4d6 Drop Lowest--Equivalent Point Buy? [Archive] - Wizards Community

4d6 Drop Lowest--Equivalent Point Buy? [Archive] - Wizards Community

Post/Author/DateTime Post
Callista
01-21-06, 07:27 PM Simple question, perhaps difficult answer:

What point buy is approximately equal to the stats you get with 4d6 drop lowest rolling?
Radijs
01-21-06, 07:48 PM I think 25 PB is roughly equal on average.
WayneTheGame
01-21-06, 08:07 PM Actually, I believe that the probability of 4d6 comes out to somewhere around 27 points, so 28 might be closer to the mark. I think I saw a website somewhere that did up the probability of rolling for stats and point buy. Of course, depending on what you roll your mileage might vary.
Raymond_Luxury_Yacht
01-21-06, 08:19 PM I think 4d6 drop lowest comes out to roughly 31 points, but I could be wrong.
Chaos_Blade
01-21-06, 08:43 PM I believe that 4d6 drop lowest can be between any of the previous ones. Sometimes you roll high sometime low
WayneTheGame
01-21-06, 08:49 PM Ah.. I found the website: http://www.math.mcgill.ca/~loisel/dnd-stats.html

Accordig to the test done on that site, the average is around 30. Pretty much the conclusion of the site is that 25 point buy is far too low compared to the standard rolling method.
trapspringer
01-21-06, 11:11 PM However, wizards of the coast suggests that twenty-five point buy will create characters of the same approximate power, not the same stats. Point buy gives you a degree of control which is balanced out by the slightly lower total point value.
WayneTheGame
01-21-06, 11:16 PM However, wizards of the coast suggestions that twenty-five point buy will create characters of the same approximate power, not the same stats. Point buy gives you a degree of control which is balanced out by the slightly lower total point value.

Yes, and we all know how reliable some of the stuff Wizards puts out is... :rolleyes: I despise the 25-point buy and would never, EVER use it. At least 28 for me.. at leat that way characters can have halfway decent stats.
trapspringer
01-21-06, 11:38 PM The difference is rather... well, it isn't that important. Those three points give you the choice of the following:

18,16,10,08,08,08
18,14,14,08,08,08
18,14,12,10,08,08
18,14,10,10,10,08
18,12,10,10,10,10
16,16,14,10,08,08
16,14,14,14,08,08
16,14,14,12,10,08
16,14,14,10,10,10
16,14,12,12,10,10
16,12,12,12,12,10
14,14,14,14,12,08
14,14,14,14,10,10
14,14,14,12,12,10
14,14,12,12,12,12

Twenty-five point buy gives you the choice of:

18,14,10,08,08,08 +1
18,12,12,08,08,08 +1
18,12,10,10,08,08 +1
18,10,10,10,10,08 +1
16,16,12,08,08,08 +1
16,16,10,10,08,08 +1
16,14,14,10,08,08 +1
16,14,12,10,10,08 +1
16,14,10,10,10,10 +1
16,12,12,10,10,10 +1
14,14,14,14,08,08 +1
14,14,14,12,10,08 +1
14,14,14,10,10,10 +1
14,14,12,12,10,10 +1
14,12,12,12,12,10 +1
12,12,12,12,12,12 +1

The highlighted set in either table indicates stats with at least one ability score that would be boosted to an eighteen by a +2 ability modifier with fewer than two dump stats. These are the most popular point-buy options available to most classes (wizards may opt for something closter to the top of the list while paladin may pick something from the bottom, depending on the player).

The twenty-eight point buy looks, to me at least, a lot better than most 4d6 drop the lowest characters I see floating around, simply because the lowest ability is always an eight and the highest is always as high as the player wants it. Twenty-five looks more on par, but isn't really much different when you consider the key abilities for any given class (accepting paladin).

But yes, I prefer 28 pt. buy because of the rounder numbers, although past level four 25 pt. buy has this same effect.
Cymraegmorgan
01-21-06, 11:55 PM Simple question, perhaps difficult answer:

What point buy is approximately equal to the stats you get with 4d6 drop lowest rolling?

28.
Tested with one hundred sets of stats on a very boring night last year.
The Hive Custodian
01-22-06, 01:22 AM I wrote a crude Scheme program to test this out, counting scores below 8 as being worth one negative point per point below 8, and not adjusting for hopeless re-rolls:

;gives the result from 4d6 drop lowest
(define (fourdeesix one two three four)
(cond ((and (< one two) (< one three) (< one four)) (+ two three four))
((and (< two three) (< two four)) (+ one three four))
((< three four) (+ one two four))
(else (+ one two three))
)
)

;gives the point result of a number
(define (points score)
(cond ((< score 15) (- score 8))
((= score 15) 8)
((= score 16) 10)
((= score 17) 13)
((= score 18) 16)
(else 0)
)
)

;goes through all 4d6 drop lowest configurations and totals points
(define (totalpoints)
(totalrec 1 1 1 1 0)
)

;the meat: the procedure that calculates the total for totalpoints
(define (totalrec one two three four acc)
(cond ((= four 7) (totalrec one two (+ three 1) 1 acc))
((= three 7) (totalrec one (+ two 1) 1 four acc))
((= two 7) (totalrec (+ one 1) 1 three four acc))
((= one 7) acc)
(else (totalrec
one
two
three
(+ four 1)
(+ acc (points (fourdeesix one two three four)))
)
)
)
)

;average points on six scores
(define (averagepoints)
(/ (totalpoints) (* 6 6 6))
)

The result: The average (mean) point total is precisely 6162/6^4 = 1027/216 on one score, or 1027/36 = 28 and 19/36 points over six scores.
danielinthewolvesden
01-22-06, 03:00 AM Right. So, you can say anything from 27 to 30 points and not be too far off.

There is one disadvantage to rolling- you get odd numbers.

13, 13, 13, 13, 13, 13= a 30 pt buy.

BUT for those 30 points you could have 14, 14, 14, 12, 12, 12.

No one in their right mind would buy the 13's when you could have 3X14's and 3X12's. Thus, when WotC says a 25 point buy isn't far off, they make a point. However, I'd say a 28 point buy = 4d6drop one.

Here's what I like to do. Give the players a 30 pt buy. Let them create their characters with it. Then, game nite 1- have each roll a D6- and that gives a +1 to that ability.
NinjaHedge
01-22-06, 09:12 AM Yes, and we all know how reliable some of the stuff Wizards puts out is... :rolleyes: I despise the 25-point buy and would never, EVER use it. At least 28 for me.. at leat that way characters can have halfway decent stats.

Hmm, well all the CRs are calculated assuming a party with 25 point buy, as are all the special abilities, magic items, spells, rules. So, pretty much if you give them more then that they're overpowered, not "halfway decent". What's so difficult about a character with a 25 point buy, what would they be missing out on?
WayneTheGame
01-22-06, 09:30 AM Hmm, well all the CRs are calculated assuming a party with 25 point buy, as are all the special abilities, magic items, spells, rules. So, pretty much if you give them more then that they're overpowered, not "halfway decent". What's so difficult about a character with a 25 point buy, what would they be missing out on?

Eh maybe you're right. Honestly I have never played with 25 point buy so I guess I have no business saying it's bad :)

Hive Custodian, I applaud you for doing that. The funny part is, even without knowing Scheme I can kinda figure out what each line in your program means. That's sad.. but I guess it means I'm becoming better as a programmer :P
Nom
01-22-06, 09:33 PM A single best 3 of 4d6 roll has a mean result of ~12.24. The mean bonus is ~ +0.87 (yes, that is less that the bonus from a score of 12 and yes, that is important).

Without reroll and treating scores below 8 as being worth -1 per point below 8, the mean PB value is ~ 4.75.

Multiplying these means by 6 (since each roll is independent) we get a total mean bonus of 5.22 and a total mean PB value of 28.5.

If we consider the reroll, we find that the probability of rolling 13 or below is 64.51%, which means the probability of no score above 13 is ~ 7.2%. I don't have numbers to hand for the probability of the sum being <= 0. Conventional wisdom is that the reroll increases the mean PB value to a little under 30.

However, mean PB value is only part of the picture. You'll notice that a single score had a mean PB value of over 4 (ie +1) but a mean bonus of only +0.87.

The first reason for this is that scores get less efficient as they increase. A 25 point buy with all scores 14 or under should have a total +6 bonus, with 1 point spare. Scores over 14 reduce this.

The second is that most PB arrays will have only 1 (or occasionally 2) odd scores. In contrast, a rolled array may well have odd scores all over the place, and not always in convenient places. Probability of any given roll being odd is 49.77%. You would expect to "waste" at least 3 "points", possibly more.

Even so, it's probably fair to argue that rolling statistically gives you slightly better overall scores than 25 point buy.

However, three final considerations:

* Control: 25 points provides the ability set weighted towards where you want it to be weighted. Standard rolling allows you to rank-order the scores, but no control over their magnitudes.

* Reliability: 25 points tends to focus scores in the "statistically likely" middle band. Even with the reroll, standard rolling has massive variance. Typically, systems with less risk do not return quite as well as those with more.

* Focus: This is related to control. When rolling, your chance of getting a score over 15 (ie +3 or better) is still only about 57% (roughly 3 in 5). In contrast, anyone using PB who wants a 16 (or an 18) can have one, if they are willing to sacrifice.
interpretivechaos
01-22-06, 11:11 PM I prefer point buy for the simple reason is it makes more interesting characters.

For demonstration I randomly rolled 4d6 drop the lowest. Although what I rolled was extreme, it demonstrates nicely the problem.

14
14
14
14
12
14

Anyway you twist it, you get a constantly slightly above average character. Bright, Strong, Tough, Nimble, Wise, and Charismatic- except for one that is a tad less above average.

Point buy on the other hand frequently becomes a game of give and take. My favorite method is to divy up the stats equally and start shifting points.

Say I want a thief- I'll start shifting to Dexterity a bit of Strength. Not content with a 14 dex, I'll shift a little more- and then I'll realize I want a bit more brawn for CC. So I'll debate shifting from Int, Cha, Con, or Wisdom. Deciding I want a witty thief, and an obsercant one as well, I decide to take from Con. Then, I decide to shift the odd points to Int, and deciding on a wittier rogue shift points from Wisdom to Charisma.

End result on 28 pt Buy

Str 12
Dex 16
Con 10
Int 14
Wis 10
Cha 14

Note that even though I have in general a much worse character (2 pts of dex), Its a character that can be RPed much easier and has a lot more character in it.
Jutter
01-23-06, 05:31 AM Simple question, perhaps difficult answer:

What point buy is approximately equal to the stats you get with 4d6 drop lowest rolling?

28,53. No 'I guess' or 'I tried a few times', but pure maths in an excel sheet. This excludes the reroll options as written in the Player's Handbook, by the way, so during character creation it'll be more.
Leukrythus
01-23-06, 09:47 PM Rolling 4d6 (and dropping the lowest) has 1296 possible combinations.

The average roll is 12.25, and the probabilities are as follows:

3 (1)
4 (4)
5 (10)
6 (21)
7 (38)
8 (62)
9 (91)
10 (122)
11 (148)
12 (167)
13 (172)
14 (160)
15 (131)
16 (94)
17 (54)
18 (21)

The odds are that you will have at least one roll of 9 or lower, and one roll 15 or higher.

Assuming that points for the buy in system could be increased one for one by decreasing stats below an 8, this system would be equal to a 28.5 point buy in.
Stuntman
01-24-06, 01:47 AM Assuming that points for the buy in system could be increased one for one by decreasing stats below an 8, this system would be equal to a 28.5 point buy in.
That's what I came up with as well. The value varies very slightly if you choose a different value for scores below 8. Since scores that low are not very likely, it doesn't affect the point buy equivalent very much.

In games that I DM, I give the player the option of using the standard (25-point) point buy if he does not like what he rolled using 4d6. The standard point buy yields lower scores, but allows for better customisation of ability scores. This customisation is sometimes worth the 3.5 points you give up on average if you really want to ensure you have a certain minimum ability scores. By rolling, you always have a chance of getting far better scores, but you may be stuck with something you are not satisfied with because you do not have scores high enough to qualify for certain feats or for multiclassing.
JulesCARV
01-24-06, 07:51 AM Wait, are you supposed to re-roll (once) a 4d6 drop lowest roll that is below 10? Like, if you roll 6 4d6 drop lowest rolls, and then you roll one which is an 8, you of re-roll the 8 and take the second result? Or is that just some crazy house rule that my DM has?
DarknessEternal
01-24-06, 10:22 AM 28 points may reflect the average of this rolling method, but it will never practially simulate it. Points buy has a huge flaw that, despite how sound the theory, buries it. Any points buy will inevitably lead to certain arrays of stats being used by all players, all the time.

It will come down to people saying things like "where'd you put your 16 and 14?" for example. While there might be differences in where the stats go, everyone has the same stats.
OctoberRaven
01-24-06, 10:30 AM ...is no point buy at all.

I heart 4d6 drop lowest as both a DM and character builder. Adds a bit of unpredictability into the mix.
Stuntman
01-25-06, 01:16 AM Wait, are you supposed to re-roll (once) a 4d6 drop lowest roll that is below 10? Like, if you roll 6 4d6 drop lowest rolls, and then you roll one which is an 8, you of re-roll the 8 and take the second result? Or is that just some crazy house rule that my DM has?
If the total ability modifiers of your 6 abilities is less than +1 or none of the 6 abilities are 14 or higher, you may re-roll all of your abilities. For example, if you get a 16, 10, 10, 10, 10, 4, the total modifiers are +3 + 0 + 0 + 0 + 0 - 3 = 0 which is less than one, you may re-roll. If you get a 13, 13, 13, 13, 13, 13, none of your scores are 14 or higher, you may re-roll.
Nom
01-25-06, 05:51 PM 28 points may reflect the average of this rolling method, but it will never practially simulate it. Points buy has a huge flaw that, despite how sound the theory, buries it. Any points buy will inevitably lead to certain arrays of stats being used by all players, all the time.

It will come down to people saying things like "where'd you put your 16 and 14?" for example. While there might be differences in where the stats go, everyone has the same stats.Well duh! The main reason for using point buy is that it provides an approximately standardised set of ability scores, as opposed to the massive variance of PH rolling.

That said, if every PB character looks exactly the same, I submit to you that the flaw lies in lack of creativity and flexibility in the user, not the ruleset.
interpretivechaos
01-25-06, 06:32 PM And perhaps between characters their will be more similarity, but with the same characters stats their isn't necessarilly a bellcurve of stats- each stat is as high as a character wants it to be.
Vaelan
01-25-06, 07:03 PM End result on 28 pt Buy

Str 12
Dex 16
Con 10
Int 14
Wis 10
Cha 14
That isn't a 28 point-buy, that is a 30 point-buy. You're forgetting that you must pay 2 points for each point above 14 you wish to raise your Dexterity.
AT-AT Assault
01-25-06, 10:41 PM Hmm, sorry to barge in, but the people in this thread should be able to answer my question. How do you figure statistics for a set of variables when you dont count all of the variables(ie 4d6 drop lowest and similar things)? And upon answering that, is there an easy way to count up the combinations for each specific total, or do have to count them up one at a time?
phelanarcetus
01-26-06, 01:30 PM Ok, the math shows that 28 points is about the average.

Now while I have tended to end up with significantly better scores than that when I roll for real (though I have rolled plenty of unplayable characters), one thing I like about the point buy system is that the different players don't start off horribly uneven. My last character was worth about a 42 point buy. 17, 15, 15, 14, 12, 11 if I recall the rolls correctly. And he was a Wizard... the guy who wanted to be a Paladin had something worth probably about 28-30 points.

That, and with a point buy, you know what sort of scores you're going to get. I tend to start with a concept. Now what happens if I have a concept that needs 3 good scores, and I roll 17, 13, 12, 11, 10, 9? Do I beg for a reroll, ditch the character, or play him with two of the "good" scores being barely above average?

My overall preference is actually for a "high-powered" point buy. It lets the players create characters who feel exceptional, while giving them equal opportunity for good stats, and avoiding anybody from being screwed over by bad but not unplayable rolls.
Ut-Napishtim
01-26-06, 02:20 PM While it's probably moot at this point, I'd like to add that I've also found a 28 PB to be about on par with 4d6 and drop the lowest. Not so much from a mathematics or statistical standpoint (never bothered to break down the numbers myself), but from a play balance one. That is, that in my games I offer both options, and have never had a problem with one overshadowing the other (which I found to be more prevalent when opting for 25 or 32 respectively).
Leukrythus
01-26-06, 07:53 PM Our games have been starting characters with an 8/10/12/14/16/18, which is an average of 13, and offers some high numbers and some low numbers.

That would equal a 38 point buy-in.
Nom
01-26-06, 09:02 PM Hmm, sorry to barge in, but the people in this thread should be able to answer my question. How do you figure statistics for a set of variables when you dont count all of the variables(ie 4d6 drop lowest and similar things)? And upon answering that, is there an easy way to count up the combinations for each specific total, or do have to count them up one at a time?For continuous variables, calculus usually works. For discrete variables (like die rolls), it's often most expedient to simply enumerate all the possible combinations - get a computer to do this for you.

Given that we have the distribution for one set of (best 3 of 4d6) we can reliably calculate means and variances for the sum, since each set is independent and identically distributed.

Post/Author/DateTime	Post
Callista 01-21-06, 07:27 PM	Simple question, perhaps difficult answer: What point buy is approximately equal to the stats you get with 4d6 drop lowest rolling?
Radijs 01-21-06, 07:48 PM	I think 25 PB is roughly equal on average.
WayneTheGame 01-21-06, 08:07 PM	Actually, I believe that the probability of 4d6 comes out to somewhere around 27 points, so 28 might be closer to the mark. I think I saw a website somewhere that did up the probability of rolling for stats and point buy. Of course, depending on what you roll your mileage might vary.
Raymond_Luxury_Yacht 01-21-06, 08:19 PM	I think 4d6 drop lowest comes out to roughly 31 points, but I could be wrong.
Chaos_Blade 01-21-06, 08:43 PM	I believe that 4d6 drop lowest can be between any of the previous ones. Sometimes you roll high sometime low
WayneTheGame 01-21-06, 08:49 PM	Ah.. I found the website: http://www.math.mcgill.ca/~loisel/dnd-stats.html Accordig to the test done on that site, the average is around 30. Pretty much the conclusion of the site is that 25 point buy is far too low compared to the standard rolling method.
trapspringer 01-21-06, 11:11 PM	However, wizards of the coast suggests that twenty-five point buy will create characters of the same approximate power, not the same stats. Point buy gives you a degree of control which is balanced out by the slightly lower total point value.
WayneTheGame 01-21-06, 11:16 PM	However, wizards of the coast suggestions that twenty-five point buy will create characters of the same approximate power, not the same stats. Point buy gives you a degree of control which is balanced out by the slightly lower total point value. Yes, and we all know how reliable some of the stuff Wizards puts out is... :rolleyes: I despise the 25-point buy and would never, EVER use it. At least 28 for me.. at leat that way characters can have halfway decent stats.
trapspringer 01-21-06, 11:38 PM	The difference is rather... well, it isn't that important. Those three points give you the choice of the following: 18,16,10,08,08,08 18,14,14,08,08,08 18,14,12,10,08,08 18,14,10,10,10,08 18,12,10,10,10,10 16,16,14,10,08,08 16,14,14,14,08,08 16,14,14,12,10,08 16,14,14,10,10,10 16,14,12,12,10,10 16,12,12,12,12,10 14,14,14,14,12,08 14,14,14,14,10,10 14,14,14,12,12,10 14,14,12,12,12,12 Twenty-five point buy gives you the choice of: 18,14,10,08,08,08 +1 18,12,12,08,08,08 +1 18,12,10,10,08,08 +1 18,10,10,10,10,08 +1 16,16,12,08,08,08 +1 16,16,10,10,08,08 +1 16,14,14,10,08,08 +1 16,14,12,10,10,08 +1 16,14,10,10,10,10 +1 16,12,12,10,10,10 +1 14,14,14,14,08,08 +1 14,14,14,12,10,08 +1 14,14,14,10,10,10 +1 14,14,12,12,10,10 +1 14,12,12,12,12,10 +1 12,12,12,12,12,12 +1 The highlighted set in either table indicates stats with at least one ability score that would be boosted to an eighteen by a +2 ability modifier with fewer than two dump stats. These are the most popular point-buy options available to most classes (wizards may opt for something closter to the top of the list while paladin may pick something from the bottom, depending on the player). The twenty-eight point buy looks, to me at least, a lot better than most 4d6 drop the lowest characters I see floating around, simply because the lowest ability is always an eight and the highest is always as high as the player wants it. Twenty-five looks more on par, but isn't really much different when you consider the key abilities for any given class (accepting paladin). But yes, I prefer 28 pt. buy because of the rounder numbers, although past level four 25 pt. buy has this same effect.
Cymraegmorgan 01-21-06, 11:55 PM	Simple question, perhaps difficult answer: What point buy is approximately equal to the stats you get with 4d6 drop lowest rolling? 28. Tested with one hundred sets of stats on a very boring night last year.
The Hive Custodian 01-22-06, 01:22 AM	I wrote a crude Scheme program to test this out, counting scores below 8 as being worth one negative point per point below 8, and not adjusting for hopeless re-rolls: ;gives the result from 4d6 drop lowest (define (fourdeesix one two three four) (cond ((and (< one two) (< one three) (< one four)) (+ two three four)) ((and (< two three) (< two four)) (+ one three four)) ((< three four) (+ one two four)) (else (+ one two three)) ) ) ;gives the point result of a number (define (points score) (cond ((< score 15) (- score 8)) ((= score 15) 8) ((= score 16) 10) ((= score 17) 13) ((= score 18) 16) (else 0) ) ) ;goes through all 4d6 drop lowest configurations and totals points (define (totalpoints) (totalrec 1 1 1 1 0) ) ;the meat: the procedure that calculates the total for totalpoints (define (totalrec one two three four acc) (cond ((= four 7) (totalrec one two (+ three 1) 1 acc)) ((= three 7) (totalrec one (+ two 1) 1 four acc)) ((= two 7) (totalrec (+ one 1) 1 three four acc)) ((= one 7) acc) (else (totalrec one two three (+ four 1) (+ acc (points (fourdeesix one two three four))) ) ) ) ) ;average points on six scores (define (averagepoints) (/ (totalpoints) (* 6 6 6)) ) The result: The average (mean) point total is precisely 6162/6^4 = 1027/216 on one score, or 1027/36 = 28 and 19/36 points over six scores.
danielinthewolvesden 01-22-06, 03:00 AM	Right. So, you can say anything from 27 to 30 points and not be too far off. There is one disadvantage to rolling- you get odd numbers. 13, 13, 13, 13, 13, 13= a 30 pt buy. BUT for those 30 points you could have 14, 14, 14, 12, 12, 12. No one in their right mind would buy the 13's when you could have 3X14's and 3X12's. Thus, when WotC says a 25 point buy isn't far off, they make a point. However, I'd say a 28 point buy = 4d6drop one. Here's what I like to do. Give the players a 30 pt buy. Let them create their characters with it. Then, game nite 1- have each roll a D6- and that gives a +1 to that ability.
NinjaHedge 01-22-06, 09:12 AM	Yes, and we all know how reliable some of the stuff Wizards puts out is... :rolleyes: I despise the 25-point buy and would never, EVER use it. At least 28 for me.. at leat that way characters can have halfway decent stats. Hmm, well all the CRs are calculated assuming a party with 25 point buy, as are all the special abilities, magic items, spells, rules. So, pretty much if you give them more then that they're overpowered, not "halfway decent". What's so difficult about a character with a 25 point buy, what would they be missing out on?
WayneTheGame 01-22-06, 09:30 AM	Hmm, well all the CRs are calculated assuming a party with 25 point buy, as are all the special abilities, magic items, spells, rules. So, pretty much if you give them more then that they're overpowered, not "halfway decent". What's so difficult about a character with a 25 point buy, what would they be missing out on? Eh maybe you're right. Honestly I have never played with 25 point buy so I guess I have no business saying it's bad :) Hive Custodian, I applaud you for doing that. The funny part is, even without knowing Scheme I can kinda figure out what each line in your program means. That's sad.. but I guess it means I'm becoming better as a programmer :P
Nom 01-22-06, 09:33 PM	A single best 3 of 4d6 roll has a mean result of ~12.24. The mean bonus is ~ +0.87 (yes, that is less that the bonus from a score of 12 and yes, that is important). Without reroll and treating scores below 8 as being worth -1 per point below 8, the mean PB value is ~ 4.75. Multiplying these means by 6 (since each roll is independent) we get a total mean bonus of 5.22 and a total mean PB value of 28.5. If we consider the reroll, we find that the probability of rolling 13 or below is 64.51%, which means the probability of no score above 13 is ~ 7.2%. I don't have numbers to hand for the probability of the sum being <= 0. Conventional wisdom is that the reroll increases the mean PB value to a little under 30. However, mean PB value is only part of the picture. You'll notice that a single score had a mean PB value of over 4 (ie +1) but a mean bonus of only +0.87. The first reason for this is that scores get less efficient as they increase. A 25 point buy with all scores 14 or under should have a total +6 bonus, with 1 point spare. Scores over 14 reduce this. The second is that most PB arrays will have only 1 (or occasionally 2) odd scores. In contrast, a rolled array may well have odd scores all over the place, and not always in convenient places. Probability of any given roll being odd is 49.77%. You would expect to "waste" at least 3 "points", possibly more. Even so, it's probably fair to argue that rolling statistically gives you slightly better overall scores than 25 point buy. However, three final considerations: * Control: 25 points provides the ability set weighted towards where you want it to be weighted. Standard rolling allows you to rank-order the scores, but no control over their magnitudes. * Reliability: 25 points tends to focus scores in the "statistically likely" middle band. Even with the reroll, standard rolling has massive variance. Typically, systems with less risk do not return quite as well as those with more. * Focus: This is related to control. When rolling, your chance of getting a score over 15 (ie +3 or better) is still only about 57% (roughly 3 in 5). In contrast, anyone using PB who wants a 16 (or an 18) can have one, if they are willing to sacrifice.
interpretivechaos 01-22-06, 11:11 PM	I prefer point buy for the simple reason is it makes more interesting characters. For demonstration I randomly rolled 4d6 drop the lowest. Although what I rolled was extreme, it demonstrates nicely the problem. 14 14 14 14 12 14 Anyway you twist it, you get a constantly slightly above average character. Bright, Strong, Tough, Nimble, Wise, and Charismatic- except for one that is a tad less above average. Point buy on the other hand frequently becomes a game of give and take. My favorite method is to divy up the stats equally and start shifting points. Say I want a thief- I'll start shifting to Dexterity a bit of Strength. Not content with a 14 dex, I'll shift a little more- and then I'll realize I want a bit more brawn for CC. So I'll debate shifting from Int, Cha, Con, or Wisdom. Deciding I want a witty thief, and an obsercant one as well, I decide to take from Con. Then, I decide to shift the odd points to Int, and deciding on a wittier rogue shift points from Wisdom to Charisma. End result on 28 pt Buy Str 12 Dex 16 Con 10 Int 14 Wis 10 Cha 14 Note that even though I have in general a much worse character (2 pts of dex), Its a character that can be RPed much easier and has a lot more character in it.
Jutter 01-23-06, 05:31 AM	Simple question, perhaps difficult answer: What point buy is approximately equal to the stats you get with 4d6 drop lowest rolling? 28,53. No 'I guess' or 'I tried a few times', but pure maths in an excel sheet. This excludes the reroll options as written in the Player's Handbook, by the way, so during character creation it'll be more.
Leukrythus 01-23-06, 09:47 PM	Rolling 4d6 (and dropping the lowest) has 1296 possible combinations. The average roll is 12.25, and the probabilities are as follows: 3 (1) 4 (4) 5 (10) 6 (21) 7 (38) 8 (62) 9 (91) 10 (122) 11 (148) 12 (167) 13 (172) 14 (160) 15 (131) 16 (94) 17 (54) 18 (21) The odds are that you will have at least one roll of 9 or lower, and one roll 15 or higher. Assuming that points for the buy in system could be increased one for one by decreasing stats below an 8, this system would be equal to a 28.5 point buy in.
Stuntman 01-24-06, 01:47 AM	Assuming that points for the buy in system could be increased one for one by decreasing stats below an 8, this system would be equal to a 28.5 point buy in. That's what I came up with as well. The value varies very slightly if you choose a different value for scores below 8. Since scores that low are not very likely, it doesn't affect the point buy equivalent very much. In games that I DM, I give the player the option of using the standard (25-point) point buy if he does not like what he rolled using 4d6. The standard point buy yields lower scores, but allows for better customisation of ability scores. This customisation is sometimes worth the 3.5 points you give up on average if you really want to ensure you have a certain minimum ability scores. By rolling, you always have a chance of getting far better scores, but you may be stuck with something you are not satisfied with because you do not have scores high enough to qualify for certain feats or for multiclassing.
JulesCARV 01-24-06, 07:51 AM	Wait, are you supposed to re-roll (once) a 4d6 drop lowest roll that is below 10? Like, if you roll 6 4d6 drop lowest rolls, and then you roll one which is an 8, you of re-roll the 8 and take the second result? Or is that just some crazy house rule that my DM has?
DarknessEternal 01-24-06, 10:22 AM	28 points may reflect the average of this rolling method, but it will never practially simulate it. Points buy has a huge flaw that, despite how sound the theory, buries it. Any points buy will inevitably lead to certain arrays of stats being used by all players, all the time. It will come down to people saying things like "where'd you put your 16 and 14?" for example. While there might be differences in where the stats go, everyone has the same stats.
OctoberRaven 01-24-06, 10:30 AM	...is no point buy at all. I heart 4d6 drop lowest as both a DM and character builder. Adds a bit of unpredictability into the mix.
Stuntman 01-25-06, 01:16 AM	Wait, are you supposed to re-roll (once) a 4d6 drop lowest roll that is below 10? Like, if you roll 6 4d6 drop lowest rolls, and then you roll one which is an 8, you of re-roll the 8 and take the second result? Or is that just some crazy house rule that my DM has? If the total ability modifiers of your 6 abilities is less than +1 or none of the 6 abilities are 14 or higher, you may re-roll all of your abilities. For example, if you get a 16, 10, 10, 10, 10, 4, the total modifiers are +3 + 0 + 0 + 0 + 0 - 3 = 0 which is less than one, you may re-roll. If you get a 13, 13, 13, 13, 13, 13, none of your scores are 14 or higher, you may re-roll.
Nom 01-25-06, 05:51 PM	28 points may reflect the average of this rolling method, but it will never practially simulate it. Points buy has a huge flaw that, despite how sound the theory, buries it. Any points buy will inevitably lead to certain arrays of stats being used by all players, all the time. It will come down to people saying things like "where'd you put your 16 and 14?" for example. While there might be differences in where the stats go, everyone has the same stats.Well duh! The main reason for using point buy is that it provides an approximately standardised set of ability scores, as opposed to the massive variance of PH rolling. That said, if every PB character looks exactly the same, I submit to you that the flaw lies in lack of creativity and flexibility in the user, not the ruleset.
interpretivechaos 01-25-06, 06:32 PM	And perhaps between characters their will be more similarity, but with the same characters stats their isn't necessarilly a bellcurve of stats- each stat is as high as a character wants it to be.
Vaelan 01-25-06, 07:03 PM	End result on 28 pt Buy Str 12 Dex 16 Con 10 Int 14 Wis 10 Cha 14 That isn't a 28 point-buy, that is a 30 point-buy. You're forgetting that you must pay 2 points for each point above 14 you wish to raise your Dexterity.
AT-AT Assault 01-25-06, 10:41 PM	Hmm, sorry to barge in, but the people in this thread should be able to answer my question. How do you figure statistics for a set of variables when you dont count all of the variables(ie 4d6 drop lowest and similar things)? And upon answering that, is there an easy way to count up the combinations for each specific total, or do have to count them up one at a time?
phelanarcetus 01-26-06, 01:30 PM	Ok, the math shows that 28 points is about the average. Now while I have tended to end up with significantly better scores than that when I roll for real (though I have rolled plenty of unplayable characters), one thing I like about the point buy system is that the different players don't start off horribly uneven. My last character was worth about a 42 point buy. 17, 15, 15, 14, 12, 11 if I recall the rolls correctly. And he was a Wizard... the guy who wanted to be a Paladin had something worth probably about 28-30 points. That, and with a point buy, you know what sort of scores you're going to get. I tend to start with a concept. Now what happens if I have a concept that needs 3 good scores, and I roll 17, 13, 12, 11, 10, 9? Do I beg for a reroll, ditch the character, or play him with two of the "good" scores being barely above average? My overall preference is actually for a "high-powered" point buy. It lets the players create characters who feel exceptional, while giving them equal opportunity for good stats, and avoiding anybody from being screwed over by bad but not unplayable rolls.
Ut-Napishtim 01-26-06, 02:20 PM	While it's probably moot at this point, I'd like to add that I've also found a 28 PB to be about on par with 4d6 and drop the lowest. Not so much from a mathematics or statistical standpoint (never bothered to break down the numbers myself), but from a play balance one. That is, that in my games I offer both options, and have never had a problem with one overshadowing the other (which I found to be more prevalent when opting for 25 or 32 respectively).
Leukrythus 01-26-06, 07:53 PM	Our games have been starting characters with an 8/10/12/14/16/18, which is an average of 13, and offers some high numbers and some low numbers. That would equal a 38 point buy-in.
Nom 01-26-06, 09:02 PM	Hmm, sorry to barge in, but the people in this thread should be able to answer my question. How do you figure statistics for a set of variables when you dont count all of the variables(ie 4d6 drop lowest and similar things)? And upon answering that, is there an easy way to count up the combinations for each specific total, or do have to count them up one at a time?For continuous variables, calculus usually works. For discrete variables (like die rolls), it's often most expedient to simply enumerate all the possible combinations - get a computer to do this for you. Given that we have the distribution for one set of (best 3 of 4d6) we can reliably calculate means and variances for the sum, since each set is independent and identically distributed.