For this installment of my Game Balance series, I decided to examine Point Buy systems and compare them to scores from randomly generated dice rolls. (See the caveats at the bottom for how scores less than those on point buy tables were treated.)
I generated 100,000 sets of ability scores and calculated their point buy equivalents for 3.5e D&D, 4e D&D, and for Pathfinder. The results I found are presented in the table below.
|Pathfinder||D&D 3.5||D&D 4|
|High Power Points||20||28||NA|
|4d6, drop one||19.48||29.11||21.89|
|reference||p. 16 PCRB||p. 169 DMG||p. 17 PHB|
For both of these systems I found that the suggested Dice method (4d6) did not match the suggested point buy values. In both systems Point Buy closely mimicked the High Power/High Fantasy hero point buy suggestions. For both Pathfinder and D&D 3.5e, the standard point buy fell in between 3d6 and 4d6 methods, but for Pathfinder using point buy to mimic the average 3d6 roll required very few points.
This may be justified when considering that using the Point Buy system is much more flexible, and hedges against very low scores, especially under a strict application of suggested dice rolling methods.
If you want to use point buy to give all players an even playing field, and most closely mimic the 4d6 dice rolling method, I would suggest using the High Power/High Fantasy point suggestions. In fact, after doing this analysis this is what I have switched to going forward in my own campaigns.
D&D 4e differs from the other two in that it only presents 1 method of dice rolling (4d6), and only one suggestion for the number of points used.
The suggested point buy value of 22 matches almost exactly my calculated value for scores generated using the 4d6 method. I find this interesting given the discrepancy in Dice Roll vs Point buy from the previous edition of D&D. There is no flexibility trade off. (I like to hope this means I've stumbled upon the type of analysis they performed when designing the system.)
Here is the spread of point buy values from the analysis on Point Buy vs Dice Rolling for 4e. Here are links to download similar images for Pathfinder and D&D 3.5e.
For both Pathfinder and D&D 3.5e, standard point buy characters will have lower average scores than those generated by the suggest dice rolling method. For these sets of rules I'd suggest dropping the dice rolling methods. It avoids cripplingly low scores. It also avoids any one character getting lucky die rolls and being able to drown out the contributions of everyone else based on stats alone. (Save that for their ability to role play their character well). In D&D 4e they will be almost identical.
It looks to me (see the caveats below), like there is a discrepancy in the standard point buy vs my previous favorite dice rolling method. Seeing this has convinced me to use point buy in the future, and specifically the High Power/High Fantasy values for any games I run using 3.5e or Pathfinder. For 4e, it is pretty much a non-brainer to go with the standard point buy system.
Rolling ability scores in D&D and Pathfinder, using either the 3d6 or 4d6 methods give you a theoretical range of 3 to 18 on the ability scores (8 to 18 using 2d6+6). The charts in the D&D 3.5e DMG (p. 169), Pathfinder Core Rulebook (p. 16), and D&D 4e PHB (p. 17) only give points for ability scores from 7 or 8 to 18. I assigned all rolled ability scores below the each systems minimum, to the minimum value each book provided (-4 for any value 7 or below in Pathfinder for instance). An alternative would have been to attempt to extrapolate negative point values for low scores beyond what was offered by the tables. Using this type of approach could have dragged the 4d6 method rolls down to a point similar to the Standard Point buy, but I haven't met many GM's that force a player to stick with a 6 or lower for an ability score. The main exception to this is when a player wants it for roleplaying purposes.
Anyone wanting to look at alternate point values for low ability scores is welcome to download the code I used to generate this analysis at, github, the main change you'll have to make is in the modifiers.py, file. Just change the values for each ability score in each systems dictionary. I've also uploaded the file I used to generate the histograms for the 4e D&D graphic above, you can make slight modifications to have it generate charts for the other rule sets.
The current method would be similar to assigning any score 6 or below to be 7 (7 or below to 8 for D&D).
Next Month (hopefully), An attempt at the effects of initiative on simple combat.
Currently the only means I have to recoup my costs are when people use the box on the left to buy stuff from Amazon.