How many Sorcery Points should this cost? Lots. At least 5, since this metamagic is better than Careful Spell, Empowered Spell and Heightened Spell combined. I'm sure you can see where I'm going with this - it's too powerful to put a realistic cost on it.

Your new metamagic option does 3 things. The first is pretty simple - it multiples damage by 1.25, or 1.5 if it's an AoE spell. I'm going to look at Fireball (a pretty classic damage spell) as a standard example.

A Fireball does 8d6 damage, averaging 28 damage. An Empowered Fireball, assuming a Charisma of 20, does 8d6 with the option to reroll up to 5 dice, for an average of 31.75 damage. A Sharpened Fireball does 8d6 * 1.5 damage, for an average of 42 damage.

At this point, you might be thinking "But Fireball does 8d6 damage, where the entry in the Spell Damage table for a 3rd-level spell is only 6d6!" Unfortunately, the advice in the Spell Damage table bears little or no resemblance to the spells that were actually published.

Note that this is also the case for single-target spells. Disintegrate (which uses a saving throw, not an attack roll) deals 10d6 + 40 (average 75), Empowered Disintegrate deals 10d6 with up to 5 rerolls + 40 (average 78.75), and Sharpened Disintegrate deals (10d6 + 40) * 1.25 (average 93.75).

At any rate, hopefully you can see how Sharpened Spell is considerably more powerful than Empowered Spell.

Moving on, the second thing Sharpened Spell does is change the target making a saving throw into the caster making an attack roll. Ostensibly, this is a loss in damage, since most (though not all) spells that use saving throws deal half damage on a successful save. However, it is far easier to make an attack roll hit than it is to make an enemy fail their saving throw.

Firstly, it's a trivial matter to give yourself advantage on an attack roll; it's an extremely non-trivial matter to give an enemy disadvantage on a saving throw. For example, you have inspiration, True Strike, the Help action, the Hide action, The Wild Magic Sorcerer's Tides of Chaos, and heaps of other things to give yourself advantage on a roll. To give disadvantage, you have Heightened Spell, or Contagion. There's not many, and they require significantly more expensive resources than the advantage options.

Secondly, most powerful monsters (the kind that would be worth sharpening a spell for) have Legendary Resistance, which makes it impossible to make them fail their saving throws, since they can just say they didn't. You can make them burn through their uses of this feature, but if they're smart they'll only use it on your best spells.

Finally, attacks are (by design) easier to hit. Everyone uses attacks, and some characters use them exclusively, so monsters can't be impossible to hit without making some players feel useless. On the other hand, not everyone uses saving throws, and everyone can still function without them. It's difficult to prove this mathematically, but anyone can quickly observe that there are extremely few monsters with AC above 20.

A mid-level sorcerer (let's say level 8) with maxed Charisma only needs to roll 12 or higher to hit an AC of 20. With advantage, which you'd better believe they'll find a way to get on their Sharpened Fireball, that's a 69.75% chance to hit.

The same sorcerer casting a regular Fireball has a save DC of 16. Let's assume the monster isn't great at Dexterity saving throws (but not too bad at them, either) and give it a +3. It has a 60% chance of failing that saving throw, which is pretty good odds for the sorcerer, but not as good as the attack roll. On the other hand, if the monster gets advantage on the saving throw (which there are a lot of ways for it to do), it has a 36% chance of failing. Not so good. And, of course, this is assuming a monster with really good AC, which is more of a worst-case scenario than a usual one.

So that's why Sharpen Spell is also better than Heighten Spell. The third thing Sharpen does is change the spell from an AoE to a single-target. This looks like a drawback, and often will be, but in those situations the sorcerer just won't do it. For the sorcerer to be thinking about Sharpening a spell, they'll have a priority target in mind. This lets them use Fireball on the Big Bad without having to worry about hurting their allies. "But they could just use a single-target spell!" Well, they could. But they have a limited number of spells known, and there are in fact no 3rd-level single-target spells. Hence, this is also better (or at least as good as) Careful Spell, albeit only when you have a priority target.

With all that out of the way, this is a really cool idea. It gives us back the Spellwarp Sniper from 3.5, which was great. Focusing Fireballs into concentrated beams of destruction? Awesome.

I strongly recommend going ahead with this, but removing the damage bonuses. If your players choose to use this, they know they're turning an AoE spell into a single-target spell, and they know they're adding a chance of total failure. They'll use it when those aren't problems, so you don't need to boost it because of those drawbacks.

With that change in place, I'd recommend this metamagic option costing 3 sorcery points, the same as Heightened Spell. Wait, what? I said earlier that it was better than Heightened Spell! Well, it is, but it requires the player spending additional resources to make it that way. It's trivial to give yourself advantage on an attack roll, but it's not free. You have to spend an inspiration point, or use your previous turn to cast True Strike or to Hide, etc.

You have an apples and oranges problem

PCs are optimized to survive and win multiple encounters per day. NPCs are are optimized for one encounter and they are expected to lose.

The spreadsheet you have linked is factoring in hit/miss chances and critical damage - CR calculations don't do that. They assume all attacks hit for average damage and that AoE affect 2 creatures.

• Your 10th level champion has a damage output of:
  2 attacks x ((4.16 x 2) average damage + 5 bonus) = 26.7 x 4 (3 round plus 1 action surge) / 3 rounds = 35.5.

• Your 20th level: 4 x ((4.16 x 2) + 5) x 4 / 3 = 71.

A champion NPC also has Second Wind to increase HPp and +1 to AC from the second fighting style (Defence is the only one that synergizes with TWF). An NPC does not have to save anything for future encounters because, win or lose, there aren't going to be any. For this reason, many PC features do things outside combat - NPC features don't.

Further, a group of PCs of different classes is far more effective than a group of the same class. Imagine your Champion fighter under the effects of Haste (1 extra attack per round), with a d10 bardic inspiration die to turn a miss into a hit, and allowing the Rogue to get sneak attack damage every round.