I am thinking about modifying how cantrips work, downscaling the damage die one step and adding ability score bonus. So the change would be d12->d10, d10->d8, d8->d6, d6->d4.

This normalizes the damage range, with the lower some higher, the higher some lower, specially for criticals, unless you maximize your ability score (so has a cost but is used in cantrips as I think should be), and the average with small change, as you can only cast one per round, is not that important.

For abilities that made to add your ability score bonus, like the Wizard Evoker, for cantrips would be to upscale the damage die one step to restore the original.

Some exception:

- Eldritch Blast: no change, uses the original and add ability score bonus only if getting the Invocation.

- Green flames blade: as it is multi-target and already uses the ability score bonus, there are some issues for applying it. It could change the damage to the same target than melee attack to d6 + ability score bonus, as much.

- In the case of Booming Blade, as it is single-target and only uses damage die, it can modified to d6 + ability score bonus for the extra damage.

But as these two already adds the melee attack ability score bonus, need some more testing.

This increases cantrip damage increasing the gap between spellcasters and martials.

Downscaling the damage dice one step decreases the damage on a hit by 1 per die but adding ability bonus will nearly always add more: Typically 

• Level 1-4: 1 damage die, about 3 ability bonus: net effect +2
• Level 5-10: 2 damage die about 4 ability bonus: net effect +2
• Level 11-16: 3 damage die about 5 ability bonus: net effect +2
• Level 17-20: 4 damage die about 5 ability bonus: net effect +1

Particularly at low levels the increase in significant a firebolt that used to do 1d10 damage (average 5.5) is now doing 1d8+3 (average 7.5) a 36% increase.

Yes but as can only cast one per round is not so important. And the criticals are lowered a good ammount for attack cantrips. Don’t think that 1-2 damage per round is for pulling the hair. The % in this case is not so important, we could have than 2 is 100% of 1, but continues to be only 2.

Can check each one by own, but after some tests the real average is very close, nothing that is going to change the game. But at the same time avoid the dissapointment of rolling 1 for the player.

At low levels it makes a huge difference. Say a party of levels 1s are fighting a group of 3 goblins (7HP each).The wizard and the cleric go before the kobolds, not being a tough fight they will keep their (very limited) levelled spells for something else. We will assume both use a cantrip and both hit. (both have +3 in their casting stat)

The wizards casting firebolt RAW has a 40% chance of killing one on a hit with your rules it is 62.5%. The Cleric then sacred flames the injured one if it still alive otherwise it attacks a second.

Under 5e rules when the Kobolds get to attack 19% of the time they are all alive, 71% of the time 1 has been killed and 10% of the time two have been killed. So on average they have killed 0.9 goblins.

Under your proposal there is no chance they are all alive, a 69% chance there is one dead and a 31% chance two are dead so on average they have killed 1.31 goblins that is huge difference. You can increase the goblins survivability by giving them an extra 2 or 3 hp but that makes them tougher for the martials to kill.

The math fits better if you scale it down two levels. It falls a bit behind at high levels but that actually helps to keep lower level slots relevant. But then native d4 and d6 cantrips have an advantage since they can't scale that low.

I'd rather do d12 > 2d6, d10 > 1d6+1d4, d8 > 2d4. It achieves the more even distribution you're wanting without messing with the features that already do what you propose.

Another thing I've instituted to fix criticals specifically is that everyone gets to max one die on a crit (max 2 dice at levels 11+). This raises the low end damage without raising the high end (which can be deadly when applied to monsters).

I really don't bother much about lower levels. If you kill goblins a bit earlier at those very low levels, well is fine for me. When reach level 5 if we compare extra die vs extra attack, adding the ability score multiple times, then there is difference.

In addition, remember that is if you maximize your stat, and in that case I think is good to apply it to damage for your base attack, for not inflicting the same if you have +0 or +5, well you increase hit chance, but this can also be applied to ranged attacks. If we remember the ranged attacks in 3E didn't use the Dex bonus for damage, and for 5E they added it. So not sure why they are so reticent to finally add them too for magic base attack.

The logic is probably the idea that they're should be some trade-off for the luxury and safety of attacking from so far away. That and the concept that casters have way more utility than martials outside of combat, so making martials better at baseline combat gives them a chance to shine.

There is overall performance to consider. Casters do a bit less damage in round 3 because they dropped fireballs in the first 2 rounds. Cantrips intentionally deal less damage in an attempt to balance the classes. 

But then after only 1 combat (2 fireballs) you are out of resources. The martial has unlimited for all day long. Noticed in my games where casters use their cantrips 80% or more of the time, as their round-by-round action, as they need to save the slots for when really required.