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.
Percentage Rating LvlSeg Start LvlSeg End Pcap A Bstart Bend Lstart Lend Pbonus Level Type Last Checked
Critical Hit Critical Rating 75 25 50 200 15000 1 75 OppLvl* U25
75 76 25 50 15000 16500 75 76 OppLvl* U25
76 100 25 50 16500 30000 75 100 OppLvl* U25
100 101 25 50 30000 33000 100 101 OppLvl* U25
101 105 25 50 33000 45000 100 105 OppLvl* U25
105 106 25 50 45000 54000 105 106 OppLvl* U25
106 115 25 50 54000 90000 106 115 OppLvl* U25
115 116 25 50 90000 99000 115 116 OppLvl* U25
116 120 25 50 99000 225000 116 120 OppLvl* U25
120 121 25 50 225000 315000 120 121 OppLvl* U25
121 25 50 315000 630000 121 130 OppLvl* U25
Devastating Hit Critical Rating 75 10 20 400 30000 1 75 OppLvl* U25
75 76 10 20 30000 33000 75 76 OppLvl* U25
76 100 10 20 33000 60000 75 100 OppLvl* U25
100 101 10 20 60000 66000 100 101 OppLvl* U25
101 105 10 20 66000 90000 100 105 OppLvl* U25
105 106 10 20 90000 108000 105 106 OppLvl* U25
106 115 10 20 108000 180000 106 115 OppLvl* U25
115 116 10 20 180000 198000 115 116 OppLvl* U25
116 120 10 20 198000 450000 116 120 OppLvl* U25
120 121 10 20 450000 630000 120 121 OppLvl* U25
121 10 20 630000 1260000 121 130 OppLvl* U25
Critical & Devastating Hit Magnitude Critical Rating 75 100 200 500 37500 1 75 OppLvl* U25
75 76 100 200 37500 41300 75 76 OppLvl* U25
76 100 100 200 41300 75000 75 100 OppLvl* U25
100 101 100 200 75000 82500 100 101 OppLvl* U25
101 105 100 200 82500 112500 100 105 OppLvl* U25
105 106 100 200 112500 135000 105 106 OppLvl* U25
106 115 100 200 135000 225000 106 115 OppLvl* U25
115 116 100 200 225000 247500 115 116 OppLvl* U25
116 120 100 200 247500 562500 116 120 OppLvl* U25
120 121 75 145 562500 787500 120 121 OppLvl* U25
121 122 75 140 787500 1575000 121 130 OppLvl* U25
122 123 75 135 787500 1575000 121 130 OppLvl* U25
123 124 75 130 787500 1575000 121 130 OppLvl* U25
124 125 75 125 787500 1575000 121 130 OppLvl* U25
125 126 75 120 787500 1575000 121 130 OppLvl* U25
126 127 75 115 787500 1575000 121 130 OppLvl* U25
127 75 112.5 787500 1575000 121 130 OppLvl* U25
Finesse Finesse 75 50 100 200 15000 1 75 OppLvl* U25
75 76 50 100 15000 16500 75 76 OppLvl* U25
76 100 50 100 16500 30000 75 100 OppLvl* U25
100 101 50 100 30000 33000 100 101 OppLvl* U25
101 105 50 100 33000 45000 100 105 OppLvl* U25
105 106 50 100 45000 54000 105 106 OppLvl* U25
106 115 50 100 54000 90000 106 115 OppLvl* U25
115 116 50 100 90000 99000 115 116 OppLvl* U25
116 120 50 100 99000 225000 116 120 OppLvl* U25
120 121 50 100 225000 315000 120 121 OppLvl* U25
121 50 100 315000 630000 121 130 OppLvl* U25
Physical Melee-, Physical Ranged- & Tactical Offence Damage Physical Mastery & Tactical Mastery 75 200 400 270 20250 1 75 OppLvl* U25
75 76 200 400 20250 22300 75 76 OppLvl* U25
76 100 200 400 22300 40500 75 100 OppLvl* U25
100 101 200 400 40500 44550 100 101 OppLvl* U25
101 105 200 400 44550 60750 100 105 OppLvl* U25
105 106 200 400 60750 72900 105 106 OppLvl* U25
106 115 200 400 72900 121500 106 115 OppLvl* U25
115 116 200 400 121500 133650 115 116 OppLvl* U25
116 120 200 400 133650 303750 116 120 OppLvl* U25
120 121 200 400 303750 425250 120 121 OppLvl* U25
121 200 400 425250 850500 121 130 OppLvl* U25
Tactical Outgoing Healing Outgoing Healing Rating 75 70 140 200 15000 1 75 CharLvl* U25
75 76 70 140 15000 16500 75 76 CharLvl* U25
76 100 70 140 16500 30000 75 100 CharLvl* U25
100 101 70 140 30000 33000 100 101 CharLvl* U25
101 105 70 140 33000 45000 100 105 CharLvl* U25
105 106 70 140 45000 54000 105 106 CharLvl* U25
106 115 70 140 54000 90000 106 115 CharLvl* U25
115 116 70 140 90000 99000 115 116 CharLvl* U25
116 120 70 140 99000 225000 116 120 CharLvl* U25
120 121 70 140 225000 315000 120 121 CharLvl* U25
121 70 140 315000 630000 121 130 CharLvl* U25
Resistance Resistance 75 50 100 200 15000 1 75 Highest* U25
75 76 50 100 15000 16500 75 76 Highest* U25
76 100 50 100 16500 30000 75 100 Highest* U25
100 101 50 100 30000 33000 100 101 Highest* U25
101 105 50 100 33000 45000 100 105 Highest* U25
105 106 50 100 45000 54000 105 106 Highest* U25
106 115 50 100 54000 90000 106 115 Highest* U25
115 116 50 100 90000 99000 115 116 Highest* U25
116 120 50 100 99000 225000 116 120 Highest* U25
120 121 50 100 225000 315000 120 121 Highest* U25
121 50 100 315000 630000 121 130 Highest* U25
Critical Defence Critical Defence 75 80 160 200 15000 1 75 Highest* U25
75 76 80 160 15000 16500 75 76 Highest* U25
76 100 80 160 16500 30000 75 100 Highest* U25
100 101 80 160 30000 33000 100 101 Highest* U25
101 105 80 160 33000 45000 100 105 Highest* U25
105 106 80 160 45000 54000 105 106 Highest* U25
106 115 80 160 54000 90000 106 115 Highest* U25
115 116 80 160 90000 99000 115 116 Highest* U25
116 120 80 160 99000 225000 116 120 Highest* U25
120 121 80 160 225000 315000 120 121 Highest* U25
121 80 160 315000 630000 121 130 Highest* U25
Incoming Healing Incoming Healing 75 25 50 200 15000 1 75 CharLvl* U25
75 76 25 50 15000 16500 75 76 CharLvl* U25
76 100 25 50 16500 30000 75 100 CharLvl* U25
100 101 25 50 30000 33000 100 101 CharLvl* U25
101 105 25 50 33000 45000 100 105 CharLvl* U25
105 106 25 50 45000 54000 105 106 CharLvl* U25
106 115 25 50 54000 90000 106 115 CharLvl* U25
115 116 25 50 90000 99000 115 116 CharLvl* U25
116 120 25 50 99000 225000 116 120 CharLvl* U25
120 121 25 50 225000 315000 120 121 CharLvl* U25
121 25 50 315000 630000 121 130 CharLvl* U25
Block, Parry & Evade Block, Parry & Evade 75 13 26 200 15000 1 75 Highest* U25
75 76 13 26 15000 16500 75 76 Highest* U25
76 100 13 26 16500 30000 75 100 Highest* U25
100 101 13 26 30000 33000 100 101 Highest* U25
101 105 13 26 33000 45000 100 105 Highest* U25
105 106 13 26 45000 54000 105 106 Highest* U25
106 115 13 26 54000 90000 106 115 Highest* U25
115 116 13 26 90000 99000 115 116 Highest* U25
116 120 13 26 99000 225000 116 120 Highest* U25
120 121 13 26 225000 315000 120 121 Highest* U25
121 13 26 315000 630000 121 130 Highest* U25
Partial Block, Partial Parry & Partial Evade Block, Parry & Evade 75 35 70 400 30000 1 75 Highest* U25
75 76 35 70 30000 33000 75 76 Highest* U25
76 100 35 70 33000 60000 75 100 Highest* U25
100 101 35 70 60000 66000 100 101 Highest* U25
101 105 35 70 66000 90000 100 105 Highest* U25
105 106 35 70 90000 108000 105 106 Highest* U25
106 115 35 70 108000 180000 106 115 Highest* U25
115 116 35 70 180000 198000 115 116 Highest* U25
116 120 35 70 198000 450000 116 120 Highest* U25
120 121 35 70 450000 630000 120 121 Highest* U25
121 35 70 630000 1260000 121 130 Highest* U25
Partial Block Mitigation, Partial Parry Mitigation & Partial Evade Mitigation Block, Parry & Evade 75 50 100 400 30000 1 75 10 Highest* U25
75 76 50 100 30000 33000 75 76 10 Highest* U25
76 100 50 100 33000 60000 75 100 10 Highest* U25
100 101 50 100 60000 66000 100 101 10 Highest* U25
101 105 50 100 66000 90000 100 105 10 Highest* U25
105 106 50 100 90000 108000 105 106 10 Highest* U25
106 115 50 100 108000 180000 106 115 10 Highest* U25
115 116 50 100 180000 198000 115 116 10 Highest* U25
116 120 50 100 198000 450000 116 120 10 Highest* U25
120 121 50 100 450000 630000 120 121 10 Highest* U25
121 50 100 630000 1260000 121 130 10 Highest* U25
Physical Mitigation, Orc-craft Mitigation, Fell-wrought Mitigation & Tactical Mitigation: Physical Mitigation, Orc-craft Mitigation, Fell-wrought Mitigation & Tactical Mitigation
Light Armour 75 40 65 93 6975 1 75 Highest U25
75 76 40 65 6975 7700 75 76 Highest U25
76 100 40 65 7700 14000 75 100 Highest U25
100 101 40 65 14000 15400 100 101 Highest U25
101 105 40 65 15400 21000 100 105 Highest U25
105 106 40 65 21000 25200 105 106 Highest U25
106 115 40 65 25200 42000 106 115 Highest U25
115 116 40 65 42000 46200 115 116 Highest U25
116 120 40 65 46200 105000 116 120 Highest U25
120 121 40 65 105000 147000 120 121 Highest U25
121 40 65 147000 294000 121 130 Highest U25
Medium Armour 75 50 85 127 9525 1 75 Highest U25
75 76 50 85 9525 10500 75 76 Highest U25
76 100 50 85 10500 19100 75 100 Highest U25
100 101 50 85 19100 21010 100 101 Highest U25
101 105 50 85 21010 28650 100 105 Highest U25
105 106 50 85 28650 34380 105 106 Highest U25
106 115 50 85 34380 57300 106 115 Highest U25
115 116 50 85 57300 63030 115 116 Highest U25
116 120 50 85 63030 143250 116 120 Highest U25
120 121 50 85 143250 200550 120 121 Highest U25
121 50 85 200550 401100 121 130 Highest U25
Heavy Armour 75 60 110 174 13050 1 75 Highest U25
75 76 60 110 13050 14400 75 76 Highest U25
76 100 60 110 14400 26100 75 100 Highest U25
100 101 60 110 26100 28710 100 101 Highest U25
101 105 60 110 28710 39150 100 105 Highest U25
105 106 60 110 39150 46980 105 106 Highest U25
106 115 60 110 46980 78300 106 115 Highest U25
115 116 60 110 78300 86130 115 116 Highest U25
116 120 60 110 86130 195750 116 120 Highest U25
120 121 60 110 195750 274050 120 121 Highest U25
121 60 110 274050 548100 121 130 Highest U25

(*) speculative

Rating Graphs

Critical Rating

GR crit130.png

Finesse Rating

GR finesse120.png

Mastery (Physical/Tactical) Ratings

GR mast120.png

Resistance Rating

GR resist120.png

Note: The results of rating penetration effects as exists in T2/T3 instances and skirmishes, are not shown in this graph. See Stat Caps for the adjusted rating values.

Critical Defence Rating

GR crdef120.png

Incoming Healing Rating

GR inheal120.png

Avoidance (Block/Parry/Evade) Ratings

GR avoid120.png

Note: The results of rating penetration effects as exists in T2/T3 instances and skirmishes, are not shown in this graph. See Stat Caps for the adjusted rating values.

Mitigation (Physical/Tactical) Ratings

GR mit120.png

Note: The results of rating penetration effects as exists in T2/T3 instances and skirmishes, are not shown in this graph. See Stat Caps for the adjusted rating values.

See also