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.

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:

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.

LvlSeg Start	LvlSeg End	Pcap	A	Bstart	Bend	Lstart	Lend	Pbonus
Critical Hit Chance (Critical Rating) by OppLvl*
1	75	25	75	300	9,000	1	75	0
75	76	25	75	9,000	9,450	75	76	0
76	100	25	75	9,450	27,100	76	100	0
100	101	25	75	27,100	28,880	100	101	0
101	105	25	75	28,880	36,000	101	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
Devastating Hit Chance (Critical Rating) by OppLvl*
1	75	10	30	400	12,000	1	75	0
75	76	10	30	12,000	12,600	75	76	0
76	100	10	30	12,600	36,000	76	100	0
100	101	10	30	36,000	38,400	100	101	0
101	105	10	30	38,400	48,000	101	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
Critical & Devastating Hit Magnitude (Critical Rating) by OppLvl*
1	75	75	225	600	18,000	1	75	0
75	76	75	225	18,000	18,900	75	76	0
76	100	75	225	18,900	54,000	76	100	0
100	101	75	225	54,000	57,600	100	101	0
101	105	75	225	57,600	72,000	101	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	122	75	225	155,000	160,330	121	122	0
122	123	75	225	160,330	165,670	122	123	0
123	124	75	225	165,670	171,000	123	124	0
124	125	75	225	171,000	176,330	124	125	0
125	126	75	225	176,330	181,670	125	126	0
126	127	75	225	181,670	187,000	126	127	0
127	128	75	225	187,000	192,330	127	128	0
128	129	75	225	192,330	197,670	128	129	0
129	130	75	225	197,670	203,000	129	130	0
130	131	75	225	203,000	233,000	130	131	0
131	140	75	225	233,000	410,000	131	140	0
Finesse (Finesse Rating) by OppLvl*
1	75	50	150	200	6,000	1	75	0
75	76	50	150	6,000	6,300	75	76	0
76	100	50	150	6,300	18,100	76	100	0
100	101	50	150	18,100	19,300	100	101	0
101	105	50	150	19,300	24,100	101	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
Physical Melee Damage, Physical Ranged Damage & Tactical Offence Damage (Physical Mastery Rating & Tactical Mastery Rating) by OppLvl*
1	75	200	600	300	9,000	1	75	0
75	76	200	600	9,000	9,450	75	76	0
76	100	200	600	9,450	27,100	76	100	0
100	101	200	600	27,100	28,880	100	101	0
101	105	200	600	28,880	36,000	101	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
Tactical Outgoing Healing (Tactical Mastery Rating & Outgoing Healing Rating) by CharLvl*
1	75	70	210	450	13,700	1	75	0
75	76	70	210	13,700	14,390	75	76	0
76	100	70	210	14,390	41,000	76	100	0
100	101	70	210	41,000	43,800	100	101	0
101	105	70	210	43,800	55,000	101	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
Resistance (Resistance Rating) by Highest*
1	75	50	150	300	9,000	1	75	0
75	76	50	150	9,000	9,450	75	76	0
76	100	50	150	9,450	27,100	76	100	0
100	101	50	150	27,100	28,880	100	101	0
101	105	50	150	28,880	36,000	101	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
Critical Defence (Critical Defence) by Highest*
1	75	80	240	200	6,000	1	75	0
75	76	80	240	6,000	6,300	75	76	0
76	100	80	240	6,300	18,100	76	100	0
100	101	80	240	18,100	19,300	100	101	0
101	105	80	240	19,300	24,100	101	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
Incoming Healing (Incoming Healing Rating) by CharLvl*
1	75	25	75	200	6,000	1	75	0
75	76	25	75	6,000	6,300	75	76	0
76	100	25	75	6,300	18,100	76	100	0
100	101	25	75	18,100	19,300	100	101	0
101	105	25	75	19,300	24,100	101	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
Block, Parry & Evade Chance (Block, Parry & Evade Rating) by Highest*
1	75	13	39	200	6,000	1	75	0
75	76	13	39	6,000	6,300	75	76	0
76	100	13	39	6,300	18,100	76	100	0
100	101	13	39	18,100	19,300	100	101	0
101	105	13	39	19,300	24,100	101	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
Partial Block, Parry & Evade Chance (Block, Parry & Evade Rating) by Highest*
1	75	25	75	350	10,700	1	75	0
75	76	25	75	10,700	11,240	75	76	0
76	100	25	75	11,240	32,000	76	100	0
100	101	25	75	32,000	34,200	100	101	0
101	105	25	75	34,200	43,000	101	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
Partial Block, Parry & Evade Mitigation (Block, Parry & Evade Rating) by Highest*
1	75	35	105	350	10,700	1	75	0.1
75	76	35	105	10,700	11,240	75	76	0.1
76	100	35	105	11,240	32,000	76	100	0.1
100	101	35	105	32,000	34,200	100	101	0.1
101	105	35	105	34,200	43,000	101	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
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	120	105	4,000	1	75	0
75	76	40	120	4,000	4,200	75	76	0
76	100	40	120	4,200	12,100	76	100	0
100	101	40	120	12,100	12,900	100	101	0
101	105	40	120	12,900	16,100	101	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
- Medium Classes -
1	75	50	150	144	5,000	1	75	0
75	76	50	150	5,000	5,250	75	76	0
76	100	50	150	5,250	15,100	76	100	0
100	101	50	150	15,100	16,100	100	101	0
101	105	50	150	16,100	20,100	101	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
- Heavy Classes -
1	75	60	180	200	6,000	1	75	0
75	76	60	180	6,000	6,300	75	76	0
76	100	60	180	6,300	18,100	76	100	0
100	101	60	180	18,100	19,300	100	101	0
101	105	60	180	19,300	24,100	101	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

(*) 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