Fairness Point-Buy and rolls other than stats

[Hejdun]

The second guy gets to roll again.

True, but does it really matter if the stats were instead:
18, 18, 18, 18, 18, 17
and
10, 10, 10, 14, 6, 12

 

[Saeviomagy]

Or worse
10, 10, 10, 10, 8 , 14 (which was a character I once rolled - luckily in that particular game, stats were less important than roleplaying and problem solving).

The worst I ever had was a 2nd ed character who got

14, 14, 14, 14, 10, 10

He had no modifiers on any stat, and none of his stats were high enough to qualify for anything interesting (all the interesting ones require 15's or higher).

Under point buy however, I've been consistently satisfied with the results. And I've yet to see this wierd phenomenon that detractors of the method seem to get where the entire group have identical stats.

 

[Conaill]

You have almost a 1 in 3 chance of getting a 17 or 18 as your best roll. That gets you up to 31. You have a one in 10 chance of getting an 18, which puts you up to 34.

Edit: The abilities above don't take into account reroll conditions. If you take those into account, the 10 should be an 11, and you get a 29 point buy.

So then where do you get your earlier statement that "to achieve what can reasonably be expected of 4d6 drop low, you need to go up to at least 38"? Or did you simply mean that the outliers for 4d6-drop-lowest can go as high as a 38 point-buy? By the same argument, you could say that "to achieve what can reasonably be expected of 4d6 drop low, you need to go down to at least 14 point-buy" (as in Saeviomagy's worst-case example). I.e. it is possible to roll a set of stats as low as this using 4d6-drop-lowest.

However, the 4d6 vs point-buy comparisons the rest of us have been making have focused on the AVERAGE behavior of 4d6. And that average is approximately a 29 point-buy (close to the point-buy value of the median scores).

As I said, if you go by the average of point buy, you are only representing the average or worse, you are not representing anything better than average. I was pointing out that if you want to take in more than half of the characters generated with 4d6 drop low, you have to go to a higher point buy.

No... if you go by the average of point buy, you are only representing the average. Not "the average or worse". Now, one could argue that we should look at the median point-buy value instead of the average, but it doesn't sound like that's what you're talking about. I don't have the numbers in front of me, but I believe the median is close to the average point-buy value of 29. Are you claiming that more than half of the characters generated with 4d6 drop low have a point buy value much higher than that?


PS: quick Google check on the phrase "run the probabilities": 41 hits. "run the statistics": 556 hits. The average is a statistic. I don't care what the probability is of exactly hitting that average.

 

[Olgar Shiverstone]

I just ran a VB program to calculate the statistics of 4d6 drop lowest.

Here's the summary:

Score Count Probability
3 1 0.0008
4 4 0.0031
5 10 0.0077
6 21 0.0162
7 38 0.0293
8 62 0.0478
9 91 0.0702
10 122 0.0941
11 148 0.1142
12 167 0.1289
13 172 0.1327
14 160 0.1235
15 131 0.1011
16 94 0.0725
17 54 0.0417
18 21 0.0162
Total 1296
Expectation: 12.24

So with a statistical expectation of 12.24 for each ability score, and six independent ability scores, this is basically an array of:

13, 12, 12, 12, 12, 12 (with .44 of a point left over)

which works out to 25-26 point buy.

Edit: Drat, table formatting. Oh well, hope y'all can read it.

 

[Mystic_23]

I personally prefer point buy. I think it balances rolls and allows people to make the characters they want to play. However, I wouldn't decide to not be in a campaign that someone used random rolls. My current character was made using this system, and he had to make some sacrifices (he's a cleric that doesn't have a high charisma, and isn't terribly good at turning the undead) but all in all, he's an enjoyable character to play.

One thing that surprised me was that a couple of people talked about forcing someone to reroll an "uber character" in the interest of fairness. It just seems to me that many people are going to be angry about having to reroll when they get killer stats. I don't know...I've never been in a game where this a DM made a player do this. (I've seen some killer stats too...even rolled a few in my day.)

Before 3e came out, we were playing a 2e campaign where we chose our stats. One caveat that the DM gave us was that, we could create "uber stat" characters, but bad things would randomly happen to them more than other characters (wizards would target them first, etc.) so that was a risk that that person took. I decided to take my highest stat as a 17 (int for a wizard) and most were around the 10 to 14 range.

For me it comes down to what the DM and players are comfortable doing.

 

[Conaill]

So with a statistical expectation of 12.24 for each ability score, and six independent ability scores, this is basically an array of:
13, 12, 12, 12, 12, 12 (with .44 of a point left over)
which works out to 25-26 point buy.

Sorry, but that is only the point-buy value of the average rolls, NOT the average of the point-buy value of a set of rolls. Because the point-buy scale is nonlinear, those two numbers are not the same! (Just like the sum of a bunch of sines is not equal to the sine of the sum.)

In your table, add a column with the point-buy value for each score, then calculate the expected *point-buy value*, instead of the expected score.

Result: 4.8562 points per stat, or an average of 29.1372 points for a set of 6 stats.

 

[Olgar Shiverstone]

Result: 4.8562 points per stat, or an average of 29.1372 points for a set of 6 stats.

EDIT: I'm tracking completely, now. I think you've just convinced me to favor 28-point buy! Now I wish they'd looked more carefully when designing the DMG.

Incidentally, for those interested in the other stats, for 4d6 drop lowest:

Mean: 12.24
Median: 11.9
Mode: 13

 

[Conaill]

I'm tracking completely, now. I think you've just convinced me to favor 28-point buy! Now I wish they'd looked more carefully when designing the DMG.

Now for the next step: assume that people using point-buy will "optimize" towards using mostly even stats. (Something that I've found to be true in >90% of all point-buy PCs.) So if a 4d6-drop-lowest set of stats might be 17, 14, 13, 11, 10, 9, the point-buyer would likely make a set that looks like this: 16, 14, 12, 10, 10, 8. He gets the same stats modifiers, but he does it with 6 fewer points.

So, let's go back to your table... we already have the point-buy values for the scores. But what are the point-buy values that a player *really* has to spend to achieve the same stats modifier? A 4d6 player might roll a 9, but a point-buy player will most likely pick an 8 and save a point. So let's replace the point-buy value of all the odd stats with the PBV of the even stats, and look at the expected PBV per stat again...

4.2442/stat, or 25.4652 points for a set of 6 stats! Tadaa...

This is the number of points a point-buy player would have to pay on average to get the same stat modifiers as the 4d6-drop lowest player.

Of course, a 9 is slightly more powerful than an 8, and a 17 is more powerful than a 16. But how often are you going to notice? The difference is not nearly as much the difference between a 9 and a 10, or between a 17 and an 18. WotC has admitted left and right that even stats are more advantageous than odd ones, and that fact has even been encoded in the recommendations to only use even stat bonuses and penalties.


PS: I'm not claiming that this is what's behind the default of 25 in the PHB. I do believe that one is due to faulty reasoning. But once you take the optimization twoards even stats into account, 25 points is pretty close...

 

[Olgar Shiverstone]

Very evil, Conaill.

I was about decided on 28 point buy; now you've convinced me to stand firm with my current 25-point buy .

Of course, a 9 is slightly more powerful than an 8, and a 17 is more powerful than a 16. But how often are you going to notice? The difference is not nearly as much the difference between a 9 and a 10, or between a 17 and an 18. WotC has admitted left and right that even stats are more advantageous than odd ones, and that fact has even been encoded in the recommendations to only use even stat bonuses and penalties.

Except for feat qualification and when it comes time to add an ability point, odd values are the same as even values, so I accept the simplification. Nice analysis.

 

[Lalato]

I much prefer dice rolling.

After playing Living Greyhawk and seeing what some people are allowed to get away with in that campaign, there is no way someone is going to convince me that point buy is more fair than dice rolling. Point buy is only fair if everyone at the table is reasonable. I can't guarantee that... so instead... I use dice.

I'm not really concerned with the concept that each character be completely balanced with the others. It doesn't matter to me that one person might have higher overall stats than another. I have never been in a campaign where that has mattered in the long run.

Recently I played a "powerful" character that was the only party member to die in an encounter. Meanwhile... other "weak" characters survived. Sure my "powerful" character had certain advantages, but not enough. A few unlucky die rolls did me in.

--sam