Rolling stats ?

rabindranath72 · Post by **rabindranath72** » Mon Sep 04, 2006 10:55 am

Mhu Thulan wrote:
It's also worth noting that 2D6+6 has a much 'flatter' distribution of results. Chance of getting an 18 with one roll:

3d6 = 1 in 216

2d6+6 = 1 in 36

So with 6 stats and 2d6+6 you'll have about one character in six with an 18 score.

(4d6, drop lowest) gives you a 1 in 61 chance of an 18 with each roll, but I think it's only skewed - the distribution is about the same shape.

rob

(Edited to turn smilies off)

Yes, the "4d6 drop lowest" distribution is a bit skewed, but the largest effect one sees is a translation of the mean. The cumulative distribution is approximately equivalent to the one of rolling 3d6+2 (except for the tails).

Cheers,

Antonio

Mhu Thulan · Post by **Mhu Thulan** » Mon Sep 04, 2006 11:53 am

Quote:
Yes, the "4d6 drop lowest" distribution is a bit skewed, but the largest effect one sees is a translation of the mean. The cumulative distribution is approximately equivalent to the one of rolling 3d6+2 (except for the tails).

Now you're going over my head!
I have some idea what you mean, but I'll need to see the graphs to make sense of it. Will perhaps generate some later today if nobody gets there first.

rob

rabindranath72 · Post by **rabindranath72** » Mon Sep 04, 2006 12:06 pm

Mhu Thulan wrote:
Now you're going over my head!
I have some idea what you mean, but I'll need to see the graphs to make sense of it. Will perhaps generate some later today if nobody gets there first.

rob

Sorry
Here is what I mean (in graphics)

As you can see, the "jumps" at each roll outcome are approximately the same on the two curves for a large range of values. The height of the jumps give the probability of the outcome. The main effect is clear: the distributions seem approximately equal, the difference between simply rolling 3d6 and 4d6 drop lowest being about 2.

Cheers,

Antonio

P.S.

Sorry I put the wrong figure. Now it is the correct one.

Mhu Thulan · Post by **Mhu Thulan** » Mon Sep 04, 2006 12:50 pm

Quote:
The main effect is clear: the distributions seem approximately equal, the difference between simply rolling 3d6 and 4d6 drop lowest being about 2.

Ah, I see what you mean now. Thanks.

The practical consequence of all this is that if you just want to generate characters slightly higher stats, but still keep them in the 3-18 range (and still use all of that range) then (4D6, drop lowest) gives stats that are, on average, about two points higher, and it doesn't have much effect on anything else.

rob

rabindranath72 · Post by **rabindranath72** » Mon Sep 04, 2006 1:08 pm

Mhu Thulan wrote:
Ah, I see what you mean now. Thanks.

The practical consequence of all this is that if you just want to generate characters slightly higher stats, but still keep them in the 3-18 range (and still use all of that range) then (4D6, drop lowest) gives stats that are, on average, about two points higher, and it doesn't have much effect on anything else.

rob

Yes, that's the practical consequence; the skewness is really negligible, (4d6 drop lowest) is nearly symmetric like 3d6. The effects are on the tails ( 5, 18 ), but they soon reduce:

outcome 3d6+2 4d6 dl

18 ~28% ~16%

17 ~4.8% ~4.2%

16 ~7% ~7.2%

5 ~0.5% ~0.8%

6 ~1.4% ~1.6%

So, if one wants to generate characters with higher stats on average, but which does not give a too much high chance of rolling 18s, (4d6 dl) is the way to go.

Cheers,

Antonio

babbage · Post by **babbage** » Mon Sep 04, 2006 1:35 pm

This all reminds me of those Bell Curve diagrams in the original 1e DMG.
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rabindranath72 · Post by **rabindranath72** » Mon Sep 04, 2006 1:59 pm

babbage wrote:
This all reminds me of those Bell Curve diagrams in the original 1e DMG.

Statistics has (almost) not changed in 25 years

Mhu Thulan · Post by **Mhu Thulan** » Mon Sep 04, 2006 8:50 pm

Hi all,

StealthSuitStanley wrote:
... as a character progresses in levels, the stats become less and less important. Around 3rd level or so, the bonus any stat could provide is overshadowed by the bonus from the level. At mid to high levels, stat bonuses are almost ineffective.

Well, you might think that at first glance... but it's not as clear cut as that.

This is due to a phenomena that, for want of a better name, I'll call "the window effect". Basically, although the stat bonus as a proportion of other bonuses seems small, the difference between having it and not having it makes a big difference between the effectiveness of two otherwise similar characters.

Why is this? Well, it's because PCs (being heroic or foolish types) are forever trying to do things that are only just within their abilities. So the window of D20 rolls that will actually let them succeed is actually quite small.

The obvious example is strength in terms of its effect on melee damage. This is more pronounced than for most other stats, because primes don't come into it:

Take a C&C fighter with specialized in the bastard sword. At level 1, his attack bonus is +2 with 12 strength, +4 with 16 strength. At level 5, make the sword +1, and it's +7 without strength, +9 without. So percentage benefit of str mod drops from 100% at level 1 to 29% at level 5. (At level 10, it's only 14%).

Level 1 fighter attacks a goblin (AC 14) - fine, str+2 increases hit chance from 45% to 55%, a 22% increase in the hit rate and therefore in damage.

Level 5 fighter could fight a goblin... but he's more likely to try it on with a troll (AC 16) - str+2 increases hit chance from 60% to 70%, a 17% increase in hit rate. It's less... but it's not much less.

Add in the direct damage benefit of +2 str mod, and it gets worse. Benefit of 1st level vs. goblin is now 60%, and 5th level vs. troll is 48%.

Take an extreme case, 5th level versus a xorn (AC 23) and the net benefit is a staggering 77%. All other things being equal, the 5th-level fighter with a strength of 16 is doing nearly twice as much damage as his comrade with strength 12.

I haven't done this for the 10th level fighter yet, because I only just ordered M&T so I don't know what typical ACs for 10HD monsters are.

Obviously, for a longsword, 18 strength, or a fighter-alike such as a Paladin, this is even more pronounced. Spells like Bless reduce the effect a bit.

The OpenOffice (2.0) spreadsheet I worked this out with can be found at http://lookatthechimneys.fastmail.co.uk ... matter.ods

(it's a bit of mess because I worked in percentages throughout, not proportions, so lots of "/100" mixed into the formulae)

rob

Mhu Thulan · Post by **Mhu Thulan** » Mon Sep 04, 2006 8:51 pm

As for saves and SIEGE rolls, it's actually even simpler. Mostly, if you follow the advice given in the PHB and on these forums, most SIEGE rolls and saves will be at roughly the level of the character who's taking them. For example, is a level 5 character tries to grab an item from a 5HD monster, the base CL is 5. Likewise for a save against a spell cast by a 5th level wizard.

If that's the case, then the benefit of high stats is constant regardless of the level of the character. Obviously it's less important than having the right prime for the roll, but it can still help a lot. (Actually, if you *don't* have the prime, having a good stat mod can make a major difference to your chance of making the roll; assuming CL=your level, an 18 stat doubles your chance of making a save if you've not got that prime).

rob

Arazmus · Post by **Arazmus** » Thu Feb 18, 2010 4:49 pm

4d6, drop the lowest, arrange to taste.
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