AD&D ability scores compared to real life
j. spolar
Years ago, someone posted that the 3d6 rolled for ability scores were
actually supposed to resemble the bell curve that "real" physical/mental
attributes might have... It may even have been a reference from the 1st
Players handbook. Therefore, the 18 ability score for, say, charisma,
would be held by 1/2% of the population (approx... 1 out of 216 rolls of
3d6 gets you an 18 so the odds are about 1/2% that you could get an 18.)
And (Although I think I originally criticized this), You could change this
discrete probability distribution system to a continuous one along a
normal bell curve, creating probabilities for 19's and 20's... Anyway,
the idea is that, if you could estimate your "intelligence" along the
distribution (Say, by the arguably invalid intelligence estimators such as
IQ's, SAT scores,...), you could transpose this into your numerical
ability and try and "play yourself."
Although some might question this, I am interested in any thoughts
regarding this. While I haven't bothered to post the statistics, there
is a statistical probability of having incredibly high ability scores
(Obviously above 18...) While I doubt I would be fortunate enough to have
such, I have a friend who would probably, IMHO, qualify for being in the
top of an random pool of 10,000 individuals (In intelligence.) Also, what
do you do about strength. Would you recommend allocating the 100% stuff
to the top 18 (So, once you were in the 1/216, then you ranked yourself
amongst 100 of those top, assuming representative distribution?). One
thought I had, to curve possible extreme ability scores, was to count the
"over 18's" as actually being 10 increments (I think it used to/still does
take 10 wishes to get above an 18?). That way, your bell curve would
shorten above 18 and make it very rare to have a 19 or 20. Also, is there
any site to a Z-score table that goes well above 3 standard deviations.
Probably around 6 or 7 or more? Thanks...
James
Silvas
Wow! And I thought I had too much time on MY hands!
Silvas
Pilakowski
From everything I understand about statistics, trying to move more than 3
SD on a Z-score table is statistically pointless since the gradations get
so small as to be meaningless... But I see the wisdom of your point
though.
Michael
Warren.bellant
j. spolar <jsp...@blue.weeg.uiowa.edu> wrote in article
<Pine.A41.3.95.970809...@green.weeg.uiowa.edu>...
> Years ago, someone posted that the 3d6 rolled for ability scores were
--snip ---
> distribution (Say, by the arguably invalid intelligence estimators such
as
> IQ's, SAT scores,...), you could transpose this into your numerical
> ability and try and "play yourself."
We "play ourselves" every day, I want fantacy! ;)
--
____ ____________________
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O-O O-O O
verkuilen john v
Here's your table of values for 100 evenly spaced probabilities from 0.99
to 1.0 as tabulated by Splus.... This should give a sense as to how
amazingly unlikely values past 3 SD are. The derivative of z(q) is _very_
small past for values of q past 2.5.
z(q) q
0.99000 2.32635
0.99010 2.33015
0.99020 2.33400
0.99030 2.33787
0.99040 2.34178
0.99051 2.34573
0.99061 2.34971
0.99071 2.35373
0.99081 2.35780
0.99091 2.36189
0.99101 2.36603
0.99111 2.37021
0.99121 2.37444
0.99131 2.37870
0.99141 2.38301
0.99152 2.38736
0.99162 2.39176
0.99172 2.39621
0.99182 2.40070
0.99192 2.40525
0.99202 2.40984
0.99212 2.41448
0.99222 2.41918
0.99232 2.42393
0.99242 2.42874
0.99253 2.43360
0.99263 2.43852
0.99273 2.44350
0.99283 2.44855
0.99293 2.45365
0.99303 2.45882
0.99313 2.46406
0.99323 2.46936
0.99333 2.47474
0.99343 2.48019
0.99354 2.48571
0.99364 2.49131
0.99374 2.49699
0.99384 2.50275
0.99394 2.50860
0.99404 2.51453
0.99414 2.52055
0.99424 2.52666
0.99434 2.53287
0.99444 2.53918
0.99455 2.54560
0.99465 2.55212
0.99475 2.55875
0.99485 2.56549
0.99495 2.57235
0.99505 2.57934
0.99515 2.58645
0.99525 2.59370
0.99535 2.60109
0.99545 2.60862
0.99556 2.61630
0.99566 2.62414
0.99576 2.63214
0.99586 2.64032
0.99596 2.64867
0.99606 2.65722
0.99616 2.66597
0.99626 2.67492
0.99636 2.68409
0.99646 2.69350
0.99657 2.70314
0.99667 2.71305
0.99677 2.72323
0.99687 2.73370
0.99697 2.74448
0.99707 2.75559
0.99717 2.76705
0.99727 2.77889
0.99737 2.79112
0.99747 2.80379
0.99758 2.81693
0.99768 2.83057
0.99778 2.84476
0.99788 2.85955
0.99798 2.87499
0.99808 2.89115
0.99818 2.90810
0.99828 2.92592
0.99838 2.94473
0.99848 2.96465
0.99859 2.98581
0.99869 3.00840
0.99879 3.03264
0.99889 3.05880
0.99899 3.08725
0.99909 3.11843
0.99919 3.15297
0.99929 3.19175
0.99939 3.23601
0.99949 3.28770
0.99960 3.35001
0.99970 3.42889
0.99980 3.53743
0.99990 3.71648
1.00000 Inf
As to using the normal distribution as a model for extreme values of game
stats, I would recommend against it on two grounds, the first statistical
and the second related to the pragmatics of the game.
Dealing with extreme values is always troublesome in real life--we know the
least about them and they are often unstable. It is fairly hard to
distinguish a Student's t(3) or a mixture distribution such as 0.95*N(0,1) +
0.05*N(1,1) from a standard normal given quite large samples of data from a
random number generator by a UMP test such as the Kolmogorov test, to say
nothing of empirical data which is _never_ clean. There's no good reason to
believe, except within the bounds of +/-2.5 SD or so of the measurements that
a distribution is normal given the standard tests of distribution. If these
extreme values are what you care about, it's a bad idea to try use a catch-all
distribution to model them. Distributions of ability might be well-scaled to
the normal in the middle ranges, where they are calibrated nicely and where
derivatives are fairly large, but all real-world measurements suffer from
substantial upper and lower boundary accumulation problems. I know a fair
number of people who scored in the upper 99% on the SAT but there are
definitely noticable differences in ability.
The second ground is one of pragmatics. People on the way extreme end of
ability are special individuals who I as GM go through a lot of trouble to
make in detail. They don't occur randomly, at least in my campaign. In this
sense, having a big distribution of values that crank out the number of
people with a 19 strength and 19 constitution is just not something I'm
too worried about.
Oh, in case anyone wonders, 3d6 is _quite_ close to an N(10.5, 8.3) random
variable (the variance is approximate as I used a sample to calculate
it), although obviously it is "lumpy."
--
J. Verkuilen ja...@uiuc.edu
"Pete Shelley is right." --me
Bob Evans
j. spolar wrote:
> Years ago, someone posted that the 3d6 rolled for ability scores were
> actually supposed to resemble the bell curve that "real"
> physical/mental
> attributes might have... It may even have been a reference from the
> 1st
> Players handbook. Therefore, the 18 ability score for, say, charisma,
>
> would be held by 1/2% of the population (approx... 1 out of 216 rolls
> of
> 3d6 gets you an 18 so the odds are about 1/2% that you could get an
> 18.)
> And (Although I think I originally criticized this), You could change
> this
> discrete probability distribution system to a continuous one along a
> normal bell curve, creating probabilities for 19's and 20's...
> Anyway,
> the idea is that, if you could estimate your "intelligence" along the
> distribution (Say, by the arguably invalid intelligence estimators
> such as
> IQ's, SAT scores,...), you could transpose this into your numerical
> ability and try and "play yourself."
A long time ago I found this in a pick your own path Xanth novel.
You don't need to agree with them, I just thought it was interesting.
STRENGTH
This is the measure of how physically powerful your hero is. It
compares the hero to others in how much the character can lift, how hard
he can punch, and just how brawny he is. The strongest a normal human
can be is to have a strength value of 18. The weakest a child would
have is a 3. Here is a table giving comparable strengths:
Strength Example
3 A 5-year-old child
6 An elderly man
7 Pee Wee Herman
8 Out of shape and over 40
10 An average 20-year-old-man
13 In good shape and works out
15 A top athlete or football running back
17 Changes auto tires without a jack
18 Arm wrestles Arnold Schwarzenegger and wins
A Tolkien-style troll, being magical, might have a strength of 19 or
20. A full-grown elephant has a strength of 23. A fifty-foot dragon
would have a strength of 30.
INTELLIGENCE
Being intelligent is not just a measure of native brain power. It also
indicates the ability to use that intelligence. The value for
intelligence also measures how aware the character is, and so how likely
he is to notice a subtle clue. Intelligence can be used to measure how
resistant a mind is to hypnosis or mental attack. A very sharp baboon
would have an intelligence of 3. Most humans (we all know exceptions)
begin at about 5. The highest value possible is an 18. Here is a table
of relative intelligence:
Intelligence Example
3 My dog
5 Lassie
6 Curly (the third Stooge)
8 Somewhat slow
9 Pee Wee Herman
10 Average person
13 College professor / good quarterback
15 Indiana Jones / Carl Sagan
17 Doc Savage / Mr. Spock
18 Leonardo dá Vinci / Isaac Asimov
Brainiac of comic-book fame would have a value of 21.
WISDOM / LUCK
Wisdom is the ability to make correct judgments, often with less than
complete facts. Wisdom is knowing what to do and when to do it.
Attacking, when running will earn you a spear in the back, is the best
part of wisdom. Being in the right place at the right time can be
called luck or wisdom. Not being discovered when hiding can be luck; if
it is because you knew enough to not hide in the poison oak, wisdom is
also a factor. Activities that are based more on instinct, the
intuitive leap, than analysis are decided by wisdom.
In many ways both wisdom and luck are further connected, especially as
wisdom also measures how friendly the ruling powers of the universe (not
the DM, the fates) are to the hero. A hero may be favored by fate or
luck because he is reverent or for no discernible reason at all. This
will give him a high wisdom value. Everyone knows those "lucky"
individuals who can fall in the mud and find a gold coin. Here is a
table measuring relative wisdom / luck:
Wisdom Example
Under 3 Cursed or totally unthinking
5 Never plans, just reacts
7 Some cunning, "street smarts"
9 Average thinking person
11 Skillful planner, good gambler
13 Successful businessman / Lee Iacocca
15 Captain Kirk (wisdom) / Conan (luck)
17 Sherlock Holmes (wisdom) / Luke Skywalker (luck)
18 Lazarus Long
CONSTITUTION
The more damage you can endure, the higher your constitution. If you
have a high constitution you are better able to survive physical damage,
emotional stress, and poisons. The higher your value for constitution,
the longer you are able to continue functioning in a difficult
situation. A character with a constitution can run farther (though not
necessarily faster) or hang by one hand longer than the average person.
A high constitution means you have more stamina, and recover more
quickly from injuries. A comparison of values for constitution:
Constitution Example
3 A terminal invalid
6 A 10-year-old child
8 Your stereotyped "98-pound weakling"
10 Average person
14 Olympic athlete / Sam Spade
16 Marathon runner / Rocky
18 Rasputin / Batman
A whale would have a constitution of 20. Superman’s must be about 50.
DEXTERITY
The value of dexterity measures not only how faster a character can
move, but how well coordinated those movements are. A surgeon, a
pianist, and a juggler all need a high value for dexterity. If you have
a high value for dexterity you can react quickly (though not necessarily
correctly), duck well, and perform sleight-of-hand magic (if you are
bright enough to learn how). Conversely, a low dexterity means you
react slowly and drop things frequently. All other things being equal,
the character with the highest dexterity will have the advantage of the
first attack in a combat. Here are some comparative examples of
dexterity:
Dexterity Example
3 or less Complete klutz
5 Inspector Clousseau
6 Can walk and chew gum, most of the time
8 Barney Fife
10 Average Person
13 Good fencer / Walter Payton
15 Brain surgeon / Houdini
16 Flying Karamazov Brothers
17 Movie ninja / Cyrano de Bergerac
18 Bruce Lee
Batman, Robin, Daredevil, and The Shadow all have a dexterity of 19. At
dexterity of 20 you don't even see the man move before he has taken your
wallet and underwear and has left the room (the Waco Kid).
CHARISMA
Charisma is more than just good looks, though they certainly don’t
hurt. It is a measure of how persuasive a hero is and how willing
others are to do what he wants. You can have average looks yet be very
persuasive, and have a high charisma. If your value for charisma is
low, you are may be ignored or even mocked, even when you right. A high
charisma value is vital to entertainers of any sort, and leaders. A
different type of charisma just as important to spies. In the final
measure a high value for charisma means people will react to you
desire. Here are some comparative values for charisma:
Charisma Example
3 Hunchback of Notre Dame
5 An ugly used-car salesman
7 Tonya Harding
10 Average person
12 Team coach
14 Magnum, P.I.
16 Henry Kissinger / Jim DiGriz
18 Dr. Who
COMELINESS
Comeliness is just good looks. You might think having good looks means
that you have a lot of charisma, but all the good looks in the world
won’t mean a thing if every time you open your mouth you insult everyone
around you. Conversely, you could have all the persuasive skills in the
world, but if you are so butt-face ugly you are chased out of town
before you can open your mouth, your high charisma won’t do you much
good. Keep in mind that a very handsome half-orc is still VERY ugly to
a gray elf, and a very handsome gray elf is VERY ugly to a dwarf, and
so on.
Comeliness Example
3 Hunchback of Notre Dame
5 An ugly used-car salesman
7 Pee Wee Herman
10 Average person
12 Team cheerleader
14 Magnum, P.I.
16 Arnold Schwarzenegger
18 Cindy Crawford / Miss Universe
--
______________________________________________________________________
Bob Evans bobe...@sprintmail.com
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`----' `----'`-----'`----'`----' `-' `-' `-'`-' `-'
KLINT
(Snip thesis on how 3d6 related to the rotation of the sun after photon
torpedos have been launched comapres to ability scores).
Whoa, dude, you've got to get out more. Find a girl, settle down, do
something else with your time. I mean, gawsh!
ThresholdMURPE
Nod. That chart/table/whatever was a bit much! =)
-Aristotle@Threshold
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Player run clans, guilds, businesses, legal system, nobility, missile
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Toby
On 10 Aug 1997, verkuilen john v wrote:
> Here's your table of values for 100 evenly spaced probabilities from 0.99
> to 1.0 as tabulated by Splus....
[starts to twitch and shudder]
You know, I just finished a stat course....
I *hate* stats.... They dirty the field of mathematics by association....
I've been trying valiantly to forget all of that infuriating crap I had to
memorize to pass the exam....
As far as I'm concerned, your post was tantamount to a ce act....
So take your random variables, your standard deviations, your normal
distributions, your expected values, your null hypotheses, and cram them
NO CARRIER
John Baughman
ThresholdMURPE wrote:
> In article <33EE90...@prodigy.net>, KLINT <kl...@prodigy.net>
> wrote:
> >(Snip thesis on how 3d6 related to the rotation of the sun after
> photon
> >torpedos have been launched comapres to ability scores).
> >
> >Whoa, dude, you've got to get out more. Find a girl, settle down, do
>
> >something else with your time. I mean, gawsh!
>
> Nod. That chart/table/whatever was a bit much! =)
>
Chill, boys. It's not exactly rocket science. To produce a table like
thattakes all of 15 seconds, 14 seconds to write a couple lines of code
and
one second for your PC to display the results. But I'll admit, to the
uninitiated it can seem dazzling.
j
verkuilen john v
KLINT <kl...@prodigy.net> writes:
>(Snip thesis on how 3d6 related to the rotation of the sun after photon
>torpedos have been launched comapres to ability scores).
>Whoa, dude, you've got to get out more. Find a girl,
I'm fairly happy in this respect, thanks. :)
>settle down,
I'm quite settled.
>do something else with your time. I mean, gawsh!
As someone else, said, it took me only a little time, about 3 minutes or so,
to generate that table, most of which involved looking up the proper function
syntax. After that it was four lines of Splus code.... The original poster
asked for it and there it is. As to the rest, after 12 statistics classes, I
_should_ understand the material. Presumably since the original poster was
asking for the table and an explanation, he wanted it. I make no pretensions
to others understanding the whole argument, however. If you want the nutshell
version though: (a) there are good mathematical reasons why a normal curve
is a bad model for extreme values (see my first post) and (b) there are
pragmatic reasons why I don't think having one distribution of ability scores
is a good idea.
XENO / Matthew L. Shelton
Here is a short 'n' sweet system which might be useful:
STR: your strength is equal to how much you can bench-press, compared to
max press. Ex: Bench-press 150 lbs, STR is 12-13 ... (roll a die to
randomly assign one if a range of values is indicated)
DEX: Your typing speed (wpm)/4, rounded up ... or, if you've never taken a
typing class, DEX equals the distance from which you can hit a dartboard
(not necessarily with any bullseye accuracy, however) with a dart, in
yards/2.
CON: The number of miles you can run in a day (it's the best I could do)
INT: ( (IQ score / 10) + (ACT score /3.6) ) / 2, rounded up. Raw reasoning
ability, I suppose, but it's as good as anything.
WIS: (Your education grade level, including 1 year for kindergarten) / 1.3,
rounded up. Someone who never went to high school = 6 (5.4), 7th grade = 7
(6.2), 8th grade = 7 (6.9), 9th grade = 8 (7.7), 10th grade = 9 (8.5), 11th
grade = 10 (9.2), 12th grade= 10 (10) ... 1 year of college = 11 (10.8), 2
years = 12 (11.5), 3 years = 13 (12.3), 4 years = 14 (13.1), 5 years = 14
(13.8), 6 years = 15 (14.6), 7 years = 16 (15.4), 8 years = 17 (16.1), 9
years = 17 (16.9), 10 years = 18 (17.7).
CHA: How many really really close, life-long best friends do you have, not
counting relatives (but spouses count) ... whichever number's # of Henchmen
that is equal to the number of best friends you have is your CHA. In case
of a range of numbers, you may as well use a die and roll randomly for one
of them.
O=O=O=O=O=O=O=O=O=O=O=O=O=O=O=O=O=O=O=O=O=O=O=O=O=O=O=O=O=O=O=O=O=O=O=O=O
XENO ***** mlsh...@cc.memphis.edu ***** www.people.memphis.edu/~mlsheltn
"By US Code Title 47, Sec.227(a)(2)(B), a computer/modem/printer meets
the definition of a telephone fax machine. By Sec.227(b)(1)(C), it is
unlawful to send any unsolicited advertisement to such equipment.
By Sec.227(b)(3)(C), a violation of the aforementioned Section is
punishable by action to recover actual monetary loss, or $500,
whichever is greater, for each violation."
Michel Julien
Waouh. My head hurt. I haven't understand anything. And i'm supposed to
have graduated from a scientific class....
Magnus
The 'legendary' Burghy
XENO / Matthew L. Shelton wrote:
> CHA: How many really really close, life-long best friends do you have, not
> counting relatives (but spouses count) ... whichever number's # of Henchmen
> that is equal to the number of best friends you have is your CHA. In case
> of a range of numbers, you may as well use a die and roll randomly for one
> of them.
My CHA is 3.
--
The Attack Dog: Red Alert | "Game of chess? What kind?"
http://home.hkstar.com/~luibr | "Strip beast game."
120+ strategies. | (remove BLA to reply)
David R. Klassen
XENO / Matthew L. Shelton wrote:
>
This was *really* cool! I liked it a lot, but there is one small error.
The "max press" is not a *bench* press number but rather a *military*
press. This is a slow, standing, over-the-head lift (i.e. NOT a
clean-and-jerk). In a gym, put weight on the bar, rest it across your
shoulders and lift. It gives you a *very* healthy respect for a STR=13!
--
David R. Klassen
Department of Astronomy
Center for Radiophysics and Space Research
304 Space Sciences Building
Cornell University
Ithaca NY 14853
phone: 607-255-6910
http://faraday.uwyo.edu/grads/dklassen/
dr...@cornell.edu
j. spolar
On Sat, 16 Aug 1997, David R. Klassen wrote:
> XENO / Matthew L. Shelton wrote:
> >
> > Here is a short 'n' sweet system which might be useful:
> <snip>
>
> This was *really* cool! I liked it a lot, but there is one small error.
> The "max press" is not a *bench* press number but rather a *military*
> press. This is a slow, standing, over-the-head lift (i.e. NOT a
> clean-and-jerk). In a gym, put weight on the bar, rest it across your
> shoulders and lift. It gives you a *very* healthy respect for a STR=13!
Yeah... Makes you wonder if the system assumes that a 10 "average"
strength is really the average male strength... One of the reasons why I
am interested in the bell curve evaluation of ability scores as opposed to
the definitional ones... I think the bell curve picture is more accurate
(although, I suppose that begs the question... Also, are those scores
based on the individual you would find in the middle ages or an individual
in the current world... how many "13" strengths do you think there were
back then, and then remember that a 13 is above average, not the best...)
James
KLINT
> Here is a short 'n' sweet system which might be useful:
>
> max press. Ex: Bench-press 150 lbs, STR is 12-13 ... (roll a die to
> randomly assign one if a range of values is indicated)
I think you might have confused the max press/bench press idea.
> DEX: Your typing speed (wpm)/4, rounded up ... or, if you've never taken a
> typing class, DEX equals the distance from which you can hit a dartboard
> (not necessarily with any bullseye accuracy, however) with a dart, in
> yards/2.
That's cool. I have a 30 DEX (I type 120 wpm). But, I couldn't hit a
dartboard at 60' (I think). You might want to just stick to the
dartboard system.
> CON: The number of miles you can run in a day (it's the best I could do)
>
> INT: ( (IQ score / 10) + (ACT score /3.6) ) / 2, rounded up. Raw reasoning
> ability, I suppose, but it's as good as anything.
Not bad - you might want to find an SAT component.
> WIS: (Your education grade level, including 1 year for kindergarten) / 1.3,
> rounded up. Someone who never went to high school = 6 (5.4), 7th grade = 7
> (6.2), 8th grade = 7 (6.9), 9th grade = 8 (7.7), 10th grade = 9 (8.5), 11th
> grade = 10 (9.2), 12th grade= 10 (10) ... 1 year of college = 11 (10.8), 2
> years = 12 (11.5), 3 years = 13 (12.3), 4 years = 14 (13.1), 5 years = 14
> (13.8), 6 years = 15 (14.6), 7 years = 16 (15.4), 8 years = 17 (16.1), 9
> years = 17 (16.9), 10 years = 18 (17.7).
This I would strongly object to. I really think that education is the
antithesis of wisdom in today's world! How many times have you run into
a Ph.D. that couldn't reason his/her way out of a wet paper bag? I've
run into far too many.
> CHA: How many really really close, life-long best friends do you have, not
> counting relatives (but spouses count) ... whichever number's # of Henchmen
> that is equal to the number of best friends you have is your CHA. In case
> of a range of numbers, you may as well use a die and roll randomly for one
> of them.
That's really good!
For what it's worth....
Wraith
bda...@moriarty.rchland.ibm.com (Brent Davis) babbled about Re: AD&D
ability scores compared to real life on 19 Aug 1997 22:06:38 GMT,
saying:
>I think what you were shooting for was something more like this:
>
>((IQ score / 10) + (ACT score/2)) / 2. In this case our 180 IQ person ends up
>with an 18 INT.
IMHO, that works quite well. Given the fact that there are people out
there who have IQ's into the low 200 range, albeit, there are very few
of them, given a high ACT score, they would have int's of 19-20.
Slightly above the human norm, but these would be very rare
individuals indeed. For example, Einstein, who had a very high IQ
(don't remember the number offhand) tested very poorly, and would
never achieve a perfect ACT score.
________________________________________
-Wraith
(remove "SPAMSUCKS" to reply)
________________________________________