D&D 5E Point Buy vs Rolling for Stats

[Maxperson]

Realism is NOT created by random stat buy generation. It simply isn't. Randomly determining stats in no way affects realism. Particularly since random generation is not tied to anything in the game world.

Yes it is. It simply is. In real life you don't get to choose your stats, so rolling randomly is more realistic than point buy or array. Period. End of story. In reality you can have stats higher than 16 or lower than 8 at the beginning of adulthood/career, so rolling is more realistic than point buy or array. Period. End of story.

I roll an 18 strength. Why is my character strong? Note, you cannot reference the background of my character since that's simply post hoc justification. You would be saying that my character is strong because I did lots of exercise, but, my character didn't. I randomly rolled that Strength score. My character has that strength score for no actual reason, other than that's what I rolled.

ROFL I love how you attempt to prevent background explanations, when in reality you would have them. It's an arbitrary limitation in order to win the internetz and I reject it completely. Regardless, even without a background rolling is more realistic for at least the two reasons I listed.

 

[Guest 6801328]

Yes it is. It simply is. In real life you don't get to choose your stats, so rolling randomly is more realistic than point buy or array. Period. End of story. In reality you can have stats higher than 16 or lower than 8 at the beginning of adulthood/career, so rolling is more realistic than point buy or array. Period. End of story.

Oh, Max. I saw you had last post in this thread, which so far hasn't interested me, and I couldn't resist dropping in to see what you said. I'm glad to see you are still Max.

 

[Harzel]

Realism is NOT created by random stat buy generation. It simply isn't. Randomly determining stats in no way affects realism. Particularly since random generation is not tied to anything in the game world.

I roll an 18 strength. Why is my character strong? Note, you cannot reference the background of my character since that's simply post hoc justification. You would be saying that my character is strong because I did lots of exercise, but, my character didn't. I randomly rolled that Strength score. My character has that strength score for no actual reason, other than that's what I rolled.

Post hoc justification is not realism. It's changing reality to fit the die roll, and, I've been told, that's incredibly bad. All those dissociative mechanics arguments are predicated on the idea that justifying rolls after the die has been rolled is immersion breaking and bad for realism.

So, how can it be more realistic to randomly determine stats when random generation of stats cannot be justified through any callback to the in game fiction except as an after the fact justification?

What? Maybe I am missing your meaning here, but if you don't "justify" (which seems like sort of an odd word choice) a roll afterwards, then when would you? I mean, if you decide what the result is beforehand, then there's no need to roll. (?)

 

[Harzel]

You mean you don't always round down in D&D?

AKA, yes it looks like I was accidentally using integer math.
The real numbers:
15.6627465
14.1746176
12.9559838
11.76172
10.4118873
8.5048237

When @Oofta did this work, I began thinking about whether you could analyze the situation fully, enumerating all possibilities, instead of sampling. Since the number of sequences of 24 d6 rolls is 6^24, which is just a bit less than 3x10^18, the answer would seem to be ‘no’, at least for brute force. However, I realized there was a way to cut the problem down quite a bit. Details are below for those interested, but the result was that I was able to calculate the frequencies/probabilities of stat arrays rolled as 6 x 4d6k3 with various properties, particularly how they relate to point buy. This is the first batch of results; I have a few more things planned. Suggestions are welcome.

The top level bucketing that I did just summarizes how the stat arrays generated by 6 x 4d6k3 will generally fall with respect to whether you can directly compare them using the standard point-buy scheme at all. It’s not ideal, but the best that I could think of.

[TABLE="class: grid, width: 600"]
[TR]
[TD]Arrays in which the values are[/TD]
[TD]Frequency[/TD]
[TD][/TD]
[/TR]
[TR]
[TD]Some < 8; All < = 15[/TD]
[TD]14.5%[/TD]
[TD]Out of range low[/TD]
[/TR]
[TR]
[TD]All >= 8; All <= 15[/TD]
[TD]28.8%[/TD]
[TD]In range[/TD]
[/TR]
[TR]
[TD]All >= 8; Some > 15[/TD]
[TD]41.5%[/TD]
[TD]Out of range high[/TD]
[/TR]
[TR]
[TD]Some < 8; Some > 15[/TD]
[TD]15.3%[/TD]
[TD]Out of range low and high[/TD]
[/TR]
[/TABLE]

For those that were in the 8/15 range, I further broke them down by point-buy value. The whole list is in the attached spreadsheet, but here are a few points that I thought were interesting.

• The most frequent point-buy value is 26 (1.76%); above and below 26, the frequencies gradually decrease. 25 points is at 1.75% and 27 points is at 1.73%.
• The total frequency for 0-27 points is 16.8%; 27-54 points is 12.0%.
• The mean point-buy value is 26.25.

Next, I plan to a) compute distributions for ranked values (highest value in array, 2^nd highest, etc.); and b) invent some extended point-buy scheme that can assign a point-buy value to all possible arrays (to induce comparability).

Oh, I just happened to look back at the first page of the thread and see that @Oofta did some analysis for which he invented some point-buy scheme for all of 3-18. I had forgotten that.

In the meantime, so as to ensure that the enlightened back and forth in this thread continues, I will note that at 1.73%, the arrays corresponding to exactly 27 points come up rather rarely. This underscores that (take your pick)

• Point buy greatly restricts the wide variety of concepts that rolling allows.
• Rolling produces a lot of results that are quite uneven.

Something for everyone.

Computational notes
[sblock]The basic observation is not all that deep. Since we are interested in properties of the stat arrays, not the underlying rolls, it would suffice to just analyze each of the possible stat arrays if we knew each one’s frequency/probability. But the frequencies are actually pretty straightforward to compute. Several others in the thread have already displayed calculations of the frequency distribution of values generated by a single 4d6k3 roll. Since (we assume) the 6 rolls for a stat array are independent, the frequency of a particular array is just the product of the frequencies of its individual elements. Given the frequency of each stat array, the frequency of some property (such as having a particular point-buy value), is just the sum of the frequencies of the arrays having that property.

Alternatively, since all 4d6 rolls (as sequences) are equally likely, you can think of the problem in terms of counting and make similar observations. We know the number of 4d6k3 rolls that map to each value, and for each particular stat array, the number of 6 x 4d6k3 rolls that produce it is just the product of the number of individual 4d6k3 rolls that produce each of its constituent values. And then the number of 6 x 4d6k3 rolls that have a particular property is the sum of the numbers of rolls that produce the individual arrays having that property.

And in fact, counting was how I conceived of the problem initially. However, computationally, that counting can involve some fairly large numbers. In fact, in an interesting (or not) coincidence, that number of distinct 6 x 4d6 rolls mentioned above, 24^6, turns out to be just a little bit shy of the largest number that can be represented in a 64-bit integer. So, since I didn’t want to have worry about massaging my arithmetic to ensure that values stayed in bounds, and since the results really need to be converted to frequencies in the end for interpretability anyway, I coded it in terms of frequency calculations using floating-point, because, after all, what’s a little round-off error between friends. (Actually, I did check by adding back together frequencies that should sum to 1, and still got more than 10 nines, so I think things are pretty much ok.)

Anyway, even using that basic observation, things still could have gone amiss, as it was not immediately clear that enumerating all possible stat arrays was going to be feasible. However, 3 to 18, inclusive, is 16 values and 16^6 is ‘only’ 16,777,216 – not that many more than the 10,000,000 @Oofta used for sampling. And in fact, just enumerating them turned out to be nearly instantaneous. Putting in the 6 floating-point multiplications for each array (to compute its frequency) did bog things down a bit – about a 5 second pause. The bits of code for analysis are just comparisons and additions and adding them in didn’t seem to hurt too much. So in the end, this seems to walk right up to but not overstep feasibility, at least for my desktop.[/sblock]

 

[Lanefan]

[MENTION=6857506]Harzel[/MENTION], in the last line of the table in post 1534 (just above this one) I think it wants to say "Some < 8; Some > 15" - you have an extra '=' in there.

Otherwise, good stuff; and I'm curious as to what your further number-crunching will show.

Lanefan

 

[Caliban]

In the meantime, so as to ensure that the enlightened back and forth in this thread continues, I will note that at 1.73%, the arrays corresponding to exactly 27 points come up rather rarely. This underscores that (take your pick)

• Point buy greatly restricts the wide variety of concepts that rolling allows.
• Rolling produces a lot of results that are quite uneven.

I still say that requiring an (extreme) stat for your character isn't a concept. It's being a prima donna.

High or low stats don't constitute a "concept". They may support or interfere with a character concept, but stats by themselves are just numbers.

 

[Yardiff]

'High or low stats don't constitute a "concept". They may support or interfere with a character concept, but stats by themselves are just numbers.'

So why then does it matter how you come up with those numbers?

'I still say that requiring an (extreme) stat for your character isn't a concept. It's being a prima donna.'

What is an 'extreme' stat?

 

[Arial Black]

It was indeed an analogy, relevant only to the issue of playing a game.

If you want your games to have randomly generated advantage and disadvantage for players, then great - do that. Knock over a few of your own pieces when you start a game of chess, or lose a couple of players from your football team before the starting whistle sounds, or perhaps start playing a game of snooker with a pool cue.

Games are in the overwhelming majority, fair - by rules and tradition. Where someone must 'start first' such as in snooker or football, or indeed chess, a random choice is made because these games cannot be played with one side starting first.

But roleplay isn't like that -

...because although role-playing games are 'games', they are also make-believe in an imaginary but believably realistic world of your (or someone else's) creation, and it is a fatal flaw to have so unrelistic a world where every person is exactly as capable/rich/lucky as every other.

- everyone has their time in the spotlight and everyone can contribute to the team. There is no requirement for random advantage at the start - there is plenty of randomness along the way, all modified by the bonuses your character's stats give you.

Reality isn't random, even if the mechanisms behind reality are so complex and intertwined that they might appear random to us.

The reason we use random rolls for stats is not because random rolls are the cause of the abilities of real people; heredity and health and disease and experiences and many things we don't yet understand contribute in such complex ways that we cannot predict what people will be like even if we know all of the information. We use random rolling because the results of random rolling resemble a real population; certainly a better representation than the results of point-buy or array.

 

[Arial Black]

Aye, I don't think you're the one this "definition of fair" argument is directed at you, as you are readily saying your preference isn't swayed by what's fair.

You want your version of realistic.

And I only say "your version" because you view the character creation rules differently than I do. You have the rules apply to model all the creatures in the game world, and I want them to model just the player characters. So you're bound to want something with a wide range of results, while I'm cool with one single set of stats.

So, to answer your question I quoted: No matter what system I use to create PCs, I'm am saying absolutely nothing about the the existence of nobles and peasants, social classes or anything else about society and tge larger world. The only thing I'm saying when I tell my players to use the Standard Array is "these four characters have these six stats."

You say that you have the whole of the population be realistically diverse, except for PCs. For me, every one of that diverse population is a valid character idea, and point-buy only lets me play a tiny fraction of them and denies me many valid character concepts.

 

[Maxperson]

What? Maybe I am missing your meaning here, but if you don't "justify" (which seems like sort of an odd word choice) a roll afterwards, then when would you? I mean, if you decide what the result is beforehand, then there's no need to roll. (?)

[MENTION=22779]Hussar[/MENTION] used the word "justify" in order to try and shed a negative light on something normal and not at all negative. The explanation for how the random stats came about does not affect the realism one way or the other. It's just an explanation. For some reason he feels that he loses if you are able to do that, though, so he made a very poor effort to shut it down.