I saw columns of powers that read like math problems
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While there were some details you could suss out with practice (like attacks that hit reflex vs AC) unfortunately everything (swinging a sword, casting a spell, or summoning angels) all fell into that same format, which made them all look like similar actions.
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4e's greatest failing, imho, isn't powers or such, but the fact that they allowed stat blocks to stand in for description. Be it powers, monsters, or magic items, WotC produced dozens of books that read like catalogs of color-coded jargon that only showed numbers and forced the reader to make them fiction.
For me none of this is a failing.
When I buy an RPG system, I want the system to generate good play experiences. When I am
reading the system, I don't want descriptions of fictional events the designer is imagining - I want clear mechanics which I can see producing the desired fictional events in play.
When I read, for instance, the deathlock wight's Horrific Visage ability, I see a fear attack vs Will in a blast that inflicts damage and pushes its targets: and I can see that, in play, this will model the wight looking at its enemies (because it is a blast and not a burst, it has facing), which causes them physical shock (untyped damage) and causes them to recoil in horror (push). In play it worked just like this, and one of the PCs even stepped backwards into a pit (but was saved because the PCs had roped together).
As I just responded to Pemerton above, the devil is in the presentation.
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Notice: the 4e verison formats them all the same; as powers. They rely on jargon (burst 2, slowed, shift) rather than explaining the effect in natural language (30 ft radius, reduce speed 10 ft, move without provoking an opportunity attack).
I'm not seeing the radical difference that you are.
The three 5e abilities all have much the same format: a heading, with a couple of paragraphs beneath them. For reasons that aren't very clear, "channel divinity" precedes "turn undead" whereas "evocation cantrip" is placed underneath "ray of frost", but both seem to be keyword classifications of some sort.
There is also plenty of jargon in the 5e text: "Wisdom saving throw", "ranged spell attack", "reaction", "opportunity attack", possibly even "holy symbol" - I can't tell from the description whether that is mere flavour text, or whether the cleric PC actually has to possess a special piece of equipment; whereas the Implement keyword in the 4e Turn Undead power sends me to a clear bit of rules text that spells this out.
Fighter Powers are indistinguishable from Magic because they are written up using the same format as Magic.
To me, this is like saying that weapons are indistinguishable from spell scrolls because both are put on equipment lists with gp values next to them; or because both are described using words.
It really does not resonate with me. Looking at pages 25 and 31 of the 5e Basic PDF, the fighting styles are formatted just the same as the wizard abilities like Sculpt Spell and Empowered Evocation. Does this mean that protecting someone with your shield is indistinguishable from casting a strong spell? That would be bizarre to me - in working out what is going on with those abilities, you wouldn't ignore that one is a fighter ability about protecting with a shield, the other a wizard ability about manipulating magic.
So why, in reading a 4e power, would you ignore that one is a melee weapon attack and another a ranged implement attack? That one does cold damage and the other does not? etc.
I mean, both weapons and spells in 5e do hp damage - does that make them indistinguishable? Both spells and bows have their ranges specified in feet - does that make them indistinguishable? I really find this claim very hard to unpack.
A fighter in 4e cannot cast ray of frost with his (nonmagical) longsword. But it doesn't matter; the fact is he is using the exact same mechanical expression.
No. The mechanical expression in 4e for a fighter attacking with a longsword is a STR attack using a weapon vs AC. The mechanical expression in 4e for a wizard attacking with ray of frost is an INT attack vs Fort, perhaps using an implement. And the damage is typed as cold. Those aren't the same mechanical expression.
In 5e, a battlemaster fighter makes an attack roll (using the regular combat rules, including picking Str or Dex to hit) and then spends a superiority die to create an effect. A wizard uses a spell slot to create a magical effect and forces the foe to make a special ability check (called a saving throw) against the effect. These are two very different styles of mechanical resolution, no?
Huh? Ray of frost involves making an attack roll, just like attacking with a sword. It's the same mechanical system, only because it is a "spell attack" it uses the characeter's "spellcasting ability modifier" (another piece of jargon) rather than DEX (which is what a ranged attack - another piece of jargon - would normally use).
Also, none of this is in the descriptions you posted. For instance, Ray of Frost doesn't describe itself as a magical effect (and it is does not involve a spell slot). To know that it is a magical effect, you have to see that it is on a list of spells. That's not very different, to my mind, from reading the description of the wizard class in the 4e PHB and seeing that it is a spell-caster.
In 4e, the fighter uses an encounter power (using the power to determine what ability score to hit with) and then does the effect as described. A wizard uses an encounter power to create a magical effect that requires him to roll to hit (using the same power resolution mechanic as the fighter, swapping Int for Str and AC for, say, Ref) and does the effect as described. Very similar, no?
No more than the similarity of rolling an attack to hit with Ray of Frost or a bow - both attack AC, both use the same system, both use the same rules for rolling and applying damage, the main difference is that they use different stats.
I still don't think Ray of Frost in 5e is very similar to a bow attack, just because they are resolved in much the same way. Presumably I could use the former but not the latter to freeze a puddle, just as I might in 4e.
By using natural language, I can easily understand the ability without reading the power block and trying to determine its use by deducing that "pushed a number of square" supposed to represent "must spend its turns fleeing".
See, when I read an ability called "turn undead" that says that creatures hit by the attack are pushed a certain distance and then immobilised, I can see the fiction quite clearly: the cleric drives back the undead, who cower in awe of the divine grace (this is reinforced by the fact that the cleric's CHA boosts the distance s/he drives the undead back).
Moreover, it doesn't look like if I blotted out the italic text and changed the class name headers, the 4e versions could be swapped around without anyone being the wiser.
Huh? One is a radiant attack that targets undead and drives the back, one a ranged attack that deals cold damage and slows its target, and one is a melee weapon attack that allows an adjacent ally to manoeuvre.
The first is obviously some sort of turn or rebuke undead effect, the second is obviousy some sort of cold or ice bolt, and the third is obviously some sort of melee attack. The turn effect could be given to an invoker as much as a cleric, the cold-bolt to a sorcerer as much as a wizard, the melee attack to a warlord as much as a fighter. But this only tells us that some classes have overlapping schticks. In AD&D paladins as well as fighters can disarm and wear heavy armour; in 5e more than one class can Cure Wounds or Raise the Dead!
I can look the 5e versions and tell they are form different classes using different resolution mechanics
Huh? How can you tell what class has Ray of Frost: it could be a cleric of winter, a sorcerer, a wizard, even perhaps a warlock that blast people with the chill of deep space.
How can you tell the manoeuvre isn't a thief ability? Only because you know, as a piece of technical jargon, that superiority dice are a fighter mechanic.
How can you tell that the turning undead isn't a paladin ability (which it was in AD&D)?