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1. Attack roll to hit touch AC (not all spells require an attack roll)
2. Penetrate enemy spell resistance, if any.
3. Enemy rolls save to reduce or avoid damage (not all spells allow for a save).
4. Damage is further reduced or eliminated by fire resistance.
Here are where the feats help you out:
1. (increases to-hit chance) High Dexterity, Basic Attack Bonus (BAB), Weapon Focus (Ray)...
2. (increases spell penetration) Spell Penetration, Greater Spell Penetration...
3. (increases Save DC) Spell Focus, Greater Spell Focus, Element Focus...
4. (ignores fire resistance) Ascendant Element Fire
Greater Dispel does not benefit from Spell Penetration or Spell Focus, because the spell bypasses spell resistance (see spell description) and you don't require the enemy to make a save. Instead, you want to improve your caster level to overcome the enemy DC to successfully dispel a spell. School Mastery Abjuration (mythic), magical items, Demon Rage (mythic path), and Arcane Exploit (class feature) are examples of ways to improve caster level (CL).
https://www.d20pfsrd.com/magic/all-spells/d/dispel-magic/
https://roll20.net/compendium/pathfinder/Dispel%20Magic#content
Spell Focus Evocation increase the difficulty class of any spell from Evocation. So it increases the chance of your fireball hurting (as it has a Reflex saving throw). Elemental Focus: Fire also increases the Spell DC but only for spells of that DC. SO if you have focus Evocation and Focus Fire, then your fire based spells from the Evocation tree (I think all fire spells are Evocation???) would gain bonus from both feats but say Cone of Code (Cold Spell) would only gain bonus from your Evocation Focus feat.
Only if you plan on using spells that require an attack roll. I usually build my wizards around spells that don't require attack rolls. This saves me taking those feats and I don't need as high dexterity. A new player may not realize this, so your advice is good.
Examples of offensive spells that don't require an attack roll:
Magic Missile, Burning Arc, Boneshaker, Boneshatter, Icy Prison, Circle of Death, Chain Lightning...
Some of the most powerful spells in the game don't require attack rolls. With over 1,000 hours between Kingmaker and Wrath, I never play wizards with Point Blank Shot or use spells that require attack rolls. Playing that way is certainly viable, but there alternatives. Boneshatter is non-typed damage with a debuff and wrecks boss enemies, even more so if you can find an empowered or maximized rod.
I want to use ray spells on Ember (on core difficulty it looked pretty good. Now, i am starting over from act 3 on hard). That's why point blank, precise shot and spell focus ray is on my list (though ray is not a priority).
I also used a lot of spells that require reflex. For that I do need school focus evocation and element focus fire, correct? School focus and element focus helps me hit them, whilst spell penetration helps me do more damage, when I hit. Do I understand it correctly or am I being an idiot?
Yes, you want a high Spell DC to beat a targets saving throws such as Reflex. So Spell Focus Evocation and Elemental Focus will both increase your spell DC. There are also items that increase spell DC for Evocation or in general, these are great for your casters.
Some items that I have found up until Act IV that improve Spell DC
Purple Stone Knife (Act 1) increases Evocation DC by 1
Cloak of Carnage = +2 DC for Evocation School
Quarterstaff of Coercion = +1 DC for Spells that target will saving throw
Quarterstaff of Warmage = +2 DC for Spells
Yes you want those feats, but not for the reason you posted. Spell Focus and Element Focus does not help you hit them. Those feats raise your spell DC and make it more difficult for the enemy to pass the Reflex save DC. Some enemies, such as Rogues, can take zero damage if they pass a Reflex Save, so in that sense improving your spell DC improves your damage output, to a point. The effect is not linear. Adding more spell DC won't increase damage to enemies who are already failing the Reflex save.
Point Blank
Precise Shot
Spell Pen
Greater Spell Pen
Evocation Focus
Greater Evocation Focus (or Elemental Focus)
Meta magic (like Maximize spell)
Meta Magic
Elemental Focus Fire
Greater Elemental Focus
(You can take the final 2 elemental focus sooner if you want but meta magic seriously increases your hitting power.) A Maximized and Empowered Fire Ray hits for 108 excluding any additional damage boosts you get
Mythic Abilites should be Ascendant Element - Fire as 1st pic, then abundant casting. Elemental Barrage is good on paper but I find it hard to work because I am also fire focused and most of my none firespells are resisted.
Mythic feats should be Mythic Spell Pen and Mythic Evocation & ELemental focus
P.S. Also thanks about a tip regarding weapons. I will look for them.