25 or 32...what's the REAL "standard" point buy?

[d4]

let me see if i understand the method you used.

you generated 12,000 sets of stats using the 4d6-L (with caveats) method.

you then averaged all the "Strengths", averaged all the "Dex's", etc. over the 12,000 characters, and ended up with a stat array that was basically six 12.3 stats.

this averages to a 25-point buy.

however, i don't think that's a valid way of measuring the "actual" average point-buy of the method, for two reasons.

one, the "average array" you came up with isn't a valid set of stats! (it has no ability greater than 13.)

secondly, the costs for higher ability scores is not a linear relationship, so that can severely skew your results. i bet if you did what stephenh did, and actually average the total point-buy of those 12,000 characters, you will get a result higher than 25.

here's one example to show what i mean about how high scores can skew the point-buy away from the average.

say you start with the array 18, 17, 16, 10, 9, 8.

if you total up and average these stats, the average comes to 13. (the total is 78, 78 / 6 = 13.)

under point-buy, a set of six 13s would be worth 30 points. (6 x 5 points = 30 points.)

on the other hand, this set of stats is actually worth 42 points. (16 + 13 + 10 + 2 + 1 + 0 = 42 points.)

if you extend this idea over many sets of stats, you can see why taking the average of the stats first, and then finding the equivalent point-buy, is going to give you different results.

even if you look at these stats as a "column" instead of a "row" -- i.e., as a set of 6 Strength scores, for example -- you can still see how averaging the stats first skews the results.

say these are the Strength scores of six characters. the average of their scores is 13, so you would assume that, on average, Strength is contributing 5 points to the point-buy cost of the "average" character.

but that's not true. those six stats are really adding 42 / 6 = 7 points to the point-buy of the "average" character, because the costs are not a linear relationship.

 

[Quirthanon]

From what I remember about statistics "d4" is right. The non-linear portion of the point buy method isn't accounted for when you average all the stats together and then calculate the point buy, as the average will always be lower than the non-linear portion.

The correct way is to calculate the stats (the 4d6-L and verify). Then calculate the points per set of stats, and then average.

 

[Creamsteak]

I don't know much about statistics, but has anyone just coded up a program to run through all the different ability score array possibilities on 4d6-L and then added up all the "viable" arrays with all stats greater than 8 point value and divided by the same number? Probably wouldn't take more than a minute to program up, and would give you the results, and you could print it out into some form so you can actually "see" everything.

 

[Graf]

32 because it doesn't matter very much to me as a DM but players enjoy the flexbility.

I've found that with the padding that attributes give them most people create more diverse, interesting characters.
In particular fighters feel more comfortable allocating points to stats like Int and creating more non-traditional builds if they have the "padding" that comes from higher stats.
Certain classes, Monks, Paladins, Clerics are more fun to play if you can cover the bases and have an additional high secondary stat.

Finally, you can give an NPC an exceptional stat without worrying too much about the impact it will have on the group.

 

[dvvega]

From what I remember about statistics "d4" is right. The non-linear portion of the point buy method isn't accounted for when you average all the stats together and then calculate the point buy, as the average will always be lower than the non-linear portion.

The correct way is to calculate the stats (the 4d6-L and verify). Then calculate the points per set of stats, and then average.

Actually I didn't roll the characters to check what happened, I rolled them just to confirm my mathematics. Statistically, the 4d6 discard lowest will average to 12.5

No matter what you say regarding points, it will average on each ability. This means that no matter what happens, statistically you will have 6x 12.5 for your stats in an infinite space.

Thus using 4d6 discard lowest will produce 12.5 for each ability. Statistically this is the case if you roll an infinite number of characters ... thus the point average will tend towards 24 since all the abilities should tend to 12.5.

 

[d4]

No matter what you say regarding points, it will average on each ability. This means that no matter what happens, statistically you will have 6x 12.5 for your stats in an infinite space.

Thus using 4d6 discard lowest will produce 12.5 for each ability. Statistically this is the case if you roll an infinite number of characters ... thus the point average will tend towards 24 since all the abilities should tend to 12.5.

no, it won't. it is very possible that X number of stats that average to 12.5 will not have the same point-buy cost as X number of stats that are all 12.5.

that's why you cannot take the average of the stats first and then find the point-buy cost second.

 

[scott-fs]

Hey all. I'm gonna start up a PBEM soon and I'm wondering if anyone can comment on a recommended point buy. The DMG tells us that 25 is "standard", and that 32 is for higher powered games. But here on enworld, my impression is that 32 is pretty much the standard...whatever "standard" means.

It all depends on what your players are used to. Admitedly, when I first started off in 3e I felt 25 was really low. Of course, coming off 2e, you need high stats to get any sort of bonuses. A 3e 14-str fighter is about as good as a 2e 18-str fighter. I suppose it really comes down to, people want as high stat characters as they can get, and the higher point total they can use, the better.

When I started my campaign, I did a very generous 4d6 method. It produced characters between 37 points and 58 points.

In a new campaign (where I was a player), we set the point total at 36 (it allows all scores to be 14). It was ok, but the DM seemed to overcompensate and each encounter could've been a fight to the death. There were an inordinate amount of criticals being rolled on the other side of the screen.

In a d20 Modern campaign I requested that the point total be dropped 6 points to 30. This was reasonable, and created decent characters. It's still a little bit higher than the game presumes. It allows all scores to be atleast 13.

If I start a new campaign, I'm considering using a point total of 20, but using the Gestalt rules from Unearthed Arcana.

Either that or a 25 point campaign using the Generic classes (Warrior, Spellcaster, Expert).

25 or 32? What should I use in my game? And is 25 really too low, or are people on enworld simply playing higher-powered games?

I don't think 25 is too low. Create a couple characters and check to see what sort of min-maxing you might be able to do. If I had the time, I'd take the opportunity to create a sample character of each class using a 25 point total. 25 points allows the following sets:

13, 12, 12, 12, 12, 12. +6 total
14, 12, 12, 12, 12, 11. +6 total
14, 14, 12, 12, 11, 10. +6 total
14, 14, 14, 12, 10, 9. +6 total
15, 14, 12, 12, 10, 9. +5 total
16, 14, 12, 10, 10, 9. +5 total
17, 12, 10, 10, 10, 10. +4 total
17, 14, 10, 10, 10, 8. +4 total
17, 14, 10, 10, 9, 9. +3 total
18, 10, 10, 10, 10, 9. +3 total
18, 12, 10, 10, 9, 8. +3 total

BTW, in my PBEM, characters will begin at 1st level. And I don't envision the world being "lower" or "higher" powered than default D&D.

Since it's a PBEM, I presume that there might be less overall combat. Certainly significant encounters, but nothing too frequent. You should be fine with a 25 point total.

I'd recommend 32 PB. The other GMs in my group use it, it works fine and creates decent but not hugely powerful PCs. 25 PB PCs are weak, and 25 PB makes several classes like Monk & Paladin so weak as to be unplayable IMO.

Personally, I don't consider that too much of a problem. I've not really liked the role of Paladins and Monks (though I played a Monk sort of character in 2e, but he had scores of 13, 12, 11, 12, 14, 9 (remember this was 2e), and he has been one of my favorite characters. One note, the character would be created with 23 points, and he would become more powerful now in 3e if he kept those stats. If I were to boost him to 25 points, they'd go directly to Charisma). I've been tempted to make Paladins a Prestige Class (as from UA).

So, that definately means I'll be sticking with a maximum of 25 points.

 

[d4]

Of course, coming off 2e, you need high stats to get any sort of bonuses. A 3e 14-str fighter is about as good as a 2e 18-str fighter.

i don't agree. remember, the opposition has been ramped up too.

a 3e 14 Strength fighter against 3e orcs (for example) is going to do worse than a 2e 18 Strength fighter against 2e orcs.

 

[stephenh]

Actually I didn't roll the characters to check what happened, I rolled them just to confirm my mathematics. Statistically, the 4d6 discard lowest will average to 12.5

No matter what you say regarding points, it will average on each ability. This means that no matter what happens, statistically you will have 6x 12.5 for your stats in an infinite space.

Thus using 4d6 discard lowest will produce 12.5 for each ability. Statistically this is the case if you roll an infinite number of characters ... thus the point average will tend towards 24 since all the abilities should tend to 12.5.

d4 and Quirthanon are both right. I don't think anyone is disagreeing that statistically the average of 4d6 drop lowest is basically 12.25. However, as has been said, the problem with your method is that you assume a simple linear relationship between points and stats, and this is clearly not the case for stats greater than 14. For example consider the following two sets of stats: 13 13 12 12 12 12 (average =12.33, 26 points) and 18 18 12 10 8 8 (average is again =12.33, points=38). Both these two sets of numbers have the same average stat value, which is approximately equal to the average you expect from 4d6 drop low. However as can be seen, they have very different points values, because one or two very high stats add a lot more points than very low values.

 

[stephenh]

Ok using 4d6 drop low, some more stats -- a breakdown by points.

Left hand column is points score. Right hand column is the percentage change of rolling something *equal to or higher* than the given points score.

points --- %chance
10 --------- 99.3
15 --------- 95.4
20 --------- 83.9
25 --------- 64.2
30 --------- 41.5
35 --------- 22.6
40 --------- 10.3
45 --------- 3.9

i.e. using 4d6 drop lowest a player has a 10.3% chance to roll a set of stats that adds up to 40 or more points.