Fairness Point-Buy and rolls other than stats

[David Argall]

Average is not expected

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

A quick rolling of dice shows you will almost never get such an average result. I rolled 5 PC with 4d6, and had a grand total of 365, or 12.17 per stat. But no PC lacked at least a 15 on at least one stat.

Our more predictable PC would be... 15, 14, 13, 12, 10, 8.
Subject to a good deal of variation, but we would expect 1 above 14, 2 above 13, & 3 above 12, 4 above 11, and 5 at 10+, with one lousy stat below 10.

 

[ced1106]

One DM of old used a random generation, but after everyone had rolled anyone could use anyone else's die rolls.

I did this. Each player would roll up six characters "straight up" (3d6 six times, no rearranging stats, yes THAT way!) then choose either one they rolled, or someone else's. This would actually create roleplaying challenges: a character would have two or three really good scores and one rather poor one; or a character would have one or two really good stats, but would be a class the player hadn't played in awhile. I felt it gave some interesting variety to the standard (of the time) of rolling 3d6 six times and putting the lowest score in CHA.

Sure, players complained all the time about making so many characters. Which was odd, considering how they'd roll 3d6 for a stat ten or twelve times until it was at least 13 then claimed they rolled up characters using the 3d6 method...


Cedric.
aka. Washu! ^O^

 

[satori01]

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

14, 14, 14, 14, 10, 10

a little off topic but those stats above demonstrate the better ability balancing of 3e, as a character with those stats is more than playable in any class he or she wants to be in.

 

[Ravellion]

I can't beleive no one mentioned the fact that you can reroll low scores per the rules in the PHB when doing 4d6 drop lowest.

This will put the roll equivalent back to 27 IIRC from someone else's calculations (even when taking into account the extra information shown above).

Rav

 

[bret]

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.

Although people do tend to take mostly even attributes, it is still true that several will take that odd attribute in order to qualify for a feat or to get to the next step at 4th level.

My most recent point buy character had two odd starting attributes: a 17 and an 11. The character was a Wizard, where a high Int makes a lot of difference. I couldn't quite bring myself to sacrifice enough to buy an 18 attribute, but wanted to get there as soon as possible. Thus I started with a 17 so that at 4th level I would get the 18. The 11 attribute was caused by having a point left over because of the 17.

We have a pretty wide diversity on attributes within our group. Part of that is because we went with 30 point buy -- I think lower point buys actually cause characters to be more like than higher points. With a few more points, you can put a few points into a secondary ability without hamstringing the character.

 

[Zappo]

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.

Me too. I strongly suspect that in reality, the weird phenomenon just doesn't happen.

As for the discrepancy between the expected value of a 4d6-drop-lowest generated character and a 25-point-buy character, you should note however that the player using point buy has greater control over how that value is allocated.

A careful use of those points can and will make a character on average just as powerful as the random one, simply because the random one will likely have a couple wasted points one way or another.

Plus IMO, avoiding randomness is a value in and of itself.

 

[ichabod]

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.

My statement is based on the third quartiles of the ordinal probabilities: 17, 15, 14, 13, 12, 10 (without reroll, I haven't calculated it with rerolls). 38 point buy.

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).

Seeing as I was saying that using the average isn't a good idea, I think I understood that. It just doesn't seem to me like a good idea when it's incredibly easy to get better than that with 4d6 drop.

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.

I was talking about the median, which with rerolls has a 29 point buy cost. In a case like this it seems natural, given as the average could never be an actual value.

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.

Hmm. And that refutes my statement about what I've heard in what way?

And I know the average is a statistic. It's just that I think of it as running the probabilities to get the statistic. You have to either do that or run the frequencies.

BTW, the probability of rolling exactly the average is 0.

And I'll say it again: you definately shouldn't represent the average or median set of 4d6 drop abilities with 13, 12, 12, 12, 12, 12. That doesn't take into account that when you roll up six values they will be spread around the average, not all sitting as close to as they can. Since the point buy system is not 1:1, you should take into account that variation.

 

[ichabod]

As for the discrepancy between the expected value of a 4d6-drop-lowest generated character and a 25-point-buy character, you should note however that the player using point buy has greater control over how that value is allocated.

A careful use of those points can and will make a character on average just as powerful as the random one, simply because the random one will likely have a couple wasted points one way or another.

Plus IMO, avoiding randomness is a value in and of itself.

I don't see that the point buy has enough control compared to just rearranging the abilities. Wasted points are only wasted points if you never get beyond 1st level. They may be wasted now, but at 4th level the odd stat will get a raise in modifiers while the point buy "wastes" a point catching up.

IMO, the point is to have fun. Avoiding or embracing randomness is irrelevant without that context.

 

[Conaill]

My statement is based on the third quartiles of the ordinal probabilities: 17, 15, 14, 13, 12, 10 (without reroll, I haven't calculated it with rerolls). 38 point buy.

Seeing as I was saying that using the average isn't a good idea, I think I understood that. It just doesn't seem to me like a good idea when it's incredibly easy to get better than that with 4d6 drop.

I don't see why you're so focused on the 75th percentile. Why not the 25th percentile, which will be much *lower* than 29 points? Sure, 4d6 has a large variance, so it's "incredibly easy" to get a better result than the 29 average. It's equally incredibly easy to get a *worse* result. Unless you assume that everyone will be playing with above-average rolls, I don't see any reason to claim 4d6-drop-lowest is equivalent to a 38 point buy. (Maybe that's not what you were trying to say, but it sure sounded like it...)