Thursday, December 30, 2010

An Analysis Of The Persistent Spell Feat

— Matt Harris @ 9:06 pm

In one of the Pathfinder Society Games I played recently, one of the other players commented that he thought the new Persistent Spell feat found in the Advanced Players Guide was overpowered. As I feel that most metamagic feats are worthless, I decided to do a little analysis of the feat to see if it was really worth a +2 to the spell level.

A summary of the feat: by increased the level of a spell by two levels, any targets that need to make saving throws need to roll two separate d20s, taking the lower of the two results. To see how this played out, I set up a spreadsheet to roll 5000 sets of 2d20, taking the lower and seeing what the percentage of each final result was. I also calculated the percentage if each was taken singly and compared that to the statistical 5% chance for each value. I ran it multiple times and got fairly similar results each time. I have shown one set of the results below, as well as a graph comparing the values.

Result Straight 1d20 Lower Of 2d20     Result Straight 1d20 Lower Of 2d20
1 5.23% 10.32%   11 4.53% 3.90%
2 5.16% 9.46%   12 4.76% 4.04%
3 5.26% 8.96%   13 5.18% 4.06%
4 4.76% 7.76%   14 4.98% 3.32%
5 4.93% 7.44%   15 5.27% 2.56%
6 4.96% 7.66%   16 4.89% 2.06%
7 4.99% 6.80%   17 5.03% 1.96%
8 5.49% 7.00%   18 4.93% 1.06%
9 4.81% 5.36%   19 4.68% 0.54%
10 5.19% 5.46%   20 4.97% 0.28%

Normally, using 1d20 you would expect a 25% chance of a roll of 5 over lower, 50% of 10 or lower and 75% chance of 15 or lower. The average roll would be 10.5.

For 2d20, take the lowest, the average was a little over 7 (7.07 in the numbers above). The odds of getting a roll of 5 or lower were about 44%, 10 or lower was about 76%, and 15 or lower was about 94%.

Range 1d20 Lower of 2d20
1 – 5 25% 43.94%
1-10 50% 76.22%
1-15 75% 94.10%

What this actually means is dependent upon the Difficulty Class of the effect and any bonuses to the saving throw. Still, I think this fairly equivalent to raising the DC by 3 to 4. As I think that +2 to a DC is worth a +1 increase in spell level, I actually think that Persistent Spell might actually be one of the few worthwhile metamagic feats.

The OpenOffice.org spreadsheet I used for the analysis can be found here

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