how about this mana point version?

[Pyrex]

I've always been torn on spell points. From a conceptual level it seems like a nice way to model character power. From a practical standpoint I've never really found a system that modeled my view of how arcanists should function without requiring the player to understand calculus. *shrug*

 

[evilbob]

I've always been torn on spell points. From a conceptual level it seems like a nice way to model character power. From a practical standpoint I've never really found a system that modeled my view of how arcanists should function without requiring the player to understand calculus. *shrug*

And I can safely say that Pyrex and I are in complete agreement on this point.

As for the idea you posted, I haven't completely digested it but I like how it's working. I'm not sure it's "even" enough of a slope, however, since it seems to have two giant bumps (3rd to 4th is 3 -> 8, and 6th to 7th is 12 -> 21), but it's certainly not linear, and therefore better than any of the crap I've said so far.


I will, however, put forth the idea that I've been kicking around in the back of my head. It -seems- complicated, but I promise it's not that bad...

So: we agree that one must have a non-linear progression, and that there -is- an upper bound on how quickly we can ramp up the point costs (that's what the 2^level one is saying: you'd have 1, 2, 4, 8, 16, 32, 64, 128, 256, and 512, which is just way too fast). It is my belief that you MUST also start with your point cost system to define the overall workings (this is the base upon which you must build), and I now believe that once you have a good point system, you can FIND the math to create a good "mana pool" system to suit it - with the "mana pool" system rules being defined by Pyrex above.

If we know we want something non-linear but short of "power of 2," we need to look at something that ramps quickly, but doesn't get as high as fast - AND it has to stay somewhat simple, and maybe even be something that folks are familiar with. So... What about squares?

Squares themselves are rather messy (64, 81, and 36 do not make for easy math), but there's a fun fact about squares: they are all at most 1 number away from a power of 5.

cost per spell = (spell level + 1)^2, then rounded to the nearest 5

As I said, seems bad, but the rounding part is simple and just makes all the numbers easier to work with. You end up with a spell cost system as such:

level  cost    cost/5
0      1       1/5
1      5       1
2      10      2
3      15      3
4      25      5
5      35      7
6      50      10
7      65      13
8      80      16
9      100     20

Now that there is a smooth progression. (4,) 5, 5, 10, 10, 15, 15, 15, 20. Seems nice and easy. You could even divide the whole thing by 5 and use those numbers, except that zero-level spells still cause a problem. That progression is also listed above.

It's not very far from linear, but it makes a good start. (I think there's a name for this kind of sequence, actually... Any high-school math team geeks wanna pitch in? ) In fact, the "regen" numbers I suggested above are not that bad for the "1 to 20" progression (or "spell level plus one squared, rounded to the nearest five, then divided by five"). Now it just needs a "mana pool" that makes sense... More to come.

 

[Pyrex]

The funny part is that once you divide that by 5 it's *very* close to the bracketing I posted above except for the top end.

1/2/3 vs 1/2/3 (SL 1-3)
5/7/10 vs 8/10/12 (SL 4-6)
13/16/20 vs 21/24/27 (SL 7-9)

I also don't think your proposal ramps quite fast enough. Forgoing one 9th level cast should get you more than 2x 6th level spells.

 

[evilbob]

Two thoughts:

evilbob's 3nd Theorem of Spell Point System Creation for DnD Magic

- Because spell points cannot increase linearly (evilbob's 1st Law), mana pool systems will also need to increase at a rate that is greater than linear in order to work.

Effectively, I see all spell points systems as having 2 parts: point cost per spell (or spell level cost), and total mana pool. Just about everything else is just flavor.

I agree with your observation. It's a good curve, but perhaps not a strong enough one.

If we examine the "increases" listed in my suggestion above, we see this pattern: 1, 1, 2, 2, 3, 3, 3, 4. Let's expand on that.

What if we made this more like another pattern I remember from math team... 1, 2, 2, 3, 3, 3, 4, 4? (Ex. 1) What if we made it (+ level) - i.e. 1, 2, 3, 4, 5, etc.? (Ex. 2) What about like XP vs. level gains, or (+ next spell level)? (Ex. 3) At least people are familiar with that one.

level  Ex. 1  Ex. 2  Ex. 3
0      ?      ?      ?
1      1      1      1
2      2      2      3
3      4      4      6
4      6      7      10
5      9      11     15
6      12     16     21
7      15     22     28
8      19     29     36
9      23     37     45

Is one 9th level spell worth two 6ths and a 3rd and a 1st? What about two 6ths and a 2nd? It is interesting that while Ex. 3 gets higher numbers quicker, it makes everything more expensive overall, as well.


Edit: When you stop and stare at Ex. 3 above, you notice another interesting trend. The numbers get "bigger" relative to each other more toward the bottom of the scale than at the top. If you look at the multiplicative values, you have:
*3, *2, *1.67, *1.5, *1.4, *1.33, *1.29, *1.25
I wonder if that's not the wrong direction to go?

2nd Edit: Eh, I think that's a red herring. Calculating the reverse of that out (and then normalizing it down to numbers you can think about) gets a progression something along the lines of:
3, 4, 5, 6, 8, 13, 21, 42, 126 - and that's just too fast at the end and too slow at the beginning.

 

[Pyrex]

Ok. So.

A 2nd level spell is stronger than a 1st level spell.

A 9th level spell is stronger than an 8th level spell.

IMO, the power-gap between an 9th->8th level spell is larger than 2nd-1st.

So what if we use a Fibonacci sequence, effectively defining 3rd level spell as being as powerful as a 1st + a 2nd and a 9th level spell = a 7th + an 8th?

Level    Cost
   0        1
   1        1
   2        2
   3        3
   4        5
   5        8
   6       13
   7       21
   8       34
   9       55

I think that's about the smoothest curve we're going to get that roughly approximates a curve somewhere between linear and exponential.

 

[evilbob]

lol

First, I'm going to show you my math.

level  Ex. 2  Ex. 4  Ex 4.1 Ex 4.2 Ex 4.3 Ex 4.4
0      ?      ?      ?      ?      ?      1
1      1      1      1      1/5    1      2
2      2      3      3      1      2      3
3      4      7      7      2      3      5
4      7      14     15     3      5      8
5      11     25     25     5      8      12
6      16     41     40     8      12     18
7      22     63     60     12     18     26
8      29     92     90     18     26     36*
9      37     129    130    26     36*    49*

10     46     175    175    35     49*
11     56     231    230    46

Ex 4.2 = 1, 1, 2, 3, 4, 6, 8, 9, 11

level  Ex. 3  Ex. 5  Ex 5.1 Ex 5.2
0      ?      ?      ?      ?
1      1      1      1      1/5
2      3      4      5      1
3      6      10     10     2
4      10     20     20     4
5      15     35     35     7
6      21     56     55     11
7      28     84     85     17
8      36     120    120    24
9      45     165    165    33

10     55     220    220    44
11     66     286    285    57

Ex 5.2 = 1, 2, 3, 4, 6, 7, 9, 11, 13

level  Ex 5.2 Ex 5.3 Ex 5.4
0      1      1      ?
1      2      2      1/2
2      4      5      1
3      7      10     2
4      11     15     3
5      17     20     4
6      24     25     5
7      33     35     7
8      44     45     9
9      57     60     12

If it doesn't make sense, that's ok! I don't even know what it all means any more.

Next, I'm going to tell you that I've discovered an interesting paradox: the faster the numbers get "big," the "bigger" the lower numbers get. Meaning, even if your 9th level spell is worth a gajillion points, if your 6th level spell is worth half a gajillion, it's still not a good system and you've just wasted like an hour of your life.

But seriously, the closest I've come to a sequence I liked is 4.1 or maybe 4.2. The reason is because the other numbers get too big too quick and then even if you have a very high last number, you're still shooting around two 6ths and a 3rd and a 1st for a 9th.


Now then.

The Fibonacci suggestion is one of the math terms I was trying to remember - and a damn good sequence! As-is you get four 6ths and a 2nd for one 9th, which is the best ratio that I've seen. If you lower all values by 1 notch, you (take care of the zero-level spell problem and) get:

Level    Cost    Rounded
   0        1    1
   1        2    2
   2        3    3
   3        5    5
   4        8    10
   5       13    15
   6       21    20    25*
   7       34    35    40*
   8       55    55    65*
   9       89    90    105*

Which gives four 6ths and a 3rd for one 9th, which is just as good. And basically either way is looking completely superior to all the crap I managed to do above.

However, it's looking kinda complicated, so I tried rounding everything above. You lose a little in the middle, but it's otherwise pretty similar in my opinion. Plus the math is easier, I think. The *'d numbers are what you'd get with changing only the 8 to a 10 in the sequence. This is a slightly greater progression, because one 9th worth four 6ths and one 4th. Another way to look at it is one 9th is worth ten 4ths and one 3rd (as opposed to nine 4ths, or even eleven 4ths as originally done).

Hmm... The main question I keep wondering is: how much -is- a 9th worth?

 

[evilbob]

My above post seems to weigh most heavily against the 3rd to 4th jump, so why not move that extra kick a little lower, where it's easier not to notice?

Level  Cost   With More Rounding
0      1      1
1      2      2
2      4      4
3      6      6
4      10     10
5      15     15
6      25     25
7      40     40
8      65     60
9      105    100

That's further from the original since it breaks the sequence twice, but it might work better. The second example just makes the bigger numbers even easier, and I don't think you lose much by lowering those two costs, since they're still higher than before. It's just a little further from the original, all in the name of making it easier. Or, you could round them up to 70 and 110.

 

[Pyrex]

1) From a "good design" standpoint it's goofy to have a 1st level spell cost anything other than 1.

1.1) If it's truly a "problem" that 0 & 1st level spells both cost 1 then either:
->Make 0 level spells cost 0. (Seriously. In any model where the caster either has a) fast regen and/or b) the ability to cast 100 1st level spells in a day does it really matter how much mana a 0th level spell costs?)

->Track 0 level spells seperately. n/day, n/hour, n/encounter, whatever. Trying to kludge a measureable cost for 0 level spells is adding more difficulty to the process than it's worth.

2) We've already defined a tier of costs, with a simple formula behind them, so rounding them to 'nearest-five' doesn't really buy any simplicity and it busts up the curve.

3) I'd rather not bump the series forward a notch anyway, because balancing a system where the costs range from 1-55 is easier than trying to balance a system where costs range from 1-89 (or whichever other value you want to round to)

 

[evilbob]

1) ...eh, I don't know about that. Maybe. To me, having a very round number for your 9th level cost seems more important.

1.1) Ok, I see you there. In the long run zero spells costing nothing doesn't matter for regen casters; you're right. If you can regen 5 casts of them per round, you're paying nothing effectively anyway. The only thing I worry about is levels 1 to 4 or so. At those levels, it might be a problem. ...Maybe. (Also, I'm not willing to conceed this point on prepared casters. Anyone who doesn't regen needs to have zero level spells cost something, or as I like to say, cure minor breaks the game.)

2) See, and here's where I say that from a "good design" standpoint, rounding helps a ton. People can add and subtract multiples of 5 in their head really easily. It's a whole lot harder to do any old number. Without rounding, calculators become (almost) a necessity. With rounding, you can probably handle it as easily as anything else. Also, rounded numbers are easier to remember.

3) This is true, I'll give you that.

I'd still rather use this than the original sequence. It's just too much cleaner. Edit: Or maybe the one where you only break "8" - that seems even a bit better. 2nd Edit: Or in order to smooth that one ever so slightly, break it twice. I think this is the best one, in my opinion.

Level    Cost   Only 8  Two Breaks
   0        0   0       0
   1        1   1       1
   2        2   2       2
   3        3   3       4
   4        5   5       6
   5       10   10      10
   6       15   15      15
   7       20   25      25
   8       35   40      40
   9       55   65      65

 

[evilbob]

Just to sum up the two different sequences, the original I called "Fib" and the modded one I called Two:

Level     Fib      Two
    0       0        0
    1       1        1
    2       2        2
    3       3        4
    4       5        6
    5       8       10
    6      13       15
    7      21       25
    8      34       40
    9      55       65

Now, either way we go, the next thing to decide, in my opinion, is how many mana points we would -want- at any given level. Based on your criteria above, I thought I'd start with a ballpark guess of mana pool = (2.25 * highest spell cost) for all even levels (still really just talking about a sorc, so even level = new spell level). This gets us, using the stats above for reference, and rounding up in general:

Sorc lvl   stat mod*  total pnts (Two)   total (Fib)
1          3          
2          3          3                  3
3          3          
4          4          5                  5
5          4          
6          4          9                  7
7          4          
8          5          14                 12
9          5          
10         6          23                 18
11         6          
12         6          34                 30
13         6          
14         7          57                 48
15         7          
16         7          90                 77
17         7          
18         7          147                124
19         8          
20         8          
*estimated

(One kinda interesting note: these total point numbers are, themselves, another Fibonacci sequence, since we're only multiplying by a static number.)

How is that looking as a base?