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The difficulty class is determined by the value which is used for the attack, regardless of magic or physical. It is class as well as weapon dependent, like how Finesse melee weapons use DEX over STR, if DEX is higher, allowing e.g. rangers to be quite proficient and good with Finesse melee weapons wheras DEX is normally used for ranged weapons.
The saving throws is accordingly to the DC of the attack or the condition the attack/status comes from - how some magic conditions e.g. attack INT/WIS, that too can be read from the type of condition/attack when you hover over it.
Once the attack or condition connects, it becomes straightforward as described
E.g. a weapon doing 3~10 damage in average is made by 1d8 +2 bonus modifier
1d8 means roll one eight-sided dice to determine the damage
ergo
2d4 means roll two four-sided dice to determine the damage
And yeah, just by looking at that you can tell 1d8 and 2d4 are to be considered playing differently for the worse or better.
Attack spells have it easier to learn from, since they are more straightforward with just 1d8, etc.
See if these can also provide you more insight
https://www.youtube.com/watch?v=D8E0F1YZaT8
https://www.youtube.com/watch?v=On4IyG4HjQs
Let's say you are going to attack an enemy with 10 AC with a greatsword (scales off strength), you have 18 strength, and you are proficient with great swords. You are level 6.
Your to hit roll is 1d20 + 3 +4
(+3 proficiency bonus for weapon you are proficient in at level 6) (+4 bonus for strength modifier, which is strength/2 -5, rounded down).
Effectively you will only miss if you roll a 1 or 2. If your weapon also has a +1 enchantment then you will only miss on a 1.
Damage roll with weapons is according to the weapon, and takes your attribute bonus into account. A basic greatsword is 2d6, or 2-12 damage. Then you add +4 for 18 strength.
Then you add on things like weapon enchantments (a +1 weapon gives +1 to hit and +1 damage), poisons, special attack modifiers, damage bonus from feats and fighting styles, smites, etc.
Spells are similar for to hit, but depending on the spell could be modified by things like attacking from above or below. It varies from spell to spell. Spells obviously are not weapons, so you don't get that bonus, but you do get the proficiency bonus for your character level (the same proficiency bonus as when you attack with a weapon you are proficient with).
Most spells do not add any attribute based damage unless you have a special ability that says it will. For example, a warlock with the Agonizing Blast eldrich invocation adds their charisma modifier to the damage when they use the eldritch blast cantrip.
Both spells and physical attacks can be made with advantage or disadvantage, depending on circumstances. An attack made with advantage will roll two dice for the to hit roll and use the die with the higher number. An attack with disadvantage rolls two dice and uses the lower number instead.
Thank you! So Gale's +5 on firebolt comes from +3 from intelligence and +2 proficiency (which is applied to all spells with spellcasting characters as I understand).
With regards to the damage, is there a way to increase spell damage or is it just increased by using higher level spells as you level up and with higher ability modifiers (again from levelling up)? Similarly, will higher damage weapons increase weapon-related spell damage?
There are various ways to increase spell damage, from your class as well as from items. You can also cast a lower level spell using a higher level spell slot, which will make it do more damage in some cases. Here are some examples:
A tempest domain cleric can use their level 2 ability, destructive wrath to use a channel divinity charge and a reaction to make a thunder or lightning spell do maximum damage.
An evocation wizard at level 10 gets empowered evocation, which adds their intelligence modifier to damage rolls with any evocation spell.
You can get items like the spellsparkler, which give you lightning charges when you deal damage with a spell or cantrip, then let you use those charges to add damage to future casts. You can also get lightning charges from other gear, combining to pretty crazy effect.
If you cast a lightning or ice spell against an enemy that is wet the spell will do double damage.
Also, ability modifiers do not increase spell damage naturally. Only in specific cases, such as the already mentioned eldritch blast. Spells get stronger through natural progression (a level one spell could do 2d8 damage. A level 6 spell could do 6d10 +40 damage), or upcasting a low level spell with a higher level spell slot.
Weapons do more damage if they are simply a better weapon. They don't naturally get better as you level up. You get better at using them, the items themselves stay static.