Standard deviation on Stat distribution?

[jeff_wilson]

Originally Posted by David Johnston2

"Valid" not necessarily meaning "having some
thing to do with the real world"?

Ultimately it does, however statistics are never expected to be a perfectly accurate description of reality. There are always numerous sources of error, and the characterization of that error is just as important if not more than the underlying principles.

If the data set doesn't reflect the original population that it purports to model, the measured error will be significantly higher than predicted, and this sort of exceptional error is one way to tell that there is such a lack of representation. However, as a representation of the data set itself, the statistical conclusions remain valid with regard to the data set, and can remain useful in predicting further data gathered in the same systematic way, and further refinement can correct for certain of the systematic inaccuracies and lead to improvements in characterization of the measured results.

This sounds like a lot of doubletalk to lay people, but in game terms "having something to do with the real world" is the desire for accuracy and realism, and the data set is the gameble abstraction given in the rule books. My conclusion that +3 attribute levels approximates a standard deviation is a characterization of that data set, and I am as dubious as anyone as to how much this says about the real world, since I just used some formulas to produce the most basic statistical conclusions available and took a few minutes to review some notes from the creation of 4/e for any gotchas.

But since it *is* a gameable abstraction, and intended to fulfill GMs' and players' needs for fair and useful results with as few anomalies as possible, we can treat its inaccuracies as systematic and still make useful statistical inferences about its behavior. There are even people who are seeking to improve it in the way above, for instance the current thread on TL improvements currently below the level of resolution.

In fact, I would go so far as say that the lack of accuracy is a feature, not a bug, even if it is a feature that not everyone wants in every product. The low-resolution SPACESHIPS series for example is gloriously unencumbered by three-digit accuracy, and this made coming up with new rule systems so much easier; in the tactical combat system, you only have a few hexes to chose from, and as long as you arrange for some errors to add and some to subtract, and don't let them accumulate, your arithmetic-only answer is right 90% as often as Mr Trigonometry's.

[Kromm]

Originally Posted by jeff_wilson

I'll be the first to agree that adventurers are not a representative sample of humanity, but I don't see how it is supportable to disclaim the statistical meaning of the canonical statements that a score of 10 represents the human average and that most normal humans have scores in the 8-12 range without also discarding their meanings as commonly understood by non-statisticians.

Once the authors assign abstract quantities to represent individual qualities and make statements about how common they are among a group of such individuals, how are they not practicing statistics?

You're making the huge and incorrect assumption that we're using "human" and "average" rigorously to refer to the real-world human population and the mathematical concept, respectively. We aren't! We're using "human" as code for "adventurers with the 0-point human racial template" and "average" to mean "the value everybody gets for free." But those concepts take more words to express, and economy of words is vital when you pay for printing by the page and shipping by the gram. All the Basic Set is saying is that in the absence of points spent to have a different racial template and/or dramatically high or low scores, you get 10s. Then it's defining "dramatically high or low" well enough to help you create suitable adventure heroes. Reading any more into it is being unnecessarily legalistic or pedantic . . . one of those.

[aesir23]

Even though it is not official doctrine, some guidelines around how common certain scores are in your world can be very helpful for players trying to determine their characters attributes.

Outside of ST (which deviates much more from person to person), I use something like:

11 = 1 person in your clique or immediate family is this smart/agile/fit. (Or 1/10)

12 = 1 person you know well is this smart/agile/fit. (or 1/100)

13 = 1 person you've met is this smart/agile/fit. (or 1/1,000)

14 = 1 person you've heard about is this smart/agile/fit. (or 1/1,000,000)

It all depends on how you feel about stat normalization. In a high point total pulp game, all of these go out the window in favor of larger than life heroes who are better at everything.

[Victor Maxus]

I look at this from a math perspective. Not so much what does each level represent, but in game terms, what each level means. This can be applied for skills and stats. For me, it is a look at what putting one level in a stat or skill can do for you compared to others or NPC's in the game. Basically, one level in either means that in a contest of skills or stats, you going from winning 50% percent of the time to almost 2 out of 3. Does not seem like much, but you are now winning twice as much os your opponent. If you go two levels, it becomes close to 3 out of 4.

Now, I like to take this and translate it into American style football. I will turn the football season into a contest of skills rolls. Let's say you have an average team, you go 8 and 8, pretty average, and your team has the average skill. Now, in the history of the NFL during the Superbowl Era, very few 8 and 8 teams make the playoffs. Some have, but it is rare. Now take this team, bump it up one point, and in the 3 dice system, they now win 62.5% per cent of the time, or out of 16 games, they win 10. Now, in the history of the Superbowl, very few 10-6 teams do NOT make the playoffs. That happens as well, it is rare, but if you reach 10 wins, you stand a very good chance of getting to the playoffs, and a few Super Bowl champions were 10-6 teams. (Remember the big upset of the Patriots by the Giants, they were 10-6) If you go to two levels above average, you are looking at a team that wins 11.8 games a year, almost 12, and no 12 win team ever missed the playoffs, and a lot of champions finished the season at 12-4 or 11-5.

I know this example is very simple, and has a lot of flaws, but I used it to demonstrate just what it means to bump up a level or two in a stat or skill. This is how I look at it. I do not try to just say what each level of a stat means in real life, or how the differences are spread out in the world. Instead, I look at what it means to give some one a certain stat, and if I were to put that person into a real life situation, how would it work out. To give some one a 13 IQ means they are winning a lot of contests of wits, a lot more than any one else. Any time the get equal training in something for a skill, they are way out performing any one else (that is to say, they take a lot of science classes in college, they are easily noticed by the others as being way better, no matter if it is biology, chemistry or physics). This person would stand out, in GURPS terms as far as success rolls are concerned.

Again, to go along with what Kromm has stated, no definate way to say in GURPS this means that in real life. Just says that in GURPS, this guy is way out performing that "average" guy.

[cmdicely]

Originally Posted by jeff_wilson

In fact, I would go so far as say that the lack of accuracy is a feature, not a bug, even if it is a feature that not everyone wants in every product. The low-resolution SPACESHIPS series for example is gloriously unencumbered by three-digit accuracy, and this made coming up with new rule systems so much easier;

I think you are confusing precision with accuracy here: the lack of three-digit precision in SPACESHIPS makes coming up with new rule systems easier, since inaccuracies in those rules systems that are smaller than the precision of the SPACESHIPS system are invisible.

[Ze'Manel Cunha]

Originally Posted by aesir23

Even though it is not official doctrine, some guidelines around how common certain scores are in your world can be very helpful for players trying to determine their characters attributes.

Outside of ST (which deviates much more from person to person), I use something like:

11 = 1 person in your clique or immediate family is this smart/agile/fit. (Or 1/10)

12 = 1 person you know well is this smart/agile/fit. (or 1/100)

13 = 1 person you've met is this smart/agile/fit. (or 1/1,000)

14 = 1 person you've heard about is this smart/agile/fit. (or 1/1,000,000)

It all depends on how you feel about stat normalization. In a high point total pulp game, all of these go out the window in favor of larger than life heroes who are better at everything.

Wow, that's radical stat normalization.

I tend to prefer setting minimums:
No athlete with a DX below 14 is worthy of a professional contract.
No professor with an IQ below 12 is worthy of a teaching job.
etc.

[jeff_wilson]

Originally Posted by cmdicely

I think you are confusing precision with accuracy here: the lack of three-digit precision in SPACESHIPS makes coming up with new rule systems easier, since inaccuracies in those rules systems that are smaller than the precision of the SPACESHIPS system are invisible.

That would not be correct, because SPACESHIPS does have 3-digit precision in various places:

"The first stage burns out and falls away after accelerating
the rocket to a delta-V of 3.12 mps; the winged second stage’s
engine then takes over, adding 2.56 mps for a total of 5.68 mps,
enough to reach low orbit."

However, due to scaling, the fanciful nature of many of the included values, and the usual compounding of error in chains of calculations, the overall accuracy is less.

[jeff_wilson]

Originally Posted by Kromm

You're making the huge and incorrect assumption that we're using "human" and "average" rigorously to refer to the real-world human population and the mathematical concept, respectively. We aren't!

I'm not either. I'm using "human" and "average human" as labels for the same abstracted entities the game addresses. I explicitly said so here:

Originally Posted by jeff_wilson

...the data set is the gameble abstraction given in the rule books. My conclusion that +3 attribute levels approximates a standard deviation is a characterization of that data set, and I am as dubious as anyone as to how much this says about the real world...

I suppose that since my writing is appearing on the forums and not in the game book, even though it is the part of the forums devoted to that game in the game book, that I should write "GURPS humans" and "GURPS average humans" to be more clear when this issues comes around.

Originally Posted by Kromm

We're using "human" as code for "adventurers with the 0-point human racial template" and "average" to mean "the value everybody gets for free."

Well okay then, but that *is* departing from the commonly understood meaning of "average," and makes "A score of 10 in any attribute is free and represents the human average" terribly, terribly circular.

[PK]

Originally Posted by aesir23

Outside of ST (which deviates much more from person to person), I use something like:

11 = 1 person in your clique or immediate family is this smart/agile/fit. (Or 1/10)

12 = 1 person you know well is this smart/agile/fit. (or 1/100)

13 = 1 person you've met is this smart/agile/fit. (or 1/1,000)

14 = 1 person you've heard about is this smart/agile/fit. (or 1/1,000,000)

That's much too restrictive IMO, though I like your way of describing it. After all, GURPS allows for attributes up to 20, and if you're continuing to multiply by 1,000 each time, it means only one person (at most!) throughout all of human existence has ever had a 16 in something!

I think I'd use something more like this, going with powers of 2 instead of 10 just because I hang with geeks:

11 = 1 person in your close circle is this smart/agile/fit (1/8).

12 = 1 person you know well is this smart/agile/fit (1/64).

13 = 1 person you know or used to know is this smart/agile/fit (1/512).

and so on. It ends up putting 20 at 1/1.074B, or about 6-7 people alive on Earth today, which seems about right for what GURPS considers a believable human maximum.

[Gizensha]

My take on 'average' was simply 'The typical protagonist in a story' and for the 8-12 stuff 'It is unremarkable for a protagonist in a story to be...' (So it's at DX13 that 'agile' would become a Big Adjective of the person)