# 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 is not the only way to limit a percentage. The calculation formula itself has the ability, with certain parameters, to limit the resulting percentage to under 100%. This mathematical "soft" cap is unatainable by any rating: the curve will always stay under 100%.

### 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.

Large jumps in required cap rating (Rcap) are caused by cap percentage (Pcap) increases or because of the large stat and difficulty increases which came with the Mordor expansion (Update 21) for levels 106-115.

## Formulas

### Required rating for percentage cap (Rcap)

As we know, Rcap increases with fixed steps, resulting in a linear (straight line) formula with:

- RcapF = a factor or multiplier which indicates the amount of Rcap increase per level (step size).
- 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.
- RcapC = a constant, offset.

### Percentage from rating (P)

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

- C = curve constant which determines the bend and starting angle of the curve.
- Rcap = required rating for percentage cap. see above.
- R = rating amount
- Pcap = maximum (cap) percentage.

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.

### Rating from percentage (R)

This formula can be used to calculate the required rating(R) for a given percentage(P) with:

- Rcap = required rating for percentage cap. see above.
- C = curve constant which determines the bend and starting angle of the curve.
- Pcap = maximum (cap) percentage.
- P = desired percentage for which to calculate the rating amount.

### The effect of "C"

This animation shows the effect of C on the shape/bend of the curve. C=0 gives a straight line.

### Advanced: AB not C

While calculating with C, Rcap and Pcap makes it more easy to understand, it's not the way calculations happen in Lotro internally. The AB formulas require less operations and so are more efficient:

P = A/(1+B/R) and R = B/(A/P-1)

A and B are derivable from C, Rcap and Pcap as follows:

A = (C+1)*Pcap/C and B = Rcap/C

A is constant for all player levels as C and Pcap never change. B or so-called B-rating changes with fixed steps in level intervals. In player level intervals above 75, the B-rating is rounded to multiples of 10 (using a common internal function which is also used elsewhere).

## 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 L-start and L-end.

Explanation of the columns:

- Pbonus = a bonus percentage which needs to be added to the percentage formula result.
- Level = what level to use in the Rcap 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.

**Note**: At levels above 75 rounding takes place in the calculation of Rcap. Rcap needs to be rounded to multiples of 10*C. For instance 10*1.6 = 16 for Light Armour Mitigations.

Percentage | Rating | L-start | L-end | C | Pcap | RcapF | RcapC | Pbonus | Level | Last Checked |
---|---|---|---|---|---|---|---|---|---|---|

Critical Hit | Critical Rating | 1 | 75 | 1 | 25 | 200 | OppLvl* | U23 | ||

76 | 76 | 1 | 25 | 4125/19 | OppLvl* | U23 | ||||

77 | 100 | 1 | 25 | 540 | -24000 | OppLvl* | U23 | |||

101 | 105 | 1 | 25 | 3000 | -270000 | OppLvl* | U23 | |||

106 | 115 | 1 | 25 | 4000 | -370000 | OppLvl* | U23 | |||

116 | 120 | 1 | 25 | 31500 | -3555000 | OppLvl* | U23 | |||

Devastating Hit | Critical Rating | 1 | 75 | 1 | 10 | 400 | OppLvl* | U23 | ||

76 | 76 | 1 | 10 | 8250/19 | OppLvl* | U23 | ||||

77 | 100 | 1 | 10 | 1080 | -48000 | OppLvl* | U23 | |||

101 | 105 | 1 | 10 | 6000 | -540000 | OppLvl* | U23 | |||

106 | 115 | 1 | 10 | 8000 | -740000 | OppLvl* | U23 | |||

116 | 120 | 1 | 10 | 63000 | -7110000 | OppLvl* | U23 | |||

Critical & Devastating Hit Magnitude | Critical Rating | 1 | 75 | 1 | 100 | 500 | OppLvl* | U23 | ||

76 | 76 | 1 | 100 | 10325/19 | OppLvl* | U23 | ||||

77 | 100 | 1 | 100 | 1348 | -59800 | OppLvl* | U23 | |||

101 | 105 | 1 | 100 | 7500 | -675000 | OppLvl* | U23 | |||

106 | 115 | 1 | 100 | 10000 | -925000 | OppLvl* | U23 | |||

116 | 120 | 1 | 100 | 78750 | -8887500 | OppLvl* | U23 | |||

Finesse | Finesse | 1 | 75 | 1 | 50 | 200 | OppLvl* | U23 | ||

76 | 76 | 1 | 50 | 4125/19 | OppLvl* | U23 | ||||

77 | 100 | 1 | 50 | 540 | -24000 | OppLvl* | U23 | |||

101 | 105 | 1 | 50 | 3000 | -270000 | OppLvl* | U23 | |||

106 | 115 | 1 | 50 | 4000 | -370000 | OppLvl* | U23 | |||

116 | 120 | 1 | 50 | 31500 | -3555000 | OppLvl* | U23 | |||

Physical Melee-, Physical Ranged- & Tactical Offence Damage | Physical Mastery & Tactical Mastery | 1 | 75 | 1 | 200 | 270 | OppLvl* | U23 | ||

76 | 76 | 1 | 200 | 5575/19 | OppLvl* | U23 | ||||

77 | 100 | 1 | 200 | 728 | -32300 | OppLvl* | U23 | |||

101 | 105 | 1 | 200 | 4050 | -364500 | OppLvl* | U23 | |||

106 | 115 | 1 | 200 | 5400 | -499500 | OppLvl* | U23 | |||

116 | 120 | 1 | 200 | 42525 | -4799250 | OppLvl* | U23 | |||

Tactical Outgoing Healing | Tactical Mastery | 1 | 75 | 1 | 70 | 200 | CharLvl* | U23 | ||

76 | 76 | 1 | 70 | 4125/19 | CharLvl* | U23 | ||||

77 | 100 | 1 | 70 | 540 | -24000 | CharLvl* | U23 | |||

101 | 105 | 1 | 70 | 3000 | -270000 | CharLvl* | U23 | |||

106 | 115 | 1 | 70 | 4000 | -370000 | CharLvl* | U23 | |||

116 | 120 | 1 | 70 | 31500 | -3555000 | CharLvl* | U23 | |||

Resistance | Resistance | 1 | 75 | 1 | 50 | 200 | Highest* | U23 | ||

76 | 76 | 1 | 50 | 4125/19 | Highest* | U23 | ||||

77 | 100 | 1 | 50 | 540 | -24000 | Highest* | U23 | |||

101 | 105 | 1 | 50 | 3000 | -270000 | Highest* | U23 | |||

106 | 115 | 1 | 50 | 4000 | -370000 | Highest* | U23 | |||

116 | 120 | 1 | 50 | 31500 | -3555000 | Highest* | U23 | |||

Critical Defence | Critical Defence | 1 | 75 | 1 | 80 | 200 | Highest* | U23 | ||

76 | 76 | 1 | 80 | 4125/19 | Highest* | U23 | ||||

77 | 100 | 1 | 80 | 540 | -24000 | Highest* | U23 | |||

101 | 105 | 1 | 80 | 3000 | -270000 | Highest* | U23 | |||

106 | 115 | 1 | 80 | 4000 | -370000 | Highest* | U23 | |||

116 | 120 | 1 | 80 | 31500 | -3555000 | Highest* | U23 | |||

Incoming Healing | Incoming Healing | 1 | 75 | 1 | 25 | 200 | CharLvl* | U23 | ||

76 | 76 | 1 | 25 | 4125/19 | CharLvl* | U23 | ||||

77 | 100 | 1 | 25 | 540 | -24000 | CharLvl* | U23 | |||

101 | 105 | 1 | 25 | 3000 | -270000 | CharLvl* | U23 | |||

106 | 115 | 1 | 25 | 4000 | -370000 | CharLvl* | U23 | |||

116 | 120 | 1 | 25 | 31500 | -3555000 | CharLvl* | U23 | |||

Block, Parry & Evade | Block, Parry & Evade | 1 | 75 | 1 | 13 | 200 | Highest* | U23 | ||

76 | 76 | 1 | 13 | 4125/19 | Highest* | U23 | ||||

77 | 100 | 1 | 13 | 540 | -24000 | Highest* | U23 | |||

101 | 105 | 1 | 13 | 3000 | -270000 | Highest* | U23 | |||

106 | 115 | 1 | 13 | 4000 | -370000 | Highest* | U23 | |||

116 | 120 | 1 | 13 | 31500 | -3555000 | Highest* | U23 | |||

Partially Block, Partially Parry & Partially Evade | Block, Parry & Evade | 1 | 75 | 1 | 35 | 400 | Highest* | U23 | ||

76 | 76 | 1 | 35 | 8250/19 | Highest* | U23 | ||||

77 | 100 | 1 | 35 | 1080 | -48000 | Highest* | U23 | |||

101 | 105 | 1 | 35 | 6000 | -540000 | Highest* | U23 | |||

106 | 115 | 1 | 35 | 8000 | -740000 | Highest* | U23 | |||

116 | 120 | 1 | 35 | 63000 | -7110000 | Highest* | U23 | |||

Partial Block Mitigation, Partial Parry Mitigation & Partial Evade Mitigation | Block, Parry & Evade | 1 | 75 | 1 | 50 | 400 | 10 | Highest* | U23 | |

76 | 76 | 1 | 50 | 8250/19 | 10 | Highest* | U23 | |||

77 | 100 | 1 | 50 | 1080 | -48000 | 10 | Highest* | U23 | ||

101 | 105 | 1 | 50 | 6000 | -540000 | 10 | Highest* | U23 | ||

106 | 115 | 1 | 50 | 8000 | -740000 | 10 | Highest* | U23 | ||

116 | 120 | 1 | 50 | 63000 | -7110000 | 10 | Highest* | U23 | ||

Physical Mitigation, Orc-craft Mitigation, Fell-wrought Mitigation & Tactical Mitigation: | Physical Mitigation, Orc-craft Mitigation, Fell-wrought Mitigation & Tactical Mitigation | |||||||||

Light Armour | 1 | 75 | 1.6 | 40 | 448/3 | Highest | U23 | |||

76 | 76 | 1.6 | 40 | 3080/19 | Highest | U23 | ||||

77 | 100 | 1.6 | 40 | 403.2 | -17920 | Highest | U23 | |||

101 | 105 | 1.6 | 40 | 2240 | -201600 | Highest | U23 | |||

106 | 115 | 1.6 | 40 | 8960/3 | -828800/3 | Highest | U23 | |||

116 | 120 | 1.6 | 40 | 23520 | -2654400 | Highest | U23 | |||

Medium Armour | 1 | 75 | 10/7 | 50 | 3820/21 | Highest | U23 | |||

76 | 76 | 10/7 | 50 | 26250/133 | Highest | U23 | ||||

77 | 100 | 10/7 | 50 | 3440/7 | -153000/7 | Highest | U23 | |||

101 | 105 | 10/7 | 50 | 19100/7 | -1719000/7 | Highest | U23 | |||

106 | 115 | 10/7 | 50 | 76400/21 | -7067000/21 | Highest | U23 | |||

116 | 120 | 10/7 | 50 | 200550/7 | -22633500/7 | Highest | U23 | |||

Heavy Armour | 1 | 75 | 1.2 | 60 | 208.8 | Highest | U23 | |||

76 | 76 | 1.2 | 60 | 4320/19 | Highest | U23 | ||||

77 | 100 | 1.2 | 60 | 561.6 | -24840 | Highest | U23 | |||

101 | 105 | 1.2 | 60 | 3132 | -281880 | Highest | U23 | |||

106 | 115 | 1.2 | 60 | 4176 | -386280 | Highest | U23 | |||

116 | 120 | 1.2 | 60 | 32886 | -3711420 | Highest | U23 |

(*) speculative

## Rating Graphs

### Critical Rating

### Finesse Rating

### Mastery (Physical/Tactical) Ratings

### Resistance Rating

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

### Incoming Healing Rating

### Avoidance (Block/Parry/Evade) Ratings

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

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.