Probability vs. Point Buy

[babomb]

In a thread on an older incarnation of the boards (circa. 2001), someone posted the following calculations

             percentile
points       of 4d6-drop-lowest
16  	     10
20 	     20
22 	     25
23 	     30
25 	     39
26 	     40
28 	     50
30 	     60
32 	     68
33 	     70
34 	     75
36 	     80
40 	     90
51 	     99
60 	     99.9

Edit: This doesn't take into account rerolls for highest stat less than 13 or total modifiers 0 or less. Percentiles are rounded to the nearest percent (except the last line). I also have the stats for straight 3d6 available.

 

[Elric]

One thing to consider about the average of ability scores when you roll: characters with higher ability scores tend to live longer. If you suppose that everyone creates a new charcter when their old one is killed, then you will see that the more often weak PCs die (compared to strong PCs), the higher your actual ability scores will be. Also, I would think that rolling especially low or high would lead to weird metagaming, where a player cares more about their luckily rolled 40 point buy character than they do about a 20 point buy one.

There is also the problem of what to do when someone does roll a very powerful character (say, point buy 44). Do you let the other characters reroll more generously than you would otherwise? If you are not comfortable with large ability score variations between characters, this situation could lead to the party being noticeably stronger than a 32 point buy party.

 

[Dannyalcatraz]

Pardon my ignorance, but I don't quite understand how you call the various methods things like "25 point buy" or "28 point buy" as a matter of terminology.

Don't get me wrong- we use points to buy stats in our campaigns, but we have a slightly different terminology.

The PCs start with no points in any stat, and then must buy each point. So for a PC to average a 12 in each stat would be a "72 point buy" in our system, a 13 in each stat would be a "78 point buy", and a 14 in each stat would be an "84 point buy."

So, what is a 25, 28 or 32 point buy?

 

[ThirdWizard]

As defined in the DMG, and isn't located in the SRD (because character creation cannot be recreated in OGL material), point buy is the process of starting with all 8s and using points to buy increases to the stats. These points come at an increased point cost the higher the stat is increased.

 

[Dannyalcatraz]

Thanks!

 

[Gotterdammerung]

Should PC's generated through a higher point-buy count earn less experience toward standard monsters?

It's my understanding that the MM stats are based on a 15-point-buy for monsters. If the PC's jump from the expected average of 25(?) points, let's say to 32 points, should monster stats be increased proportionately to maintain CR balance?

I would think that, since ability scores are tied to almost everything a character or monster can do, there needs to be some mechanism in place to balance both sides of the equation.

-eric

 

[Vrecknidj]

Has anyone worked out the probabilities for the following sort of system?

Everyone starts with all six stats of, say, 13. Then the player manipulates the scores this way: for every one point added to one score, two points are subtracted from another score. The player gets to add and subtract scores in this way, to his heart's content, with the standard limits of nothing greater than 18 and nothing lower than 3. Like usual, racial modifiers go last.

I'm curious because, on the official point-buy systems, it's not possible to get a score lower than 8 (without racial modifiers). Also, I'm curious because I'd like to know what the starting scores should be to be equivalent to 25-point-buy or 32-point-buy, or whatever.

Dave

 

[Timely Drought]

Should PC's generated through a higher point-buy count earn less experience toward standard monsters?

It's my understanding that the MM stats are based on a 15-point-buy for monsters. If the PC's jump from the expected average of 25(?) points, let's say to 32 points, should monster stats be increased proportionately to maintain CR balance?

I would think that, since ability scores are tied to almost everything a character or monster can do, there needs to be some mechanism in place to balance both sides of the equation.

If you consider that 28 point buy is the average of the standard random character creation method, then presumably things should be balanced. I prefer fairness in character creation above whatever reason the current authors had of keeping the awful random ability score generation. Especially in a game like D&D where challenges are meant to be calibrated against the PCs. In the end the DM always needs to adjust CR to ensure encounter level fairness, and a point buy averaged to the standard random roll method makes that easier.

Some groups use non-standard point-buy where getting high ability scores does not scale in cost like standard point buy, making maxed favored scores and pathetically low dump stats extremely attractive. I would not hesitate to lower rewards for such PCs to compensate the lower challenge they are facing compared to standard characters.

Going for 28 point buy (seems like a consensus from this thread) ensures that character creation is fair while the PCs are not at a disadvantage compared to PCs with randomly generated ability scores.

For the matter of 25 point buy being more fair since it gives more control over where points go compared to random rolling: considering the number of stats rolled and the fact that the numbers can be assigned where the player wants, I don't believe that imposing a 3+ point penalty balances anything at all. Further, if all players use the point buy method, there is no reason to compare the two beyond finding the point where the random method averages. If I alllowed both methods at the player's choice, I would still use 28 point buy and let the player decide if he wants to take a chance to get better numbers.

 

[Gizzard]

26 40
28 50
30 60
32 68
33 70
34 75
36 80

The math in this chart seems a bit funky. Note strangeness at 33-34. Interpolating the numbers which aren't explicitly stated, the population for each number looks like:

30 ~= 5.0%
31 ~= 4.0%
32 ~= 4.0%
33 == 2.0%
34 == 5.0%
35 ~= 2.5%
36 ~= 2.5%

Which doesn't make much sense. Is there a typo for 33 or 34?

 

[Creamsteak]

Making corrections...