D&D 5E Point Buy vs Rolling for Stats

[Lanefan]

What about some combination of point-buy and rolling to minimize some of the issues with either method. For example:
First point buy. Then re-roll each ability once (in-order) and keep the higher. [with DM to eliminate cheating]

(adjust both the point-buy total and/or the roll (3d6 vs 4d6 keep 3) to tune strategy)
You should generate a good character for your class - but with a chance of something interesting.

This allows for stats in the 16-18 range but still doesn't allow for anything lower than 8, and in fact even makes 8 less likely.

The way to game this one is to PB to a 15-15-15-8-8-8 stat line and then roll. Odds are very high that at least two of those 8s will significantly improve...

Lanefan

 

[Oofta]

Overall averages of these two stat lines are 11.50 for the first one and 12.50 for the second.

I'm not sure I agree with your math here. 4d6x1 gives an overall long-term average of 12.24. Point-buy can give a higher average, as you've shown above with the 13-13-13-13-13-10 line, but only if you make the stats a) mostly the same and b) rather pedestrian. As soon as you start varying the stats (which by default means buying higher ones) your average starts to drop because you're getting less bang for each point spent, until at the other extreme (15-15-15-8-8-8) you're down to an 11.50 average.

For comparison, the standard array has a 12.00 average and straight 3d6 gives a 10.50 average.

Compare this to rolling. Rolling a particular set of stats is obviously going to give a different average every time, but almost half the time it'll be higher than 12.24 and almost half the time it'll be lower; with an occasional occurrence of hitting it bang-on filling in the last few percent.

Every time the average is higher or the same (so, very slightly over 50% of the time) as 12.24 one can easily argue you've done better than point buy would usually give you. The range between 12.01 and 12.23 is a more open question: you've beaten array here but are roughly in the range of what a normal point-buy might look like. Anything at or below 12.00 means you've done worse than array and probably worse than most normal point-buys.

So...I have to say the odds when rolling of a higher stat average are at worst flat and more likely slightly in one's favour over point-buy and certainly in one's favour over array; and this is in exclusion of any re-roll options. Your point about not liking to gamble is fair enough, but saying the odds are against you in this case is, I posit, incorrect.

Lanefan

I'd need to do a little more analysis on this. How do you define "better"? For example, I know that most characters will have an average range of ability scores from 8-15 based on crunching I did before. Now, if I take that narrow range, the average is a little under 27.

Then you have to say "how many are close enough to the average to be effectively the same"? Is 28 point buy the same? 26? How many deviations do you go?

Then you get the numbers outside of the 8-15 range. While those are out of the norm, you'd still have to account for them as well.

So ... I'd say a large percentage are going to be effectively the same as point buy. Probably around (as a swag) around 10-20%. Since a big chunk is already the same as point buy then less than half will be better.

I may do some more playing with this, just not sure how to define it.

EDIT: you can also refer to this analysis if you don't believe me.

 

[Lanefan]

I'd need to do a little more analysis on this. How do you define "better"? For example, I know that most characters will have an average range of ability scores from 8-15 based on crunching I did before. Now, if I take that narrow range, the average is a little under 27.

Then you have to say "how many are close enough to the average to be effectively the same"? Is 28 point buy the same? 26? How many deviations do you go?

We're looking at different things.

You're looking at point-buy cost, which isn't linear - it skews as stats get higher (or lower, if buys below 8 are allowed).

I'm looking at the straight average of the 6 stats, generated by whatever means and before racial adjust.

Then you get the numbers outside of the 8-15 range. While those are out of the norm, you'd still have to account for them as well.

So ... I'd say a large percentage are going to be effectively the same as point buy. Probably around (as a swag) around 10-20%. Since a big chunk is already the same as point buy then less than half will be better.

Some will be results that are achievable with point buy, no doubt; you've already shown that point-buy's range of stat averages runs from 11.50 to 12.50 which is pretty wide. With 4d6x1 giving an overall average of 12.24 it's fairly obvious that more rolls will fall outside the higher end of this range than the lower.

 

[Oofta]

We're looking at different things.

You're looking at point-buy cost, which isn't linear - it skews as stats get higher (or lower, if buys below 8 are allowed).

I'm looking at the straight average of the 6 stats, generated by whatever means and before racial adjust.

Some will be results that are achievable with point buy, no doubt; you've already shown that point-buy's range of stat averages runs from 11.50 to 12.50 which is pretty wide. With 4d6x1 giving an overall average of 12.24 it's fairly obvious that more rolls will fall outside the higher end of this range than the lower.

The reason point buy costs more for higher numbers is to mimic percentages; you are far less likely to roll an 18 than a 12. Comparing averages is one way of doing the analysis, but for every 18 you get a number of 5 or less.

In other words, I think you are over-simplifying your analysis. On the other hand if you a single 16 (a 56.76% possibility) while ignoring all other numbers as "better" then you are correct.

All depends on how you slice the numbers. There are lies, damn lies and statistics after all.

 

[Tony Vargas]

The reason point buy costs more for higher numbers is to mimic percentages

Is it? I feel like it's more an attempt to capture the greater impact of high stats compared to moderate stats, and, especially, of shaving several stats a point or two to boost one stat as high as possible...
...it also makes life just slightly easier on MAD builds...


I say 'attempt' in part because, if there were a calculus that'd get that exactly right there wouldn't be any reason to have the 15/8 limit.

 

[Oofta]

Is it? I feel like it's more an attempt to capture the greater impact of high stats compared to moderate stats, and, especially, of shaving several stats a point or two to boost one stat as high as possible...
...it also makes life just slightly easier on MAD builds...


I say 'attempt' in part because, if there were a calculus that'd get that exactly right there wouldn't be any reason to have the 15/8 limit.

OK, I should have qualified that with "I always assumed that...".

As far as the 15/8 limit, that is the average high and low a character will have with standard 4d6 drop lowest.

To correctly do the analysis you'd have to figure out the norm and standard deviations of the 4d6 drop lowest method and ... well there would be too much math for my brain at the moment.

It would be interesting to ask though, and why they didn't just use the point buy systems of previous editions.

 

[Lanefan]

OK, I should have qualified that with "I always assumed that...".

As far as the 15/8 limit, that is the average high and low a character will have with standard 4d6 drop lowest.

Hmmm. I didn't know this, though on a quick glance it makes tons of sense.

Any idea how often one or more rolls would fall outside this range? My guess would be about twice per three characters (two rolls per eighteen); I don't think it's as high as once per character (one roll in six) but I'm just eyeballing it - it could be.

To correctly do the analysis you'd have to figure out the norm and standard deviations of the 4d6 drop lowest method and ... well there would be too much math for my brain at the moment.

Mine too.

It would be interesting to ask though, and why they didn't just use the point buy systems of previous editions.

Limiting the range makes the underlying math easier to work with for organized play and-or adventure designers, is my guess; at least at low levels. Not enough of a rationale to justify it, IMO, but then I don't do organized play and am thus a little biased...

 

[Maxperson]

Then you're just guaranteeing higher ability scores, with some lucky people getting much higher and others just a little bit higher.

If a character needs high ability scores to be interesting, why not just allow more points in your point buy and allow people to buy numbers above 15?

It wouldn't solve the main issue I have with it, which is lack of realism. People can't select the stats they have. Instead, they're born with whatever stats they have and make do. Plus, it isn't all about high stats for a lot of people who roll.

 

[Maxperson]

The reason point buy costs more for higher numbers is to mimic percentages; you are far less likely to roll an 18 than a 12. Comparing averages is one way of doing the analysis, but for every 18 you get a number of 5 or less.

You're around half a percent(33%) more likely to get an 18 than a 5 or lower, but the odds change drastically if you look at the proper range of numbers, rather than just an 18 and then 5 or lower. For example, the odds of getting a 3-6 with any given roll is around 2.7%. The odds of getting 15-18 on any given roll is around 23%. That's the top 4 and bottom 4 numbers.

 

[Baldurs_Underdark]

OK, I should have qualified that with "I always assumed that...".

As far as the 15/8 limit, that is the average high and low a character will have with standard 4d6 drop lowest.

To correctly do the analysis you'd have to figure out the norm and standard deviations of the 4d6 drop lowest method and ... well there would be too much math for my brain at the moment.

It would be interesting to ask though, and why they didn't just use the point buy systems of previous editions.

I actually once wrote out all the possible combos of 4d6 (all 6*6*6*6 = 1296 of them). Then I took out the lowest number, and added up the remaining three. (I'm sure I could have calculated this with a smart formula, but I just used smart copy-pasting and wrote out all the possibilities). Turns out the average value is 12.24, and a total of 73.47 points.

With point buy, the higher total is obtained with stats like 13,13,13,12,12,12, which totals 75. The lower total is obtained by a list like 15,15,15,8,8,8, which results in a total of 69. The rolls therefore fall nicely between the max and min score with point buy. Also the standard array of 8,10,12,13,14,15 (average of 12) comes pretty close to the average. However, if you use the 15,15,15,8,8,8 list, you get quite a few points less than with rolling, simply because those higher stats are more "expensive". With rolling, there is no such penalty.

I also dumped all the results into a chart, to see the frequency with which all the possible resulting stats occur.



Hope this helps in this epic discussion!

Personally, I'm about to start a new campaign, and I am actually gonna let the players decide what they want to do. If we roll, I will however allow rerolls (discard all 6 stats, roll 6 new ones), so to smoothe out the potentially large differences between the high and low rolls. Yes, that will result in high stats on average. I'll just adjust the difficulty of the encounters.