Custom Power level trade-offs

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1

I have been trying to wrap my head around the Custom Powers Trade-Offs table. The line “The Judge may devise other options along these lines as desired” implied to me that there was a mathematical or logical relationship involved, but I haven’t been able to completely suss it out.

Here’s what I have sussed. I would love comments, corrections, or alternatives with a smoother progression.

Basic Swap

Swap one power for two powers at a much later level. The later level is as shown below.
level 1 -> 7 level 7 -> 11 level 8 -> 11.5 level 9 -> 12 level 10 -> 12.5 level 11 -> 13 level 12 -> 13.5

The closest approximation I could manage is:

(13-level)x0.5 + level + (levelx0.1, rounded).

Of course, there’s no way to no if that equation is actually correct, but it gives these numbers:

level 1 -> 7 level 2 -> 7.5 level 3 -> 8 level 4 -> 8.5 level 5 -> 10 level 6 -> 10.5 level 7 -> 11 level 8 -> 11.5 level 9 -> 12 level 10 -> 12.5 level 11 -> 13 level 12 -> 13.5 level 13 -> 14

Complex Swap

Swap two powers for three powers at a later level, as shown below:
level 1 -> 5

With only one data point, I could map any equation to it I wanted. But it seems reasonable to build off the previous equation and use:

(13-level)x0.35 + level + (levelx0.1, rounded to the nearest half)

That gives these numbers:

level 1 -> 5 level 2 -> 6 level 3 -> 7 level 4 -> 7.5 level 5 -> 8.5 level 6 -> 9 level 7 -> 9.5 level 8 -> 11 level 9 -> 11.5 level 10 -> 12 level 11 -> 12.5 level 12 -> 13.5 level 13 -> 14.5

Lump for Lump

Shift one power up a level and another power down a level, or up and down half a level for the fractional starting points. The power being bumped down a level must be at least one level higher than the original power that was swapped out to get it.
2

In order to reverse-engineer the system, you need to make a spreadsheet that assigns a value to class powers based on what level they unlock.

1. Start with the assumption that a character spends 1/14th of his adventuring career at each of 14 levels.

2. Set the value of a power available at level 1 as 1 point.

3. Calculate the relative value of any  power as equal to the value of a power at level 1 x the amount of time the power is available to the character over the course of his career.

EXAMPLE: A power avalailable at level 8 is worth (14-7/14) x 1 = 0.5, because it's available for half the character's adventuring career.

EXAMPLE: A power available at level 14 is worth (14-13/14) x1 = 0.071, because it's available for 1/4th the character's adventuring career.

At this point you'll be close to the answer, but not quite. In practice, a character doesn't *actually* spend 1/14th of his career at every level; because of fatalities, retirement, and the nature of campaigns, the actual value of powers needs to be reduced after level 1.  

Therefore, assume that you can trade off 1 point of value at level 1 for 1.142 points of powers at later levels. 

This will let you calculate the value of the various trade offs. to within 0.1. 

EXAMPLE: The value of a power at level 4 is (11/14) 0.785. The value of a power at level 10 is (5/14) 0.357. The sum is 1.142. Therefore, a trade-off of 1 power at level 1 for powers at level 4 and 10 costs 1 power.

EXAMPLE: The value of a power at level 7 is (8/14) 0.571. Two powers at level 7 are worth (0.571+0.571) 1.142. Therefore, a trade-off of 1 power at level 1 for 2 powers at level 7 costs 1 power.

Etc.

 

 

 

3

Thank you. That entirely eliminates the ugly hack of (levelx0.1, rounded), which is much appreciated.

I suspect I will house rule this for 14th level (since there is no level afterward, it is possible to run a character’s twilight years for some extra period of time), but even assuming that, it is quite sensible.

4

No problem. It's always fun to reveal the method behind the madness.