Rating to percentage formula

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

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

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

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:

• 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.

Percentage from rating (P)

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

• 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:

• 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:

• 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:

• 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.

Optimal Rating (Roptimal)

This formula can be used to calculate the optimal rating:

• 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.

The resulting B-rating needs to be rounded:

• lvl 1-50: 0 decimals
• lvl 51-105, 116-130: -1 decimals (10s)
• lvl 106-115, 131-150: -2 decimals (100s)
LvlSeg Start LvlSeg End Pcap A Bstart Bend Lstart Lend Pbonus
Critical Hit Chance (Critical Rating) by OppLvl*
1 50 25 75 300 3,000 1 50 0
50 60 25 75 3,000 4,500 50 60 0
60 65 25 75 4,500 6,000 60 65 0
65 75 25 75 6,000 9,000 65 75 0
75 85 25 75 9,000 13,500 75 85 0
85 95 25 75 13,500 19,500 85 95 0
95 100 25 75 19,500 27,100 95 100 0
100 105 25 75 27,100 36,000 100 105 0
105 106 25 75 36,000 40,000 105 106 0
106 115 25 75 40,000 54,000 106 115 0
115 116 25 75 54,000 62,000 115 116 0
116 120 25 75 62,000 68,000 116 120 0
120 121 25 75 68,000 78,000 120 121 0
121 130 25 75 78,000 102,000 121 130 0
130 131 25 75 102,000 117,000 130 131 0
131 140 25 75 117,000 204,000 131 140 0
140 141 25 75 204,000 265,000 140 141 0
141 150 25 75 265,000 450,000 141 150 0
Devastating Hit Chance (Critical Rating) by OppLvl*
1 50 10 30 400 4,000 1 50 0
50 60 10 30 4,000 6,000 50 60 0
60 65 10 30 6,000 8,000 60 65 0
65 75 10 30 8,000 12,000 65 75 0
75 85 10 30 12,000 18,000 75 85 0
85 95 10 30 18,000 26,000 85 95 0
95 100 10 30 26,000 36,000 95 100 0
100 105 10 30 36,000 48,000 100 105 0
105 106 10 30 48,000 53,000 105 106 0
106 115 10 30 53,000 72,000 106 115 0
115 116 10 30 72,000 83,000 115 116 0
116 120 10 30 83,000 90,000 116 120 0
120 121 10 30 90,000 104,000 120 121 0
121 130 10 30 104,000 135,000 121 130 0
130 131 10 30 135,000 155,000 130 131 0
131 140 10 30 155,000 270,000 131 140 0
140 141 10 30 270,000 350,000 140 141 0
141 150 10 30 350,000 600,000 141 150 0
Critical & Devastating Hit Magnitude (Critical Rating) by OppLvl*
1 50 75 225 600 6,000 1 50 0
50 60 75 225 6,000 9,000 50 60 0
60 65 75 225 9,000 12,000 60 65 0
65 75 75 225 12,000 18,000 65 75 0
75 85 75 225 18,000 27,000 75 85 0
85 95 75 225 27,000 39,000 85 95 0
95 100 75 225 39,000 54,000 95 100 0
100 105 75 225 54,000 72,000 100 105 0
105 106 75 225 72,000 79,000 105 106 0
106 115 75 225 79,000 108,000 106 115 0
115 116 75 225 108,000 124,000 115 116 0
116 120 75 225 124,000 135,000 116 120 0
120 121 75 225 135,000 155,000 120 121 0
121 130 75 225 155,000 203,000 121 130 0
130 131 75 225 203,000 233,000 130 131 0
131 140 75 225 233,000 410,000 131 140 0
140 141 75 225 410,000 530,000 140 141 0
141 150 75 225 530,000 900,000 141 150 0
Finesse (Finesse Rating) by OppLvl*
1 50 50 150 200 2,000 1 50 0
50 60 50 150 2,000 3,000 50 60 0
60 65 50 150 3,000 4,000 60 65 0
65 75 50 150 4,000 6,000 65 75 0
75 85 50 150 6,000 9,000 75 85 0
85 95 50 150 9,000 13,000 85 95 0
95 100 50 150 13,000 18,100 95 100 0
100 105 50 150 18,100 24,100 100 105 0
105 106 50 150 24,100 26,500 105 106 0
106 115 50 150 26,500 36,000 106 115 0
115 116 50 150 36,000 41,000 115 116 0
116 120 50 150 41,000 45,000 116 120 0
120 121 50 150 45,000 52,000 120 121 0
121 130 50 150 52,000 68,000 121 130 0
130 131 50 150 68,000 78,000 130 131 0
131 140 50 150 78,000 136,000 131 140 0
140 141 50 150 136,000 177,000 140 141 0
141 150 50 150 177,000 300,000 141 150 0
Physical Melee Damage, Physical Ranged Damage & Tactical Offence Damage
(Physical Mastery Rating & Tactical Mastery Rating) by OppLvl*
1 50 200 600 300 3,000 1 50 0
50 60 200 600 3,000 4,500 50 60 0
60 65 200 600 4,500 6,000 60 65 0
65 75 200 600 6,000 9,000 65 75 0
75 85 200 600 9,000 13,500 75 85 0
85 95 200 600 13,500 19,500 85 95 0
95 100 200 600 19,500 27,100 95 100 0
100 105 200 600 27,100 36,000 100 105 0
105 106 200 600 36,000 40,000 105 106 0
106 115 200 600 40,000 54,000 106 115 0
115 116 200 600 54,000 62,000 115 116 0
116 120 200 600 62,000 68,000 116 120 0
120 121 200 600 68,000 78,000 120 121 0
121 130 200 600 78,000 102,000 121 130 0
130 131 200 600 102,000 117,000 130 131 0
131 140 200 600 117,000 204,000 131 140 0
140 141 200 600 204,000 265,000 140 141 0
141 150 200 600 265,000 450,000 141 150 0
Tactical Outgoing Healing (Tactical Mastery Rating & Outgoing Healing Rating) by CharLvl*
1 50 70 210 450 4,500 1 50 0
50 60 70 210 4,500 6,800 50 60 0
60 65 70 210 6,800 9,100 60 65 0
65 75 70 210 9,100 13,700 65 75 0
75 85 70 210 13,700 20,600 75 85 0
85 95 70 210 20,600 29,800 85 95 0
95 100 70 210 29,800 41,000 95 100 0
100 105 70 210 41,000 55,000 100 105 0
105 106 70 210 55,000 61,000 105 106 0
106 115 70 210 61,000 83,000 106 115 0
115 116 70 210 83,000 95,000 115 116 0
116 120 70 210 95,000 104,000 116 120 0
120 121 70 210 104,000 120,000 120 121 0
121 130 70 210 120,000 156,000 121 130 0
130 131 70 210 156,000 179,000 130 131 0
131 140 70 210 179,000 312,000 131 140 0
140 141 70 210 312,000 410,000 140 141 0
141 150 70 210 410,000 690,000 141 150 0
Resistance (Resistance Rating) by Highest*
1 50 50 150 300 3,000 1 50 0
50 60 50 150 3,000 4,500 50 60 0
60 65 50 150 4,500 6,000 60 65 0
65 75 50 150 6,000 9,000 65 75 0
75 85 50 150 9,000 13,500 75 85 0
85 95 50 150 13,500 19,500 85 95 0
95 100 50 150 19,500 27,100 95 100 0
100 105 50 150 27,100 36,000 100 105 0
105 106 50 150 36,000 40,000 105 106 0
106 115 50 150 40,000 54,000 106 115 0
115 116 50 150 54,000 62,000 115 116 0
116 120 50 150 62,000 68,000 116 120 0
120 121 50 150 68,000 78,000 120 121 0
121 130 50 150 78,000 102,000 121 130 0
130 131 50 150 102,000 117,000 130 131 0
131 140 50 150 117,000 204,000 131 140 0
140 141 50 150 204,000 265,000 140 141 0
141 150 50 150 265,000 450,000 141 150 0
Critical Defence (Critical Defence) by Highest*
1 50 80 240 200 2,000 1 50 0
50 60 80 240 2,000 3,000 50 60 0
60 65 80 240 3,000 4,000 60 65 0
65 75 80 240 4,000 6,000 65 75 0
75 85 80 240 6,000 9,000 75 85 0
85 95 80 240 9,000 13,000 85 95 0
95 100 80 240 13,000 18,100 95 100 0
100 105 80 240 18,100 24,100 100 105 0
105 106 80 240 24,100 26,500 105 106 0
106 115 80 240 26,500 36,000 106 115 0
115 116 80 240 36,000 41,000 115 116 0
116 120 80 240 41,000 45,000 116 120 0
120 121 80 240 45,000 52,000 120 121 0
121 130 80 240 52,000 68,000 121 130 0
130 131 80 240 68,000 78,000 130 131 0
131 140 80 240 78,000 136,000 131 140 0
140 141 80 240 136,000 177,000 140 141 0
141 150 80 240 177,000 300,000 141 150 0
Incoming Healing (Incoming Healing Rating) by CharLvl*
1 50 25 75 200 2,000 1 50 0
50 60 25 75 2,000 3,000 50 60 0
60 65 25 75 3,000 4,000 60 65 0
65 75 25 75 4,000 6,000 65 75 0
75 85 25 75 6,000 9,000 75 85 0
85 95 25 75 9,000 13,000 85 95 0
95 100 25 75 13,000 18,100 95 100 0
100 105 25 75 18,100 24,100 100 105 0
105 106 25 75 24,100 26,500 105 106 0
106 115 25 75 26,500 36,000 106 115 0
115 116 25 75 36,000 41,000 115 116 0
116 120 25 75 41,000 45,000 116 120 0
120 121 25 75 45,000 52,000 120 121 0
121 130 25 75 52,000 68,000 121 130 0
130 131 25 75 68,000 78,000 130 131 0
131 140 25 75 78,000 136,000 131 140 0
140 141 25 75 136,000 177,000 140 141 0
141 150 25 75 177,000 300,000 141 150 0
Block, Parry & Evade Chance (Block, Parry & Evade Rating) by Highest*
1 50 13 39 200 2,000 1 50 0
50 60 13 39 2,000 3,000 50 60 0
60 65 13 39 3,000 4,000 60 65 0
65 75 13 39 4,000 6,000 65 75 0
75 85 13 39 6,000 9,000 75 85 0
85 95 13 39 9,000 13,000 85 95 0
95 100 13 39 13,000 18,100 95 100 0
100 105 13 39 18,100 24,100 100 105 0
105 106 13 39 24,100 26,500 105 106 0
106 115 13 39 26,500 36,000 106 115 0
115 116 13 39 36,000 41,000 115 116 0
116 120 13 39 41,000 45,000 116 120 0
120 121 13 39 45,000 52,000 120 121 0
121 130 13 39 52,000 68,000 121 130 0
130 131 13 39 68,000 78,000 130 131 0
131 140 13 39 78,000 136,000 131 140 0
140 141 13 39 136,000 177,000 140 141 0
141 150 13 39 177,000 300,000 141 150 0
Partial Block, Parry & Evade Chance (Block, Parry & Evade Rating) by Highest*
1 50 25 75 350 3,500 1 50 0
50 60 25 75 3,500 5,300 50 60 0
60 65 25 75 5,300 7,100 60 65 0
65 75 25 75 7,100 10,700 65 75 0
75 85 25 75 10,700 16,100 75 85 0
85 95 25 75 16,100 23,300 85 95 0
95 100 25 75 23,300 32,000 95 100 0
100 105 25 75 32,000 43,000 100 105 0
105 106 25 75 43,000 47,000 105 106 0
106 115 25 75 47,000 65,000 106 115 0
115 116 25 75 65,000 75,000 115 116 0
116 120 25 75 75,000 81,000 116 120 0
120 121 25 75 81,000 93,000 120 121 0
121 130 25 75 93,000 122,000 121 130 0
130 131 25 75 122,000 140,000 130 131 0
131 140 25 75 140,000 244,000 131 140 0
140 141 25 75 244,000 320,000 140 141 0
141 150 25 75 320,000 540,000 141 150 0
Partial Block, Parry & Evade Mitigation (Block, Parry & Evade Rating) by Highest*
1 50 35 105 350 3,500 1 50 0.1
50 60 35 105 3,500 5,300 50 60 0.1
60 65 35 105 5,300 7,100 60 65 0.1
65 75 35 105 7,100 10,700 65 75 0.1
75 85 35 105 10,700 16,100 75 85 0.1
85 95 35 105 16,100 23,300 85 95 0.1
95 100 35 105 23,300 32,000 95 100 0.1
100 105 35 105 32,000 43,000 100 105 0.1
105 106 35 105 43,000 47,000 105 106 0.1
106 115 35 105 47,000 65,000 106 115 0.1
115 116 35 105 65,000 75,000 115 116 0.1
116 120 35 105 75,000 81,000 116 120 0.1
120 121 35 105 81,000 93,000 120 121 0.1
121 130 35 105 93,000 122,000 121 130 0.1
130 131 35 105 122,000 140,000 130 131 0.1
131 140 35 105 140,000 244,000 131 140 0.1
140 141 35 105 244,000 320,000 140 141 0.1
141 150 35 105 320,000 540,000 141 150 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 50 40 120 105 1,330 1 50 0
50 60 40 120 1,330 2,000 50 60 0
60 65 40 120 2,000 2,660 60 65 0
65 75 40 120 2,660 4,000 65 75 0
75 85 40 120 4,000 6,000 75 85 0
85 95 40 120 6,000 8,700 85 95 0
95 100 40 120 8,700 12,100 95 100 0
100 105 40 120 12,100 16,100 100 105 0
105 106 40 120 16,100 17,600 105 106 0
106 115 40 120 17,600 24,000 106 115 0
115 116 40 120 24,000 27,300 115 116 0
116 120 40 120 27,300 30,000 116 120 0
120 121 40 120 30,000 35,000 120 121 0
121 130 40 120 35,000 45,000 121 130 0
130 131 40 120 45,000 52,000 130 131 0
131 140 40 120 52,000 91,000 131 140 0
140 141 40 120 91,000 118,000 140 141 0
141 150 40 120 118,000 200,000 141 150 0
- Medium Classes -
1 50 50 150 144 1,670 1 50 0
50 60 50 150 1,670 2,500 50 60 0
60 65 50 150 2,500 3,300 60 65 0
65 75 50 150 3,300 5,000 65 75 0
75 85 50 150 5,000 7,500 75 85 0
85 95 50 150 7,500 10,800 85 95 0
95 100 50 150 10,800 15,100 95 100 0
100 105 50 150 15,100 20,100 100 105 0
105 106 50 150 20,100 22,100 105 106 0
106 115 50 150 22,100 30,000 106 115 0
115 116 50 150 30,000 34,000 115 116 0
116 120 50 150 34,000 37,000 116 120 0
120 121 50 150 37,000 43,000 120 121 0
121 130 50 150 43,000 57,000 121 130 0
130 131 50 150 57,000 65,000 130 131 0
131 140 50 150 65,000 113,000 131 140 0
140 141 50 150 113,000 147,000 140 141 0
141 150 50 150 147,000 250,000 141 150 0
- Heavy Classes -
1 50 60 180 200 2,000 1 50 0
50 60 60 180 2,000 3,000 50 60 0
60 65 60 180 3,000 4,000 60 65 0
65 75 60 180 4,000 6,000 65 75 0
75 85 60 180 6,000 9,000 75 85 0
85 95 60 180 9,000 13,000 85 95 0
95 100 60 180 13,000 18,100 95 100 0
100 105 60 180 18,100 24,100 100 105 0
105 106 60 180 24,100 26,500 105 106 0
106 115 60 180 26,500 36,000 106 115 0
115 116 60 180 36,000 41,000 115 116 0
116 120 60 180 41,000 45,000 116 120 0
120 121 60 180 45,000 52,000 120 121 0
121 130 60 180 52,000 68,000 121 130 0
130 131 60 180 68,000 78,000 130 131 0
131 140 60 180 78,000 136,000 131 140 0
140 141 60 180 136,000 177,000 140 141 0
141 150 60 180 177,000 300,000 141 150 0

(*) speculative

Rating Graphs

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.