An Argument against Stat Normalization

[AlexanderHowl]

My background is humanities, social sciences, and physical sciences, though my fiancee is the physical sciences expert between us. Anything below 2 SD is meaningless when it comes to determining significance in the social sciences (technically, 1.96 SD is the threshold, but I am rounding up). Remember though, unless SD is specified as one-tailed, the assumption is a two-tailed distribution (meaning on both sides of the mean), so a 2 SD is either the top 2.5% or bottom 2.5% (in the case of attributes, that would be 12+ or 8-). I define attributes from 9-11 within the realm of average performance, aperson with IQ 9 will be a little slow while a person with IQ 11 will be a little fast, but the difference is minimal when you add in skills and talents.

As for the lack of importance of skills, that is the result of the game design. If every level in a skills above the relevant attribute also reduced total penalties by one, I do not think anyone would complain about the relevance of skills. A person with Shortsword at DX+10 would reduce total penalties by 10. If every level below attribute also increase penalties by one, up to twice the total penalties of the roll, I do not think that people would complain about defaults, as defaults would only matter in controlled circumstances.

[pgb]

Originally Posted by AlexanderHowl

My background is humanities, social sciences, and physical sciences, though my fiancee is the physical sciences expert between us. Anything below 2 SD is meaningless when it comes to determining significance in the social sciences (technically, 1.96 SD is the threshold, but I am rounding up).

No, not really. I think you are conflating a number of different ideas there. A more precise statement is some thing like "a test statistic less than 2 standard errors away from its null value is no evidence against the null hypothesis". The standard error is the standard deviation of the estimator, not of the population. An approach like this certainly doesn't mean that differences between individuals of less than 2 population SDs are not important - "significance" here is a technical term anyway, not anything to do with the meaningfulness as such.

Originally Posted by AlexanderHowl

Remember though, unless SD is specified as one-tailed, the assumption is a two-tailed distribution (meaning on both sides of the mean), so a 2 SD is either the top 2.5% or bottom 2.5% (in the case of attributes, that would be 12+ or 8-). I define attributes from 9-11 within the realm of average performance, aperson with IQ 9 will be a little slow while a person with IQ 11 will be a little fast, but the difference is minimal when you add in skills and talents.

Any argument of this sort depends on the value of the SD of the population, as others have said. You can't just assert "2 SD is ... 12+ or 8-" - that's essentially a decision about the level of normalization, for the population at large, in itself.

Paul Blackwell.

[Tomsdad]

Originally Posted by Kromm

Not to mention that normal distributions tend to be associated with things found in the real world, which have thermodynamic, sociodynamic, or similar reasons to take that shape. Given that GURPS attributes are artificial constructs intended to facilitate dramatic storytelling, and dramatic storytelling in even the most familiar settings and least over-the-top genres includes a good dose of imagination and fantasy, I'd be very, very hesitant to assume that those attributes are normally distributed. I can state as one of the designers that we certainly never imagined them that way. "Attributes are normally distributed" is one of those persistent myths like "GURPS IQ = (real-world IQ test score)/10" or "1 point always equals 200 hours of study" that isn't actually among the designers' assumptions for the game.

True enough, although to be fair the 3d6 bell curve (when it applies), isn't that far off a normal distribution, it's probably why I like GURPS :-)!

Cheers

TD

[whswhs]

Originally Posted by Kromm

Not to mention that normal distributions tend to be associated with things found in the real world, which have thermodynamic, sociodynamic, or similar reasons to take that shape. Given that GURPS attributes are artificial constructs intended to facilitate dramatic storytelling, and dramatic storytelling in even the most familiar settings and least over-the-top genres includes a good dose of imagination and fantasy, I'd be very, very hesitant to assume that those attributes are normally distributed. I can state as one of the designers that we certainly never imagined them that way. "Attributes are normally distributed" is one of those persistent myths like "GURPS IQ = (real-world IQ test score)/10" or "1 point always equals 200 hours of study" that isn't actually among the designers' assumptions for the game.

The roll of 3d approximates a normal distribution with standard deviation 3. But that's a normal distribution of task outcome success chances; it has no relation to any hypothetical underlying trait. Even for traits that are approximately normally distributed in the real world, there is no defined tradeoff of +1 standard deviation equals N points of a GURPS trait. It would be perfectly fair to represent +1 standard deviation as 5 points, or 0.5; either is equally arbitrary—and so is a more "moderate" 1 or 2 points.

[Kromm]

Originally Posted by whswhs

The roll of 3d approximates a normal distribution with standard deviation 3. But that's a normal distribution of task outcome success chances; it has no relation to any hypothetical underlying trait.

Precisely so – thank you!

—

To go off on this tangent:

A character's attributes aren't rolled randomly in GURPS, as they were lo those many years ago in, say, D&D or AD&D First Edition. They are bought. Thus, while the 3d curve looks pretty, it is a distribution of outcomes. Assuming traits are perforce distributed the same way would be an error, and is indeed a common error arising in these sorts of discussions.

As a game designer, I could decree that because my game is about Big Damn Heroes, all PCs start at 15 and can't have lower than 10 (or higher than 20), but still use "3d6, roll low" to resolve tasks. Or I could assert that since the cost of each +1 is the same, each +1 corresponds to an equal-sized slice of the population, with as many people between 10 and 11 as between 19 and 20. Or lots of things. Once attributes are bought on a linear scale, talk of normal distributions of said scores goes right out the window and into the sea with an anvil tied to it.

I personally favor a model where 8-12 are all about equally probable attribute scores among humans, nobody much has a 7 or less, and scores of 13+ are common among PCs who live in Big Damn Hero land, but aren't meant to be realistic . . . and are roughly equally common right out until you hit a wall imposed by the campaign's power level. That's one abnormal distribution!

[SilvercatMoonpaw]

Originally Posted by AlexanderHowl

If every level in a skills above the relevant attribute also reduced total penalties by one, I do not think anyone would complain about the relevance of skills. A person with Shortsword at DX+10 would reduce total penalties by 10. If every level below attribute also increase penalties by one, up to twice the total penalties of the roll, I do not think that people would complain about defaults, as defaults would only matter in controlled circumstances.

What penalties are you talking about? (<-- Does not have a complete working model of GURPS yet.)

[Brandy]

I'm one of just a handful of the Stat Normalizers from the earliest days of 4e, so I suppose it falls to me to play Devil's advocate here. :)

(All of this comes with a "this is how I see it/ how I did it" implied -- some of the other posters who were outspoken back in the day did see things a little differently.)

First, Stat Normalizing wasn't about telling players how to build their characters or putting hard caps on attributes (which isn't to say that's always a bad thing), but it was about helping them understand how their characters would fit into the game world.

If a player wants their character to be the "Pro from Dover" for DX-related things, I want to be able to tell them, within the context of the game world, just how "special" DX scores from 12-17 are. I also feel that I need to hold to that as the game goes on, even as power levels rise.

The other thing that I did with the idea of using normal distributions to generate traits (like primary attributes and some others) was to develop large groups of NPCs quickly. One quick example: the characters had become the leaders of a group of about 200 soldiers, armed with swords and early firearms. One of the players wanted his character to lead a group of sharpshooters, taking the 12 best marksmen in the group to lead as a specialist company. There are lots of valid approaches here ranging from 12 identical quick-and-dirty designed NPCs to taking the time to do full write-ups on all 12.

For me, having thought about stat normalization, the ages of the soldiers in this group, and some other factors, let me use a spreadsheet to quickly identify characteristics (not just attributes but things like age, appearance, gender, social class, etc.) for a dozen NPCs within their soldier group. This gave me a really great starting point for making all 12 of these characters distinct and interesting, all while holding to my existing assumptions about those factors within the game world.

That's been the real value to me -- setting out some simple guidelines and then letting the individual distinctions emerge randomly from the simple rules that I've put in place. Other, more naturally creative people, would probably not have to do it that way but for me letting a random element take the first design steps for me allowed me to interpret the results creatively and have some really interesting characters come out of the process -- very different than if I'd started from nothing, just making things up.

Last point - while I've used a normal distribution as the foundation for values of DX, IQ, and HT, the distribution among the population is not normal. In creating large groups of NPCs, I think about the factors that would cause those attributes to develop -- access to education or experiences for IQ, a lifestyle with different kinds of physical demands for DX, access to good nutrition or medical care for HT just as examples. By identifying things that can make the attributes go up, and applying those factors to groups, you end up with a distribution that's skew right rather than symmetric, and I think that's desirable.

[AlexanderHowl]

Originally Posted by SilvercatMoonpaw

What penalties are you talking about? (<-- Does not have a complete working model of GURPS yet.)

Pain, visibility, targeting, distance, etc. There are also penalties for equipment quality, position, and stability. For example, a character who suffered Severe Pain (-6), in near darkness (-9), aiming at the vitals of a target (-3), at 100 yards away (-10), with a damaged rifle without sights or scope (-3), hanging upside down (-4), from a swaying branch (-2), would suffer a cumulative -37 to skill to hit their target.

A character with DX 12 and Guns (Rifle) DX+15 [52]-27 would not have even a chance under the standard rules, as their skill would be -10. With the rules that I suggested though, they would have an effective skill of '5', as their experience would reduce the penalty from -37 to -22, reducing their skill from 27 to 5.

[Black Leviathan]

You're the GM. We don't tend to get to have a lot of characters with stats of 14+ or skills at 20+. However, If you see statistics above 14 as a problem, create a solution. However rather than monkeying with point values. If you think having a statistic above 14 is unusual, tag it to an Unusual Background.

[whswhs]

Originally Posted by AlexanderHowl

Pain, visibility, targeting, distance, etc. There are also penalties for equipment quality, position, and stability. For example, a character who suffered Severe Pain (-6), in near darkness (-9), aiming at the vitals of a target (-3), at 100 yards away (-10), with a damaged rifle without sights or scope (-3), hanging upside down (-4), from a swaying branch (-2), would suffer a cumulative -37 to skill to hit their target.

Yes, and you know, I don't have a problem with their not being able to do that. I can't imagine any campaign I would run, not even high-end supers, where I would feel that "you can't do that" is an inappropriate answer.