Research suggests the upper, and middle, tree bonuses of the skills used to cast Pragi's Fiery Gaze, and all other spells, significantly affect both the damage and casting speed of Pragi's Fiery Gaze, and all other spells in addition to the age-old specific skills (such as fire).
For example, since a specific magic tree skill used to cast Pragi's Fiery Gaze is magic.methods.elemental.fire, then the middle, and upper, tree skill bonus level of magic.methods.elemental is involved in the above mentioned damage calculations used to determine the damage of this spell.
This is useful additional information since it can be useful to plan a Wizards' selected Order, and to advance specific skills in order to maximize damage, and casting speed.
Another example is as follows: If a player wishes to specialize in casting Pragi's Fiery Gaze as their primary offensive spell, then selecting the Circle as their chosen specialization is ideal since all of the elemental skills are Circle primaries.
If a player chooses Circle and advances all the elemental primaries of fire, air, earth, and water to 300 early, then the overall magic.methods.elemental bonus will be higher than another Order that does not have all 4 elemental skills as primaries.
Another view to consider is as follows:
If a Circle Wizard advances their 4 elemental primaries of fire, air, earth, and water each to 300, then the upper magic tree skill of magic.methods.elemental will be level 300 without further XP spent.
If a Wizard in another Order with only 1 element as a primary advances only that 1 elemental type to 300 in order to guild max it, then their overall magic.methods.elemental level will be about 75, and not 300, since 1/4th of 300 possible guildmaxed primary levels is 75 levels in this situation.
A Circle Wizard will also have 300 levels of magic.methods.elemental once they guildmax all 4 elemental primaries, and this allows to Circle Wizard to spend less overall XP on leveling their magic.methods.elemental bonus for other spells, such as JHSD. This effect is also beneficial for other elemental-based spells, and the same general reasoning applies to other spells, and even other skill trees such as fighting, faith, covert, etc.
If the original damage formula is based on:
((offensive + average of methods) / 2) * 1 to 5
Then we can expand the damage formula to consider the average of the upper and middle portions of the relevant magic skill tree for the magical skills used in Pragi's Fiery Gaze. This is also true of all magical spells, and other skill trees such as fighting, faith, etc.
For example, using Pragi's Fiery Gaze, we can expand and adjust the damage formula to include the average of the upper, and middle, portion of the methods bonuses of all the used skills to cast Pragi's Fiery Gaze. The upper and middle portions of the magical skill tree skills involved are as follows, along with the specific skills:
The Specific Skills
The "Specific" Skills are: evoking, channeling, enchanting, animating, and fire.
The "Specific" Skills are listed 4th by name in the skill tree format. For example, the 4th is: magic(1st).methods(2nd).elemental-or-mental-physical-etc(3rd).fire(4th)
Each of these is listed under magic.methods as:
The Middle Skills:
The "Middle" Skills are: physical, mental, and elemental
The "Middle" skills are listed 3rd by name in the skill tree format
The Upper Skills:
The "Upper" Skills are: methods
The "Upper" Skills are listed 2nd by name in the skill tree format
The "Main" Skills:
The "Main" Skill is simply the type of root skill, and in this case, it is magic.
Using the original damage formula, we can calculate the damage formula using 4 levels of Skills, which are the Specific Skills, Middle Skills, Upper Skills, and the Main skill.
Like the original damage formula calculation, we can arrive at an advanced damage formula calculation by calculating the average of each of the 4 skills separately, then adding the offensive bonus to each skill. When you look at the average bonus of each of the 4 skills, it provides a better indication as to what the predicted damage of each Pragi's Fiery Gaze cast will be. Lower bonuses in the Middle and Specific skills usually lead to lower damage per cast of Pragi's Fiery Gaze if the bonus of the Upper Skills are not at least what the bonus of the Specific and Middle skills are. However, achieving a higher damage per cast is not about the ratio of the bonuses averaging closer together, it is about the ratio of all 4 Skills bonuses ratioing closer together AND ensuring the Upper bonus of Methods remains very high as well (consider how a Circle Wizard who has guild maxed all Elemental primaries will have a 300 magic.methods.elemental bonus, and a non-circle Wizard with 1 elemental primary guild maxed will have only a 75 bonus in magic.methods.elemental.
Thus, the higher the average bonuses in all of the 4 skills, along with a high bonus in Offensive, is necessary to increase damage predictably. Research shows having 400+ bonus in magic.methods.elemental.fire and even a 500+ bonus in magic.spells.offensive, but a 200 bonus in magic.methods.elemental will still produce consistently weaker casts of Pragi's Fiery Gaze on average. The recommended course of action here is not to increase Offensive, or even Fire, it would be to increase the overall bonus of magic.methods.elemental to be closer to the 400 and 500+ bonuses in Fire and Offensive.
The same can hold true in Wizards who have lower bonuses, or for those who neglect to raise their bonuses in magic.methods.mental AND magic.methods.physical since these bonuses are a large portion of how Pragi's Fiery Gaze damage is calculated.
Over time, even as the raw and root magic skill bonus and level increases, the overall strength of each cast of Pragi's Fiery Gaze will increase. Obtaining the highest damage casts of Pragi's Fiery Gaze is about having high levels of magic.spells.offensive AND still keeping your bonuses in all 4 of the Skills as high as possible.
More research is still required to see if the actual magic.methods.elemental.fire bonus somehow works as a standalone way to increase damage, just as how Offensive does, and there is actually some data to support this, much as how the number of KOF fire bunnies might be influenced by the actual Fire damage bonus in theory.
The new way to calculate Pragi's Fiery Gaze damage per cast based on this would be:
((offensive + average of all Specific Skills) / 2) * 1 to 5
((offensive + average of all Middle Skills) / 2) * 1 to 5
((offensive + average of all Upper Skills) / 2) * 1 to 5
It is recommended to get the average of all bonuses for each of the 4 Skills separately and then add the offensive bonus to each separate bonus number, then divide by 2, then times that by 1 to 5. This is shown in the paragraph above.
You should have 3-4 separate numbers, and each will give a good indication of how much damage you could expect to cause, on average, per cast of Pragi's Fiery Gaze. These 3-4 separate numbers can also be averaged to arrive at how much damage you can expect per cast of Pragi's Fiery Gaze.
If any of the bonuses are lower in relation to others from one of the 3-4 separate calculations, the maximum damage for one of the Skills will be lower, and this should help indicate you should consider advancing whatever skills cause the lower bonuses.
Middle or Upper Skill bonuses that are significantly lower then Specific Skill bonuses can cause a significant decrease in the average damage caused by each cast of Pragi's Fiery Gaze, and this can explain why many experienced Wizards with high Offensive bonuses still can only singe/burn consistently, etc despite having Offensive bonuses in excess of 400 - 500.
It is better to make sure your bonuses in all 4 Skills are not too low, since increasing lower bonuses can reduce the number of singes/burns, etc, per cast, causing your average damage per cast to significantly increase. Without doubt, many singes/burns are caused by random number generators rolling a 1, or 2, though eliminating lower average bonuses can help achieve more damage per cast either way, despite what damage multiplier number is rolled between 1 - 5.
Damage multipliers of 1 - 5 might even be rolled on 4 separate calculations, 1 for each Skill, so having a higher average bonus in all 4 Skills will, without a doubt, significantly increase damage per cast of Pragi's Fiery Gaze.