmentedRcapByLevel.png

The amount of rating needed to reach percentage caps (Rcap) is raised with level increase of the player. This is to provide a continuing challenge to the player. This means that whenever a player levels up:

  • Rcap increases by a fixed amount.
  • consequently with the same rating, the rating to percentage formula outputs to a 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.

As you can see in the example figure, the graphs for Rcap is a straight line (constant rating increases per level), but over the whole level span this is segmented. The reason for this is in direct connection with the difficulty of the game on various levels. And game difficulty depends in turn on the various game expansions which were developed for certain level segments.

Formulas

B-rating (B)

B-rating and not the cap rating (Rcap) is used in the calculations. This formula can be used to calculate the B-rating from a straight line between two progression points (Lstart,Bstart) - (Lend,Bend) where Lstart <> Lend:

BFormula.png
  • Lstart = start point combat level.
  • Lend = end point combat level.
  • Bstart = start point B-rating.
  • Bend = end point B-rating.
  • L = combat level. For stats in the character panel this is always the player's level, but your opponent's level plays a major roll as well in reality.

Note for levels higher than 75: B-ratings from in-between points (so excluding start and end) should be rounded to 10s.

Percentage from rating (P)

This is the curve formula which is used for the rating to percentages conversion:

PercentageFormula.png
  • A = soft percentage cap (Soft-Pcap).
  • B = B-rating.
  • R = rating amount.

For percentages in the character panel, you'll need to add 0.0002 to this formula's result to be accurate. It's unknown if this only for display purposes (rounding errors) or if this is used for calculations as well.
The resulting percentage of this formula should be capped by Pcap.

Rating from percentage (R)

This formula can be used to calculate the required rating for a given percentage:

RatingFormula.png
  • A = soft percentage cap (Soft-Pcap).
  • B = B-rating.
  • P = desired percentage for which to calculate the rating amount.

The resulting rating of this formula should be capped by Rcap.

Required rating for percentage cap (Rcap)

The cap rating can be calculated by using the rating formula and using the cap percentage as percentage:

RcapFormula.png
  • A = soft percentage cap (Soft-Pcap).
  • B = B-rating.
  • Pcap = hard percentage cap (Hard-Pcap).

Usually, Rcap is equal to B-rating because the Curve Constant is often 1 (Hard-Pcap = Soft-Pcap / 2). Exceptions are mitigations and Critical/Devastating Hit Magnitude.

Curve constant (C)

This formula can be used to calculate the curve constant:

CFormula.png
  • Pcap = hard percentage cap (Hard-Pcap).
  • A = soft percentage cap (Soft-Pcap).

The Curve constant is a measure of the bending of a curve. If it's positive then the curve bends down, if it's negative then the curve's slope goes up and if the curve constant is zero then it's not a curve but a straight line.

TheEffectOfC.gif

Optimal Rating (Roptimal)

This formula can be used to calculate the optimal rating:

ROptimalFormula.png
  • C = Curve constant
  • Rcap = cap rating

The optimal rating is the rating pivot point where you have the most percentage profit from the curve versus a straight line. For many rating percentages with C=1 this is (SQRT(2)-1)*Rcap.

Ratings Graph Data

This table shows all the information which is needed for calculations. For to find the right information row:

  • Locate the needed rating percentage.
  • Search the right segment for your level between LvlSeg Start and LvlSeg End (LvlSeg Start < Level <= LvlSeg End).

Explanation of the columns:

  • Pbonus = a bonus percentage which needs to be added to the percentage formula result.
  • Level = what combat level to use in the B-rating formula? Highest: maximum of both sides. Lowest: minimum of both sides. CharLvl: player's level. OppLvl: opponent's level. This is highly speculative for most percentages, except for mitigations.
LvlSeg Start LvlSeg End Pcap A Bstart Bend Lstart Lend Pbonus
Critical Hit Chance (Critical Rating) by OppLvl*
1 75 25 50 200 15,000 1 75 0
75 76 25 50 15,000 16,500 75 76 0
76 100 25 50 16,500 30,000 75 100 0
100 101 25 50 30,000 33,000 100 101 0
101 105 25 50 33,000 45,000 100 105 0
105 106 25 50 45,000 54,000 105 106 0
106 115 25 50 54,000 90,000 106 115 0
115 116 25 50 90,000 99,000 115 116 0
116 120 25 50 99,000 225,000 116 120 0
120 121 25 50 225,000 315,000 120 121 0
121 130 25 50 315,000 630,000 121 130 0
130 131 25 75 630,000 1,247,000 130 131 0
131 140 25 75 1,247,000 2,494,000 131 140 0
Devastating Hit Chance (Critical Rating) by OppLvl*
1 75 10 20 400 30,000 1 75 0
75 76 10 20 30,000 33,000 75 76 0
76 100 10 20 33,000 60,000 75 100 0
100 101 10 20 60,000 66,000 100 101 0
101 105 10 20 66,000 90,000 100 105 0
105 106 10 20 90,000 108,000 105 106 0
106 115 10 20 108,000 180,000 106 115 0
115 116 10 20 180,000 198,000 115 116 0
116 120 10 20 198,000 450,000 116 120 0
120 121 10 20 450,000 630,000 120 121 0
121 130 10 20 630,000 1,260,000 121 130 0
130 131 10 30 1,260,000 2,495,000 130 131 0
131 140 10 30 2,495,000 4,990,000 131 140 0
Critical & Devastating Hit Magnitude (Critical Rating) by OppLvl*
1 75 100 200 500 37,500 1 75 0
75 76 100 200 37,500 41,300 75 76 0
76 100 100 200 41,300 75,000 75 100 0
100 101 100 200 75,000 82,500 100 101 0
101 105 100 200 82,500 112,500 100 105 0
105 106 100 200 112,500 135,000 105 106 0
106 115 100 200 135,000 225,000 106 115 0
115 116 100 200 225,000 247,500 115 116 0
116 120 100 200 247,500 562,500 116 120 0
120 121 75 145 562,500 787,500 120 121 0
121 122 75 140 787,500 1,575,000 121 130 0
122 123 75 135 787,500 1,575,000 121 130 0
123 124 75 130 787,500 1,575,000 121 130 0
124 125 75 125 787,500 1,575,000 121 130 0
125 126 75 120 787,500 1,575,000 121 130 0
126 127 75 115 787,500 1,575,000 121 130 0
127 128 75 112.5 787,500 1,575,000 121 130 0
128 129 75 112.5 787,500 1,575,000 121 130 0
129 130 75 112.5 787,500 1,575,000 121 130 0
130 131 75 225 1,575,000 5,198,000 130 131 0
131 140 75 225 5,198,000 10,396,000 131 140 0
Finesse (Finesse Rating) by OppLvl*
1 75 50 100 200 15,000 1 75 0
75 76 50 100 15,000 16,500 75 76 0
76 100 50 100 16,500 30,000 75 100 0
100 101 50 100 30,000 33,000 100 101 0
101 105 50 100 33,000 45,000 100 105 0
105 106 50 100 45,000 54,000 105 106 0
106 115 50 100 54,000 90,000 106 115 0
115 116 50 100 90,000 99,000 115 116 0
116 120 50 100 99,000 225,000 116 120 0
120 121 50 100 225,000 315,000 120 121 0
121 130 50 100 315,000 630,000 121 130 0
130 131 50 150 630,000 1,247,000 130 131 0
131 140 50 150 1,247,000 2,494,000 131 140 0
Physical Melee Damage, Physical Ranged Damage & Tactical Offence Damage
(Physical Mastery Rating & Tactical Mastery Rating) by OppLvl*
1 75 200 400 270 20,250 1 75 0
75 76 200 400 20,250 22,300 75 76 0
76 100 200 400 22,300 40,500 75 100 0
100 101 200 400 40,500 44,550 100 101 0
101 105 200 400 44,550 60,750 100 105 0
105 106 200 400 60,750 72,900 105 106 0
106 115 200 400 72,900 121,500 106 115 0
115 116 200 400 121,500 133,650 115 116 0
116 120 200 400 133,650 303,750 116 120 0
120 121 200 400 303,750 425,250 120 121 0
121 130 200 400 425,250 850,500 121 130 0
130 131 200 600 850,500 1,684,000 130 131 0
131 140 200 600 1,684,000 3,368,000 131 140 0
Tactical Outgoing Healing (Tactical Mastery Rating & Outgoing Healing Rating) by CharLvl*
1 75 70 140 400 30,000 1 75 0
75 76 70 140 30,000 33,000 75 76 0
76 100 70 140 33,000 60,000 75 100 0
100 101 70 140 60,000 66,000 100 101 0
101 105 70 140 66,000 90,000 100 105 0
105 106 70 140 90,000 108,000 105 106 0
106 115 70 140 108,000 180,000 106 115 0
115 116 70 140 180,000 198,000 115 116 0
116 120 70 140 198,000 450,000 116 120 0
120 121 70 140 450,000 630,000 120 121 0
121 130 70 140 630,000 1,260,000 121 130 0
130 131 70 210 1,260,000 2,495,000 130 131 0
131 140 70 210 2,495,000 4,990,000 131 140 0
Resistance (Resistance Rating) by Highest*
1 75 50 100 200 15,000 1 75 0
75 76 50 100 15,000 16,500 75 76 0
76 100 50 100 16,500 30,000 75 100 0
100 101 50 100 30,000 33,000 100 101 0
101 105 50 100 33,000 45,000 100 105 0
105 106 50 100 45,000 54,000 105 106 0
106 115 50 100 54,000 90,000 106 115 0
115 116 50 100 90,000 99,000 115 116 0
116 120 50 100 99,000 225,000 116 120 0
120 121 50 100 225,000 315,000 120 121 0
121 130 50 100 315,000 630,000 121 130 0
130 131 50 150 630,000 1,247,000 130 131 0
131 140 50 150 1,247,000 2,494,000 131 140 0
Critical Defence (Critical Defence) by Highest*
1 75 80 160 200 15,000 1 75 0
75 76 80 160 15,000 16,500 75 76 0
76 100 80 160 16,500 30,000 75 100 0
100 101 80 160 30,000 33,000 100 101 0
101 105 80 160 33,000 45,000 100 105 0
105 106 80 160 45,000 54,000 105 106 0
106 115 80 160 54,000 90,000 106 115 0
115 116 80 160 90,000 99,000 115 116 0
116 120 80 160 99,000 225,000 116 120 0
120 121 80 160 225,000 315,000 120 121 0
121 130 80 160 315,000 630,000 121 130 0
130 131 80 240 630,000 1,247,000 130 131 0
131 140 80 240 1,247,000 2,494,000 131 140 0
Incoming Healing (Incoming Healing Rating) by CharLvl*
1 75 25 50 200 15,000 1 75 0
75 76 25 50 15,000 16,500 75 76 0
76 100 25 50 16,500 30,000 75 100 0
100 101 25 50 30,000 33,000 100 101 0
101 105 25 50 33,000 45,000 100 105 0
105 106 25 50 45,000 54,000 105 106 0
106 115 25 50 54,000 90,000 106 115 0
115 116 25 50 90,000 99,000 115 116 0
116 120 25 50 99,000 225,000 116 120 0
120 121 25 50 225,000 315,000 120 121 0
121 130 25 50 315,000 630,000 121 130 0
130 131 25 75 630,000 1,247,000 130 131 0
131 140 25 75 1,247,000 2,494,000 131 140 0
Block, Parry & Evade Chance (Block, Parry & Evade Rating) by Highest*
1 75 13 26 200 15,000 1 75 0
75 76 13 26 15,000 16,500 75 76 0
76 100 13 26 16,500 30,000 75 100 0
100 101 13 26 30,000 33,000 100 101 0
101 105 13 26 33,000 45,000 100 105 0
105 106 13 26 45,000 54,000 105 106 0
106 115 13 26 54,000 90,000 106 115 0
115 116 13 26 90,000 99,000 115 116 0
116 120 13 26 99,000 225,000 116 120 0
120 121 13 26 225,000 315,000 120 121 0
121 130 13 26 315,000 630,000 121 130 0
130 131 13 39 630,000 1,247,000 130 131 0
131 140 13 39 1,247,000 2,494,000 131 140 0
Partial Block, Parry & Evade Chance (Block, Parry & Evade Rating) by Highest*
1 75 35 70 350 26,250 1 75 0
75 76 35 70 26,250 28,900 75 76 0
76 100 35 70 28,900 52,500 75 100 0
100 101 35 70 52,500 57,750 100 101 0
101 105 35 70 57,750 78,750 100 105 0
105 106 35 70 78,750 94,500 105 106 0
106 115 35 70 94,500 157,500 106 115 0
115 116 35 70 157,500 173,250 115 116 0
116 120 35 70 173,250 393,750 116 120 0
120 121 35 70 393,750 551,250 120 121 0
121 130 35 70 551,250 1,102,500 121 130 0
130 131 25 75 1,102,500 1,558,750 130 131 0
131 140 25 75 1,558,750 3,117,500 131 140 0
Partial Block, Parry & Evade Mitigation (Block, Parry & Evade Rating) by Highest*
1 75 50 100 350 26,250 1 75 0.1
75 76 50 100 26,250 28,900 75 76 0.1
76 100 50 100 28,900 52,500 75 100 0.1
100 101 50 100 52,500 57,750 100 101 0.1
101 105 50 100 57,750 78,750 100 105 0.1
105 106 50 100 78,750 94,500 105 106 0.1
106 115 50 100 94,500 157,500 106 115 0.1
115 116 50 100 157,500 173,250 115 116 0.1
116 120 50 100 173,250 393,750 116 120 0.1
120 121 50 100 393,750 551,250 120 121 0.1
121 130 50 100 551,250 1,102,500 121 130 0.1
130 131 35 105 1,102,500 1,558,750 130 131 0.1
131 140 35 105 1,558,750 3,117,500 131 140 0.1
Mitigations
Physical Mitigation (+Orc-craft, Fell-wrought) (Physical Mitigation) by Highest*
Tactical Mitigation (+Fire, Lightning, Frost, Acid, Shadow) (Tactical Mitigation) by Highest*
- Light Classes -
1 75 40 65 93 6,975 1 75 0
75 76 40 65 6,975 7,700 75 76 0
76 100 40 65 7,700 14,000 75 100 0
100 101 40 65 14,000 15,400 100 101 0
101 105 40 65 15,400 21,000 100 105 0
105 106 40 65 21,000 25,200 105 106 0
106 115 40 65 25,200 42,000 106 115 0
115 116 40 65 42,000 46,200 115 116 0
116 120 40 65 46,200 105,000 116 120 0
120 121 40 65 105,000 147,000 120 121 0
121 130 40 65 147,000 294,000 121 130 0
130 131 40 120 294,000 832,000 130 131 0
131 140 40 120 832,000 1,664,000 131 140 0
- Medium Classes -
1 75 50 85 127 9,525 1 75 0
75 76 50 85 9,525 10,500 75 76 0
76 100 50 85 10,500 19,100 75 100 0
100 101 50 85 19,100 21,010 100 101 0
101 105 50 85 21,010 28,650 100 105 0
105 106 50 85 28,650 34,380 105 106 0
106 115 50 85 34,380 57,300 106 115 0
115 116 50 85 57,300 63,030 115 116 0
116 120 50 85 63,030 143,250 116 120 0
120 121 50 85 143,250 200,550 120 121 0
121 130 50 85 200,550 401,100 121 130 0
130 131 50 150 401,100 1,045,000 130 131 0
131 140 50 150 1,045,000 2,090,000 131 140 0
- Heavy Classes -
1 75 60 110 174 13,050 1 75 0
75 76 60 110 13,050 14,400 75 76 0
76 100 60 110 14,400 26,100 75 100 0
100 101 60 110 26,100 28,710 100 101 0
101 105 60 110 28,710 39,150 100 105 0
105 106 60 110 39,150 46,980 105 106 0
106 115 60 110 46,980 78,300 106 115 0
115 116 60 110 78,300 86,130 115 116 0
116 120 60 110 86,130 195,750 116 120 0
120 121 60 110 195,750 274,050 120 121 0
121 130 60 110 274,050 548,100 121 130 0
130 131 60 180 548,100 1,252,000 130 131 0
131 140 60 180 1,252,000 2,504,000 131 140 0

(*) speculative

Rating Graphs

Critical Rating


Finesse Rating


Mastery (Physical/Tactical) Ratings


Outgoing Healing Rating


Resistance Rating


Note: The results of rating penetration effects as exists in T2-5 instances, are not shown in this graph. See Stat Caps for the adjusted rating values.

Critical Defence Rating


Incoming Healing Rating


Avoidance (Block/Parry/Evade) Ratings


Note: The results of rating penetration effects as exists in T2-5 instances, are not shown in these graphs. See Stat Caps for the adjusted rating values.

Mitigation (Physical/Tactical) Ratings


Note: The results of rating penetration effects as exists in T2-5 instances, are not shown in these graphs. See Stat Caps for the adjusted rating values.

See also