The power level of NPCs in your world determine the power level of PCs in the fiction.
If the typical professional soldier is a "Guard" (CR 1/8), the world feels different than if he typical professional soldier is the "Veteran" or "Knight" (CR 2), or even Champion (CR 9).
Similarly, if every small town has a Diviner (CR 9), PC magic competence will seem really low. OTOH, if most clergy are mundanes with blessed artifacts that allow rare casting of spells on holy days after long rituals, even a level 1 cleric is amazing.
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The baseline math of 5e is about damage.
Round down.
Offensive Level: Total PC damage over first 3 typical rounds (account for number of encounters). Divide by 9, subtract 3.
Your attack modifier is expected to be 5 + L/3 (or DC 13+L/3). Each point different is worth about +/-10% offensive level.
Defensive Level: PC HP divided by 10. Your AC is expected to be 15 + L/6. Each point of AC above/below is worth +/-10% defensive level.
Heals (or mitigation) you can expect to do in the first 3 rounds of the fight also count as HP.
L 1 TWF rogue
16 dex rogue with 2 short swords level 1 and 14 con, leather armor.
10 HP (defensive level 0), 14 AC (1 below), so 0.
2 short swords (10 DPR, +3.5 sneak attack) is 13.5. But the SA has 2 chances to hit, makes it worth 50% more. Offensive level of 2.
Overall level is (0+2)/2 = 1.
A L 1 PAM fighter with shield and chainmail. 18 AC, 12 HP, 6.5 healing, 1d6+1d4+10 damage (16) per round.
L 2 offensive, L 2 defensive.
Overall L2 power level.
A level 5 PAM Spear Fighter in Plate+Shield, 14 con, 18 attack stat.
AC 20, 44 HP, 10.5 self heal
2d6+1d4+18 DPR + 2d6+12 Action Surge = 101.5 3 round damage
+7 accuracy
101.5/9 - 3 is 8.3 offensive level, expected accuracy of 7, so L 8 offensive.
5.45 defensive level, expected AC of 15, so +50% for L 8 defensive
Overall power level is 8.
A level 5 Rogue Booming Blade, 18 dex, studded, rapier and booming blade.
AC 16 38 HP. Defensive roll every turn for ~15 mitigation. On-target AC. Defensive level L 4.
2d8+4+3d6 damage is 23.5 * 3 = 70.5 damage. Use aim to get advantage, increases effective damage by 30%ish. Overall offensive level 7.
Overall L 5.
You can also factor in saving throws. Add up all saving throw modifiers, doubling Dex/Wis/Con. Every point different than (20+Defensive level) modifies defensive level by +/- 1%. (+/- 1 to all saves is worth about as much as +1 to AC, as a rough measure).
Anyhow, this very roughly tracks. The point of this is you can then use it to measure what your changes do.
+1 weapons on a 2 attack PC add 0.666 offensive level +10% from accuracy.
+1 armor/shields adds +10% defensive level each.
+2 attack stat adds +0.666 offensive level, and multiplication +10% offensive level and +1% defensive level.
+2 all stats adds +0.666 offensive (assuming 2 attacks), +0.1 defensive level per PC level (HP), +10% offensive and 9% to 19% defensive (saves and AC)
Doubling HP, well it doubles offensive level but also makes your AC fall behind. Has a larger impact at lower levels.
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This is based roughly on my "make monsters based on Level instead of CR" work.