Statistic growth rate: Difference between revisions

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(Basically rewrote the entire article. I was more than liberal in basically redefining what Growth Interval Means. See Discussion page for more details.)
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==Summary==
'''Statistic growth rates''' are a number which determines the rate at which a [[character]]'s various [[stat]]s grow at each level. The growth rate could be expressed as a fraction, which would be the [[stat]]istic divided by the '''statistic growth rate''', rounded down. The resulting fraction would be the number of levels a character would have to gain to gain 1 point in that stat. For example, if you set a statistic with a growth rate of 30 to be 55, the rate of increase would be 55/30, or 1.833. Since you round down, the rate of increase is 1, which means you gain 1 point in that stat for every level you gain. However, if the growth rate was 10, the rate of increase would be 5.5, or 5, so the character would gain 1 point in that stat for every 5 levels he gains.
'''Statistic growth rates''' are fixed integers for a given race/profession combination which determine the rate at which a [[character]]'s various [[stat]]s grow. In particular, each statistic growth rate determine an integer dependent on the current statistic value known as the '''Statistic Growth Intervals (GI)''' which is the number of levels between statistic gains.


==Definition of a statistic's GI==
These values are always taken at total levels, not levels since the last statistic gain. So, if your rate of increase was 5, and you made level 55, since level 55 is divisable by 5, you gain a point in that stat. Levels with a lot of prime factors between 2 and 9 generally see the most statistic gains, such as level 36 (36 = 2 × 2 × 3 × 3, meaning that this level will gain points in stats with ROIs of 2, 3, 4, 6, and 9).
Let '''S''' be a statistic
and '''R''' be that statistic's growth rate. Then the '''GI''' for that statistic is found by dividing '''S''' by '''R''' and rounding the result down to the nearest
integer. If '''S''' is less than '''R''', and consequently '''S''' divided by '''R''' rounded down is 0, the GI for '''S''' is defined to be 1.
In other words if G denotes the Growth Interval for S, then '''G:=max(trunc(S/R),1)'''.

''If a character's next level is divisible by a statistic's GI, then that statistic will increment by 1 when the character attains the next level.'' Thought of another way, a statistic's GI is the ''interval of levels between that statistic's increase''. For instance, a statistic with a GI of 2
will increment at even levels, with an interval of 2 between increments. A statistic with an GI of 3 will increment at levels divisible by 3,
with three levels between increments, etc.

==Examples==
'''Example 1:''' Suppose a level 45 character has Strength=61 with statistic growth rate of 30. The GI for Strength is then trunc(61/30)=2. Since the next level is 45+1=46, and 2 divides 46, upon reaching level 46 Stength will increase from 61 to 62.

'''Example 2:''' Let's generalize Example 1 a bit. Suppose a character is level 0 with Strength=20 with statistic growth rate 30. Initially,
Strength's GI is 1 and it will remain 1 until Strength reaches 60. In particular, from levels 1-40 Strength will increment at every single level. At level 40, Strength=60 and so Strength's GI is now trunc(60/30)=2. The GI remains 2
until Strength=90. So at levels 42, 44, 46, ..., 98, 100 Strength will increment. Finally at level 100 Strength is 90, and thus has a GI of 3.

{| {{prettytable}}
|+ '''Example 2'''
|-
! width=80px | ''Level''
! width=80px | [[0-39]] || width=80px | [[40-99]] || width=80px | [[100]] ||
|- align = center
| '''Stat Value''' ||20-59||60-89||90||
|- align = center
| '''GI''' ||1||2||3||
|- align = center
|}

'''Example 3 (a neat trick):''' Suppose my Charisma's statistic growth rate is 10. Suppose my level 0 Charisma is 89. Initially my Charisma's GI is 8.
Thus at level 8 my Charisma will increment to 90. Now my Charisma's GI is 9. Since my next level is 9, my Charisma will increment again to 91 once I reach level 9. Suppose on the other hand my level 0 Charisma were 90. Then the GI is 9 and my Charisma increments to 91 at level 9.
It's clearly advantageous to place an 89 in Charisma instead of a 90.

'''Example 4:''' Let's look at a slight variant of Example 3. Suppose at level 0 my Logic is 39, with a statistic growth rate of 20. Initially
the GI is 1, so at level 1 my Logic increments to 40. Now the GI is 2, and so at level 2 my Logic increments to 41. Again, suppose
that instead I had placed my logic at 40. Then the GI is initially 2 and at level 2 my Logic increments to 41.

Examples 3 and 4 illustrate the prudence in placing statistics at the maximum for a given GI, or in other words at an integer so
that the next time the statistic increases, the GI changes. Another interesting observation is that levels which have high powers of 2
and 3 in their prime decomposition tend to see a lot of statistic increases, while levels which are prime will not see as many. For instance,
upon reaching level 72=8 x 9=2x2x2x3x3, any stat with an GI of 2, 3, 4, 6, 8, 12, 18 will increase. However, if you reach level 17, only
stats with an GI of 17 will increment.

Since the lowest statistic growth rate for any combination of race/profession is currently 5, statistic GI's must be integers between
1 and 19.

==Remark on Terminology==

The terminology used to describe statistical growth suffers from a lack of standardization. Throughout Krakiipedia the use of the term
Statistic Growth Rate is consistent. Early profession guides (such as Tavarion's Statistical Cleric Guide) and even the official website
tend not to distinguish between a statistic's current growth interval and its growth rate. Therefor what Krakiipedia lists as
a growth rate is often called simply the statistic's growth interval. The number we call the statistic's GI would then be called n*GI,
where the integer n is the number we computed in this article to find GI. Below is an example using the Krakiipedia terminology and also older terminology.

Krakiipedia: A dwarven rogue has a Logic growth rate of 20. Thus if the rogue's current Logic is 60, their GI is 3 and thus Logic will
increment when the rogue attains the next level divisible by 3.

Older terminology: A dwarven rogue has a Logic growth interval of 20. Thus if the rogue's current Logic is 60, it has a 3*GI and so will
increment at the next level which is divisible by 3.

==Table of Statisc Growth Rates by Profession==


{| {{prettytable}}
{| {{prettytable}}
|+ '''Growth Rate by Profession'''
|+ '''Stat Growth Rates by Profession'''
|-
|-
! width=80px | ''Profession''
! width=80px | ''Profession''

Revision as of 13:50, 12 December 2009

Summary

Statistic growth rates are fixed integers for a given race/profession combination which determine the rate at which a character's various stats grow. In particular, each statistic growth rate determine an integer dependent on the current statistic value known as the Statistic Growth Intervals (GI) which is the number of levels between statistic gains.

Definition of a statistic's GI

Let S be a statistic and R be that statistic's growth rate. Then the GI for that statistic is found by dividing S by R and rounding the result down to the nearest integer. If S is less than R, and consequently S divided by R rounded down is 0, the GI for S is defined to be 1. In other words if G denotes the Growth Interval for S, then G:=max(trunc(S/R),1).

If a character's next level is divisible by a statistic's GI, then that statistic will increment by 1 when the character attains the next level. Thought of another way, a statistic's GI is the interval of levels between that statistic's increase. For instance, a statistic with a GI of 2 will increment at even levels, with an interval of 2 between increments. A statistic with an GI of 3 will increment at levels divisible by 3, with three levels between increments, etc.

Examples

Example 1: Suppose a level 45 character has Strength=61 with statistic growth rate of 30. The GI for Strength is then trunc(61/30)=2. Since the next level is 45+1=46, and 2 divides 46, upon reaching level 46 Stength will increase from 61 to 62.

Example 2: Let's generalize Example 1 a bit. Suppose a character is level 0 with Strength=20 with statistic growth rate 30. Initially, Strength's GI is 1 and it will remain 1 until Strength reaches 60. In particular, from levels 1-40 Strength will increment at every single level. At level 40, Strength=60 and so Strength's GI is now trunc(60/30)=2. The GI remains 2 until Strength=90. So at levels 42, 44, 46, ..., 98, 100 Strength will increment. Finally at level 100 Strength is 90, and thus has a GI of 3.

Example 2
Level 0-39 40-99 100
Stat Value 20-59 60-89 90
GI 1 2 3

Example 3 (a neat trick): Suppose my Charisma's statistic growth rate is 10. Suppose my level 0 Charisma is 89. Initially my Charisma's GI is 8. Thus at level 8 my Charisma will increment to 90. Now my Charisma's GI is 9. Since my next level is 9, my Charisma will increment again to 91 once I reach level 9. Suppose on the other hand my level 0 Charisma were 90. Then the GI is 9 and my Charisma increments to 91 at level 9. It's clearly advantageous to place an 89 in Charisma instead of a 90.

Example 4: Let's look at a slight variant of Example 3. Suppose at level 0 my Logic is 39, with a statistic growth rate of 20. Initially the GI is 1, so at level 1 my Logic increments to 40. Now the GI is 2, and so at level 2 my Logic increments to 41. Again, suppose that instead I had placed my logic at 40. Then the GI is initially 2 and at level 2 my Logic increments to 41.

Examples 3 and 4 illustrate the prudence in placing statistics at the maximum for a given GI, or in other words at an integer so that the next time the statistic increases, the GI changes. Another interesting observation is that levels which have high powers of 2 and 3 in their prime decomposition tend to see a lot of statistic increases, while levels which are prime will not see as many. For instance, upon reaching level 72=8 x 9=2x2x2x3x3, any stat with an GI of 2, 3, 4, 6, 8, 12, 18 will increase. However, if you reach level 17, only stats with an GI of 17 will increment.

Since the lowest statistic growth rate for any combination of race/profession is currently 5, statistic GI's must be integers between 1 and 19.

Remark on Terminology

The terminology used to describe statistical growth suffers from a lack of standardization. Throughout Krakiipedia the use of the term Statistic Growth Rate is consistent. Early profession guides (such as Tavarion's Statistical Cleric Guide) and even the official website tend not to distinguish between a statistic's current growth interval and its growth rate. Therefor what Krakiipedia lists as a growth rate is often called simply the statistic's growth interval. The number we call the statistic's GI would then be called n*GI, where the integer n is the number we computed in this article to find GI. Below is an example using the Krakiipedia terminology and also older terminology.

Krakiipedia: A dwarven rogue has a Logic growth rate of 20. Thus if the rogue's current Logic is 60, their GI is 3 and thus Logic will increment when the rogue attains the next level divisible by 3.

Older terminology: A dwarven rogue has a Logic growth interval of 20. Thus if the rogue's current Logic is 60, it has a 3*GI and so will increment at the next level which is divisible by 3.


Table of Statisc Growth Rates by Profession

Stat Growth Rates by Profession
Profession Strength Constitution Dexterity Agility Discipline Aura Logic Intuition Wisdom Influence
Bard 25 20 25 20 15 25 10 15 20 30
Cleric 20 20 10 15 25 15 25 25 30 20
Empath 10 20 15 15 25 20 25 20 30 25
Paladin 25 20 25 20 15 25 10 15 20 30
Ranger 25 20 30 20 20 15 15 25 25 10
Rogue 25 20 25 30 20 15 20 25 10 15
Sorcerer 10 15 20 15 25 30 25 20 25 20
Warrior 30 25 25 25 20 15 10 20 15 20
Wizard 10 15 25 15 20 30 25 25 20 20

Note: The table above is the baseline statistic growth rates. These values are actually modified for every race in GemStone IV, including humans.