Assuming that you have an abundant amount of ranged accuracy, so adding AGI will not help much more with regards to your ranged hit rate – number of arrows hit / total number of arrows fired. Also assuming the increases in STR and AGI can be equivalently found from the same slot of armor, just different pieces.
Considering normal ranged attack:
- Damage = (WD + AD + fSTR2) x pDiF
Only STR will change the value of fSTR2 and pDiF, while AGI will not do anything for your damage here, so STR will obviously benefit more.
Considering weapon skill for Archery:
- WSC = floor(floor((0.16 x total_STR)+(0.25 x total_AGI) x 0.83))
- Damage = floor ((WD + AD + fSTR2 + WSC) x 5.0 x pDiF)
1 STR vs 1 AGI
If adding 1 STR, fSTR2 and WSC will change by either 0 or 1 depending on truncation problem of the total_STR and fSTR2 calculation, also pDiF may change by 1/mob’s defense if total_STR is odd. If adding 1 AGI, WSC will change by either 0 or 1, depending on truncation problem of total_AGI.
So, adding 1 STR will change Damage by anywhere from 0 to 10 x (pDiF + 1/mob’s defense), while adding 1 STR will change Damage by anywhere from 0 to 5 pDiF. The comparison thus can be ambiguous in general. Specific conclusion must be based on specific STR and AGI.
2 STR vs 2 AGI
Adding 2 AGI will change WSC by either 0 or 1. Adding 2 STR will change WSC by either 0 or 1, but will definitely change fSTR2 by 1 approximately, and also change pDiF by 1/mob’s defense.
So at most, adding 2 AGI can change Damage by at most 5 x pDiF, while adding 2 STR can change Damage by at least 5.0 x (pDiF + 1/mob’s defense), which is clearly higher. Therefore, adding 2 STR will always win here.
>2 STR vs >2 AGI
The minimum amount of AGI needed to increase WSC by 1 in general is : 1 = floor(0.25 x AGI x 0.83) -> AGI = 4.82 ~ 5
So one needs at least 6 AGI increase to put WSC by 2 assuming that total_AGI is short of only 1 AGI to increase WSC by 1 after truncation. Total increase in Damage is 10 x pDiF.
An increase of 6 STR will increase fSTR2 by 3, while pushing pDiF up by 3/mob’s defense. Total increase in Damage is 15 x (pDiF + 3/mob’s defense).
Therefore, an increase of equivalent amount (>2) STR will always be better than AGI.
Considering weapon skill for Markmanship:
- WSC = floor(0.3 x total_AGI x 0.83)
- Damage = floor ((WD + AD + fSTR2 + WSC) x 5.0 x pDiF)
1 STR vs 1 AGI
If adding 1 STR, fSTR2 will change by either 0 or 1, also pDiF may change by 1/mob’s defense if total_STR is odd. If adding 1 AGI, WSC will change by either 0 or 1.
So, adding 1 STR will change Damage by anywhere from 0 to 5 x (pDiF + 1/mob’s defense), while adding 1 STR will change Damage by anywhere from 0 to 5 x pDiF. The comparison thus can be ambiguous in general. Specific conclusion must be based on specific STR and AGI.
2 STR vs 2 AGI
Adding 2 AGI will change WSC by either 0 or 1. Adding 2 STR will change fSTR2 by 1 approximately, and also change pDiF by 1/mob’s defense.
So at most, adding 2 AGI can change Damage by at most 5 x pDiF, while adding 2 STR can change Damage by at least 5.0 x (pDiF + 1/mob’s defense), which is clearly higher. Therefore, adding 2 STR will always win here.
>2 STR vs >2 AGI
The minimum amount of AGI needed to increase WSC by 1 in general is : 1 = floor(0.3 x AGI x 0.83) -> AGI = 4.01 ~ 5 (round up to smallest integer that is higher than the calculation).
So one needs at least 6 AGI increase to put WSC by 2 assuming that total_AGI is short of only 1 AGI to increase WSC by 1 after truncation. Total increase in Damage is 10 x pDiF.
An increase of 6 STR will increase fSTR2 by 3, while pushing pDiF up by 3/mob’s defense. Total increase in Damage is 15 x (pDiF + 3/mob’s defense).
Therefore, an increase of equivalent amount (>2) STR will always be better than AGI.