D&D 5E (2014) Spell point cost values—what's the rationale?

I was looking at the Variant Spell Points section in the DMG (pg. 288). I believe I understand how it's suppose to work, but I don't really understand why the cost values are chosen this way.

Here are the spell levels and their corresponding costs according to the DMG. (Included Cantrips as level 0 for completeness.)

Spell level: 0, 1, 2, 3, 4, 5, 6, 7, 8, 9
Point Cost: 0, 2, 3, 5, 6, 7, 9, 10, 11, 13

Questions I have
  1. Why are the numbers like this? Why is the gap between the costs changing like this? (2, 1, 2, 1, 1, 2, 1, 1, 2)
  2. Are there variant cost values that are... a bit more intuitive?
 

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The logic of spell point progression is the base cost of 2 for a 1st-level spell, then a 1-point increase per spell level, except at spell levels that correspond with tier breakpoints - character levels 5, 11, and 17 for 3rd, 6th, and 9th-level spells - which have a 2-point increase.

The spell points up to 5th level spells are the same as the sorcery point costs for sorcerers to create spell slots of a given level.
 

I was looking at the Variant Spell Points section in the DMG (pg. 288). I believe I understand how it's suppose to work, but I don't really understand why the cost values are chosen this way.

Here are the spell levels and their corresponding costs according to the DMG. (Included Cantrips as level 0 for completeness.)

Spell level: 0, 1, 2, 3, 4, 5, 6, 7, 8, 9
Point Cost: 0, 2, 3, 5, 6, 7, 9, 10, 11, 13

Questions I have
  1. Why are the numbers like this? Why is the gap between the costs changing like this? (2, 1, 2, 1, 1, 2, 1, 1, 2)
  2. Are there variant cost values that are... a bit more intuitive?
It's based on hit dice values, and the same progression dictates Ki/Focus Points for the Monk, who is essentially a Spell-Point Short Rest Half-caster.
 

I was looking at the Variant Spell Points section in the DMG (pg. 288). I believe I understand how it's suppose to work, but I don't really understand why the cost values are chosen this way.

Here are the spell levels and their corresponding costs according to the DMG. (Included Cantrips as level 0 for completeness.)

Spell level: 0, 1, 2, 3, 4, 5, 6, 7, 8, 9
Point Cost: 0, 2, 3, 5, 6, 7, 9, 10, 11, 13

Questions I have
  1. Why are the numbers like this? Why is the gap between the costs changing like this? (2, 1, 2, 1, 1, 2, 1, 1, 2)
  2. Are there variant cost values that are... a bit more intuitive?
Some levels give more power than others.
Specifically, level 5, 11, and 17 are bigger improvements for most classes
I.e. fighter gets their 2nd, 3rd, and 2nd action surge.

And correspondingly, spells get more powerful too. For example.
1st level Burning hands is 3d6
2nd level Shattet is 3d8
3rd level Fireball is 8d6
 

Thanks for all the responses! This is all starting to make sense—it's like a simplest progression that attempts to capture some power jumps that is consistent with the game's overall class progression model.

After all, one could make the jump from level-2 to level-3 (+2) & jump from level-8 to level-9 to (+4), but they chose to keep all the bigger jumps +2, keeping the numbers low as possible.

I suppose that also explains why the cost of level-1 is 2 instead of 1, since level-1 spells are meant to be a tier above cantrips, and cantrips cost 0.

It is strange to me though, that there are no spells that cost just 1 spell point. You can be left with just 1 point, that you can't spend in anyway. I do wonder how much the game would change if there was a way to power up a cantrip by spending a single spell point.

EDIT: Answering my own musing—if all casters could spend a single spell point to power up a cantrip, it would make Sorcerers really sad.

EDIT 2: But what if you could cast a level 1 spell at half-power using just a single spell point? I just want to use up that last point some how!!!!
 
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Spell level: 0, 1, 2, 3, 4, 5, 6, 7, 8, 9
Point Cost: 0, 2, 3, 5, 6, 7, 9, 10, 11, 13

Questions I have
  1. Why are the numbers like this? Why is the gap between the costs changing like this? (2, 1, 2, 1, 1, 2, 1, 1, 2)
I guess it helps to look at another way. Rather than comparing the jump in spell point cost from one spell level to the next, look at the difference between the spell point cost and the spell level. The progression is:

0, 1, 1, 2, 2, 2, 3, 3, 3, 4
 

i'd like to see an attempt at a spell point mechanic where, rather than progression happening by you getting a bigger pool of spell points to cast higher spells that cost more, as you level up it costs less points to cast spells of increasing levels.

so like, at 3rd level you have 15+mod spell points, and it costs 5 points to cast a 1st level spell and 8 points to cast a 2nd level one, but at 7th level you still have 15+mod spell points but it only costs 2 points for a 1st level spell, 3 for a 2nd, then 5 for a 3rd and 8 for a 4th level spell.
 

I guess it helps to look at another way. Rather than comparing the jump in spell point cost from one spell level to the next, look at the difference between the spell point cost and the spell level. The progression is:

0, 1, 1, 2, 2, 2, 3, 3, 3, 4
This is pretty neat. Not gonna lie, this makes me want to make cantrips cost 1 spell point just to make the pattern consistent.

spell_level: 0, 1, 2, 3, 4, 5, 6, 7, 8, 9
spell_cost: 1, 2, 3, 5, 6, 7, 9, 10, 11, 13
cost-level: 1, 1, 1, 2, 2, 2, 3, 3, 3, 4
cost_jump: 1, 1, 2, 1, 1, 2, 1, 1, 2
 

i'd like to see an attempt at a spell point mechanic where, rather than progression happening by you getting a bigger pool of spell points to cast higher spells that cost more, as you level up it costs less points to cast spells of increasing levels.

so like, at 3rd level you have 15+mod spell points, and it costs 5 points to cast a 1st level spell and 8 points to cast a 2nd level one, but at 7th level you still have 15+mod spell points but it only costs 2 points for a 1st level spell, 3 for a 2nd, then 5 for a 3rd and 8 for a 4th level spell.

That's a pretty interesting idea. I think one way to approach this is to work backwards. What should the costs be by the time the character reaches level-20, then bring up the costs. I would want to make sure that
  1. A higher level spell must cost at least 1 point more than a lower level spell.
  2. A slotted spell must cost at least 1 point.
  3. (Optional) The cost jump between spell levels of different tiers must be at least 2.
  4. (Optional?) Cantrips always cost 0.
It might very well be that we start with the spell-point cost table at level-20, then increase the costs as you level down somehow.
 
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That's a pretty interesting idea. I think one way to approach this is to work backwards. What should the costs be by the time the character reaches level-20, then bring up the costs. I would want to make sure that
  1. A higher level spell must cost at least 1 point more than a lower level spell.
  2. A slotted spell must cost at least 1 point.
  3. (Optional) The cost jump between spell levels of different tiers must be at least 2.
  4. (Optional?) Cantrips always cost 0.
It might very well be that we start with the spell-point cost table at level-20, then increase the costs as you level down somehow.
I can see where you’re coming from but I disagree with your first (and third) points, especially considering a 20th level character, a level 20 pc with 20 spell points (15+max mod) the difference between a 1st and 2nd level or 3rd and 4th level spell is negligible, for 20th level i think id maybe cost spells at:
1st/2nd - 1pt
3rd/4th - 2pts
5th/6th - 4pts
7th - 6pts
8th - 8pts
9th - 11pts

Given the amount of spell slots 20th level casters get this is almost certainly a downgrade in casting.
 

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