Sunday, November 14, 2010

Alternate Character Statistic Generation

When I started out on Septimus I just adopted the traditional 3d6, 3-18 ability score regime we're all familiar with. However, I don't really care for it. It requires translation via a table to get ability score modifiers, it uses a totally unique dice mechanic separate from anything else in the game, and it has a lot of baggage. When someone sees that they've got a 7 for a stat they look sad. They may think they need 18s in their primary stats to succeed. While those aren't true in Septimus, it is a perception issue.

So, this is the variant system I'm toying with.

Roll 3d6. Drop the lowest and the highest. The remaining score is your ability score. Caveats:
  • If the attribute is your "prime" then roll 2d6 and pick the highest number. If you rolled boxcars, the score is 7!
    If the attribute is a double prime, then roll 3d6 and pick the highest number (i.e. drop nothing). Boxcars = 7, 666 = 8.
  • If the attribute is a "flaw" then roll 2d6 and pick the lowest remaining number. If you rolled snake eyes, the score is 0!
  • Any "4+MOD" factor in the old system (generating a range from 1 to 7) is simply "equal to your attribute."
  • Any "1+MOD" factor in the old system (generating a range from 0 to 4) is "equal to your attribute -3."
  • Improving attributes: Roll the exact same dice pool as used in character creation. If the result is greater than the current score, increase the current score by one.
The main downside of this system is that there is less granularity. Under the old system, it took three rolls before you'd go up a modifier. However, in play test, DW was actually quite unhappy about this; it felt like there was too little progress. Also, extreme results are slightly more likely. I think I'm willing to live with that however.

The upsides include:
  • No baggage.
  • Rapid stat generation; no need to cross reference a table to convert a 3-18 score to a modifier.
  • More noticeable effects at level-up/stat improvement time.
  • Commonality of mechanic.

UPDATE:

What do these distributions look like (courtesy of troll)?

AVERAGE RUN OF THE MILL ABILITY SCORE

Old School, 3d6 convert to Modifier (1 = -3, 6 = +2):
Average = 3.5
Spread = 1.02288625775
Mean deviation = 0.861111111111

1 1.852100.000


2 14.352 98.148


3 33.796 83.796


4 33.796 50.000


5 14.352 16.204


6 1.852 1.852




New -- "Normal" (3d6 take the middle)
Average = 3.5
Spread = 1.37099585325
Mean deviation = 1.16666666667

Value% = % ≥Probability graph
1 7.407100.000


2 18.519 92.593


3 24.074 74.074


4 24.074 50.000


5 18.519 25.926


6 7.407 7.407



Distribution roughly appears like a bell curve, although it is really parabolic, without the aracteristic tapering at the ends. It is roughly equivalent, though; the odds of getting a 16-18 on 3d6 (the same as my "6" above) are about 5%. We're in the same ballpark above.


ABOVE AVERAGE ABILITY SCORE

Old School: 4d6 drop the lowest (then convert to modifiers)
Value% = % ≥Probability graph
1 0.386100.000


2 5.324 99.614


3 21.219 94.290


4 37.577 73.071


5 29.707 35.494


6 5.787 5.787



Average = 4.0825617284
Spread = 0.990762073825
Mean deviation = 0.767008649596

The odds for a Prime are the same as my core mechanic, although obviously inverted for Flawed scores. That is, the mean increases by one (3.5 --> 4.5) and lower numbers become very unlikely.

Average = 4.47222222222
Spread = 1.40408355068
Mean deviation = 1.1975308642


Value% = % ≥Probability graph
1 2.778100.000


2 8.333 97.222


3 13.889 88.889


4 19.444 75.000


5 25.000 55.556


6 30.556 30.556


The chart doesn't reflect my "Boxcars = 7" rule, but Boxcars should occur 1/36 of the time (2.7%), and it would reduce the percentage of the time that you get a "6" as one six is a prereq for boxcars.

WAY ABOVE AVERAGE ABILITY SCORE

Old School: 5d6 drop the lowest two yields...

Probability distribution:

Value% = % ≥Probability graph
1 0.077100.000


2 1.878 99.923


3 12.037 98.045


4 33.449 86.008


5 41.165 52.559


6 11.394 11.394



Average = 4.47929526749
Spread = 0.916573125002
Mean deviation = 0.775236687698


And finally, for a so-called "Double Prime," you get this.

Average = 4.95833333333
Spread = 1.14387458844
Mean deviation = 0.901234567901



Value% = % ≥Probability graph
1 0.463100.000


2 3.241 99.537


3 8.796 96.296


4 17.130 87.500


5 28.241 70.370


6 42.130 42.130


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