User:Dandin/Expending TDPs on Attributes
The primary and most effective way to better your character with TDPs is to spend them training character stats. Due to the incremental nature of this sort of training, it is rarely observed from a wide perspective. In this article, I will attempt to examine the total TDP costs of optimizing character attributes.
Initial State
Despite any complexity introduced by species, all attributes initialize in one of 5 possible states, each a function of the stat's racial modifier: (-3, -2, -1, 0, +1, ,+2, +3). Each of these racial modifiers determines the stat's initial state (all -3 modifiers start at 16 ranks, etc) This is described by the following formula:
TDP costs
Attribute progression is an incremental process, with the number of TDPs required to raise an attribute by a value of one increasing by 3, scaled by the racial modifier for that attribute. This is expressed with the following formula:
However, since we'll be interested in total TDP costs for a stat, actually want to use this formula:
In the general case, there are 3 variables to this formula (target, current and racial), however, since we would like to consider the total cost of raising the attribute, our target will be set at 99 (the current stat cap), and our current will be set to our initial state, which is dependent upon the racial modifier, therefore, there is only one independent variable. The formula is thus reduced to the following polynomial form:
Since there are only 7 racial modifiers, it would make sense for us to make a table at this point:
| Racial Modifier | Total Cost |
|---|---|
| -3 | 7096.5 |
| -2 | 9520 |
| -1 | 11962.5 |
| 0 | 14418 |
| +1 | 16880.5 |
| +2 | 19344 |
| +3 | 21802.5 |
Conclusions at this point
The differences between racial modifiers are significant.
| Racial Modifier Magnitude | 1 | 2 | 3 |
|---|---|---|---|
| Difference between + and 0 | 2462.5 | 4926 | 7384.5 |
| Difference between 0 and - | 2455.5 | 4898 | 7321.5 |
| Difference between + and - | 4918 | 9824 | 14706 |
| Normalized difference (+-diff/magnitude) | 4918 | 4912 | 4902 |
Comparing Races
Using the above table, we can determine the total costs for each attribute of each race:
| Race | Strength | Reflex | Agility | Charisma | Discipline | Wisdom | Intelligence | Stamina | Total Cost |
|---|---|---|---|---|---|---|---|---|---|
| Dwarf | 14418 | 16880.5 | 16880.5 | 14418 | 11962.5 | 14418 | 14418 | 11962.5 | 115358 |
| Elf | 16880.5 | 11962.5 | 11962.5 | 11962.5 | 16880.5 | 14418 | 14418 | 16880.5 | 115365 |
| Elothean | 16880.5 | 11962.5 | 14418 | 14418 | 14418 | 11962.5 | 11962.5 | 19344 | 115366 |
| Gor'Tog | 7096.5 | 16880.5 | 14418 | 14418 | 14418 | 19344 | 19344 | 9520 | 115439 |
| Gnome | 21802.5 | 9520 | 11962.5 | 14418 | 14418 | 14418 | 9520 | 19344 | 115403 |
| Halfling | 19344 | 11962.5 | 9520 | 14418 | 16880.5 | 16880.5 | 14418 | 11962.5 | 115386 |
| Human | 14418 | 14418 | 14418 | 14418 | 14418 | 14418 | 14418 | 14418 | 115344 |
| Kaldar | 11962.5 | 14418 | 14418 | 11962.5 | 14418 | 16880.5 | 16880.5 | 14418 | 115358 |
| Prydaen | 14418 | 9520 | 14418 | 11962.5 | 16880.5 | 19344 | 14418 | 14418 | 115379 |
| Rakash | 14418 | 11962.5 | 16880.5 | 14418 | 11962.5 | 16880.5 | 19344 | 9520 | 115386 |
| S'Kra Mur | 11962.5 | 11962.5 | 14418 | 14418 | 14418 | 16880.5 | 16880.5 | 14418 | 115358 |
Article is incomplete, I'll be back (today) to finish it --Dandin 10:36, 15 December 2010 (UTC)