Statistic growth rate

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. Each statistic growth rate determines an integer dependent on the current statistic value known as the Statistic Growth Interval (GI) which is the number of levels between statistic value increments.

Definition of a statistic's GI

Let S be a statistic's current value 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 current GI, then that statistic will increment by 1 when the character levels up. 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 GSWiki 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. Therefore, what GSWiki 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 GSWiki terminology and also older terminology.

GSWiki: 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.