Probability vs. Point Buy

[Timely Drought]

Has there been a probability breakdown of 4d6 drop lowest to determine which point buy is closest?

The suggested 25 points seems absurdly low. I'm guessing 28 or 30 point buy is closer to the average of 4d6 drop lowest but I'm no mathematician. Anyone here worked this out?

 

[Thanee]

28

The average on the 4d6 drop lowest is higher than this (IIRC 29.something), but PB gives more control, so that is just fair.

Bye
Thanee

 

[stephenh]

The average of a straight 4d6 drop low is about 29.1. If you exclude non viable builds the average increases slightly to about 30-31, but as has already been said you don't have as much freedom to place these points.

For what its worth, with 4d6 drop low (and excluding non viable) about a quarter of characters will roll stats worth 25 points or less and about a quarter will roll stats worth 36 points or more.

 

[Quickbeam]

Cool topic. I thought this was going to be another discussion on the merits (and personal biases) of the two character creation methods. Glad it's not .

 

[Lonely Tylenol]

I use 32-point buy. I started doing it after: 1. Seeing the breakdown of how many points 4d6-drop-lowest gives if you exclude "hopeless" characters, and 2. My munchkin players keep trying to get me to allow them to reroll their stats until they have "a workable build". Now it's 32 points, period.

It tends to allow the players to be a reasonable generalist (for a monk or ranger or other generalist character) with a 14/14/14/14/12/12 build, or to be a good specialist with one high stat, a couple medium ones, and a couple mediocre. I really like the spread.

 

[nhl_1997]

Why do I actually enjoy problems such as this? Am I sick?

Anyway, there are different methods of looking at this problem. Depending on what the player actually makes the stats, either a 28 or a 25 point buy can be more realistic.

Example 1:
18-10-10-10-10-9 (25-point buy) has a 2.8e-6 probability from rolling 4d6 drop low
16-14-13-12-11-8 (28-point buy) has a 6.02e-4 probability from rolling
Obviously, the 28-point buy is more realistic.

Example 2:
15-14-13-12-10-8 (25-pt) has a 6.92e-4 probability
18-11-11-10-10-10 (28-pt) has a 1.06e-5 probability
Obviously, the 25-point buy is more realistic.

A better way to look at the problem is "what is the most probable result from rolling"? The answer to that question is 15-14-13-12-11-10 (with a 1.65e-3 probability). To replicate that result, you need a 28-point buy.

 

[The Souljourner]

I suggest 32. In my experience, it is rare that people actually roll 4d6 6 times and just keep those results. There's always multiple sets, or rerolling ones, or rerolling one die, or plain old cheating.

28 is probably a perfect fit for what 4d6 would get you if you actually used that rule, but I think 32 gives people just enough extra elbow room to make it feel like a "good" set of 4d6 rolls.

-The Souljourner

 

[Christian]

Average score on 4d6, drop the lowest, is about 12.25. Roughly, an 'average' character on the standard method would have 4 1/2 12's and 1 1/2 13's; 4+4+4+4+4.5+5 = 25.5 points. So 25 is fairly close. Of course, there's the increased cost of higher stats, the extra control-there's a balancing act there that can't be solved mathematically.

Interesting tidbit I worked out once relating the point-buy levels to attribute levels rolled on 3d6 flat. Since this is the presumed default for common NPC's overall, you can compare the probability curves for those rolls to the results of the different point buys to see where the 'heroic' PC's stand in relation to the bulk of metahumankind ...

Point Buy Percentile
15 50
21 75
25 90
28 95
32 99

Interesting to note that the standard numbers correspond to mathematically 'natural' divisions in the normal distribution. (Everyone who thinks Jonathan Tweet had something to do with this, raise your hand. ) If you think, for example, that heroes should have natural ability levels overall in the top 5% of the population, then 28-point buy is the right number for you ...

 

[the Jester]

This thread is really interesting.

I think that the interesting thing is that you can have two characters that 'cost the same' in point buy with vastly different odds of being rolled... and you might have the same odds of rolling two characters with vastly different 'costs' in point buy.

 

[Lonely Tylenol]

28 is probably a perfect fit for what 4d6 would get you if you actually used that rule, but I think 32 gives people just enough extra elbow room to make it feel like a "good" set of 4d6 rolls.

Yeah, pretty much. I would use 28 in an ideal game, but I think my players would revolt...they're a little bit munchkiny. This way they feel like their characters have a little extra "fat" around the edges.