Monday, 10 January 2011

An ability score of 3 is unplayable (Argument 2a)

[Drum roll]            More Statistics and the Strength ability score

So let’s recap for a moment where we are with this topic.

Argument 1 – Using the ability score of intelligence as presented in the rules I argued that an Intelligence Score of 3 (was one step more intelligent than a dog – Intelligence 2). Additionally I argued that EGG strongly implied that your IQ divided by 10 was equal to your intelligence score. Therefore an Intelligence Score of 3 = IQ 30, which is severely mentally handicapped. 
Argument 1a – I supported Argument 1 by exploring the spell Feeblemind, which lowers a spell casters intelligence score (AD&D Moronic child, Intelligence score 5-7; B/X & Mentzer idiot, Intelligence score 2), which Mentzer describes as ‘helpless’.
Argument 2 – Comparing bell curves to a normal distribution (as is often done with the Intelligence score) and drawing on an excellent external post by Daniel Collins, I argued that applying a normal distribution to a 3-18 ability score is poor statistics and distorts ability scores at the extremes. If used on the Intelligence score, it makes clever people regard themselves as geniuses. If such poor statistics were applied to low Intelligence scores than an Intelligence score of 3 would be even worse than it is usually considered.       

My conclusion to date:
Reroll, readd, redo - An ability score of 3 is unplayable

Brains ready… here’s some more statistics! If you hold out it gets more interesting further below when I get to strength.

Disclaimer: Please I’m not a statistician, though I have taught statistics. To a statistician everything I say is likely to be over-simplified and not 100% true, but I think my general thrust is correct.

I wonder what Delta thinks?

Let’s look at how data can be categorized.

Data Type
Data is in a category, the category has no rank, in that no category is better than another
D&D class or race
D&D alignment
Data is in categories, sometimes has a number or letter and the categories/number/letter have an order or a rank. However the gap between each rank or number is not equal (or what each rank represents is not the same step between each rank).
1st, 2nd and 3rd in a race (1st is not twice as good or fast as 2nd)
IQ (see below)
D&D Treasure Tables (Category A is not twice as good as category B, sort of true but the order is chaotic)
D&D spell levels (a level 3 spell is not clearly three times as dangerous as a level 1 spell, you know it’s better but you can’t know by how much)
D&D level (since a different XP is required for each level, level 4 is not four times better than level 1. We know it is better but can’t say by how much)
D&D Ability scores (see below)
Numerical (Discrete / Interval)
Data is a number, the gap (interval) between each number is the same, but there is no zero (without a zero one cannot say that one number is twice or half another number)
Temperature in Fahrenheit or Celsius (50 F is not half of 100 F – it’s not trust me; were we talking in Kelvin which has an absolute zero minus 273Celsius, than 100K is twice 50K)
D&D Armor class (an AC of 2 is not twice as hard to hit as AC 4, but each step between AC 2,3,4 is equal on the monster ‘to hit’ chart anyway)

Continuous (Ratio)
Data is a number, the gap between each number is the same, and there is a zero (so one can easily say something is half of something else - ratio). Often is normally distributed in the population for human and natural biometric values.
Height, weight (all can be zero)
D&D hit points, encumbrance, movement, experience points

Right got that?

Let’s pick up two ordinal values: IQ and ability scores.

Interestingly and perhaps surprisingly IQ is ordinal and not numerical or continuous, yet often it is treated, even in psychosocial literature, as being a normally distributed continuous variable. This is because the IQ test is a man made test that ranks people into categories depending on their result (ordinal). In the same way if someone got twice as much in an exam as you it is wrong to say they are twice as smart, they may be but the test doesn’t tell you that. IQ is not a measurement in the true sense of the word and an IQ of 120 is not twice as smart as 60, it is likely to be much more in fact. Even the gap in intelligence between 100 to 120 is not necessarily the same as the gap between 80 and 100 (so not numerical).
For further information or explanation see

Ability scores
When one looks at the below B/X table
Ability Score

The table looks so symmetrical it must be numerical.
But the gap or effect between 16 and 12 (+2) is not the same as 12 and 8 (-1). There is order 16 better than 12 better than 8, but one can’t say that 16 is twice as strong, smart, good looking as 8. The data is therefore ordinal.

This is even more apparent if one looks at retainers for Charisma (3 – 1 retainer, 18 - 7 retainers), Intelligence (3 – trouble speaking to 18 - +3 languages), XP adjustments (3 – 20%, 18 - +10%).

So what’s my point?

I think people often play D&D as if 3 is only half as bad as 6 or 3 times worse than 9. That is a 3 ain’t that bad. For intelligence score I think I have convincingly shown in my previous postings why this is not the case - 3 is awful, 3 is unplayable. But the other ability scores are more problematic. The way the ability scores are in the table above -3 to hit and damage is a disadvantage but not unplayable. Let’s think carefully here, it’s only a minus 15% chance to hit! You could live with that.

Or could you?

The ability score of Strength

In my first posting on this topic I said, "Intelligence is the only ability score that is related in the rules to a real life comparator." Spawn of Endra pointed out something I had overlooked in the Players Handbook (page 9). Strength of 3 = the ability to military press a maximum of 30 pounds, 18 strength, 180 pounds. (From the above that would make it a continuous variable, since at zero strength one could lift zero pounds and 18 strength is six times more than 3 and can also lift six times as much)

So like intelligence EGG identifies a real life comparator for strength that is divisible by 10 into an ability score. What a shame there is nothing for wisdom, dexterity, constitution (breath holding, fitness, colds per year perhaps) and charisma.

I must say researching strength has been very interesting if a little frustrating.  Interesting because if you thought we were an obsessive bunch of bloggers or had one up man ship dominating our hobby, you should see the body builder forums and blogs. Frustrating because what I really wanted to find was a normative table for the military press – I never found one.

The dreaded military press was properly performed standing, with legs unbent, and the weight lifted above ones head. It was military because it was used to test strength to get into the military and was once considered the preeminent test of strength. So why can’t I find a table!

Let’s look at maximum 30 pounds, strength 3.
This is very weak.
The bar for weightlifting (Olympic standard) for men is 44 pounds, women 33 pounds.

So at strength 3 one cannot even lift over your head the bar, without any weights.

I would love to know what a child could do and how this compares. I don’t have any weights at home (hey I’m a nerd, hence this blog). I tried getting my four year old son and six year old daughter to lift some random objects over their head (carefully!). They had trouble holding the objects more than the weight so the experiment broke down. My daughter can lift her uncle who is about 65kg momentarily off the ground (feet together arms around waist). I’m 75kg and she can’t lift me.  So I wonder if she could manage 30 pounds weight over her head.

Now the military press is notoriously harder than other weight lifting, so maybe she couldn’t. Let’s assume for the sake of this argument she could, or maybe an eight year old could. Anyone got gym gear, a child and a tolerant wife to test this theory? Are we saying that an eight year old who we are assigning a strength of 3, would this eight year old in combat with a monster be only -15% to hit compared to the average man, and do a minimum of 1 damage, which in two hits would start killing normal men and women? I find this hard to believe.

Now D&D doesn’t have to be realistic but it does have to be internally consistent. Let's ask it again - Can someone who can only lift 30 pounds over their head really only be -15% to hit compared to the average man and do a minimum of 1 damage, which in two hits would start killing normal men?

No, I don’t think so.

I perceive there is internal illogic. The desire for symmetry in B/X ability scores is leading to some strange conclusions. AD&D has less symmetry (18 strength +1 to hit,+2 damage; 3 strength -3 to hit, -1 damage) but does not fare much better. Can only lift 30 pounds but weight allowance for encumbrance is only -350 pounds compared to normal.

Also I don’t think EGG is correct in relating strength to real life military press.

You see with Intelligence the natural human range is 0-228 (Marilyn Vos Savant)
Einstein 160, Stephen Hawking 160, Bobby Fischer 187

I don’t care how accurate or inaccurate these numbers are, the point is that on a D&D 0-25 score system (3-18 for most of the D&D world), in encapsulates the breadth of mankind and even extremes above and below mankind, to account for gods etc.

The military press world record: the heaviest recorded military press was 535lbs ,242.67 kgs, and was set by Dj maestro.

According to EGG that’s a strength of 53, twice as strong as the strongest god.

There’s a club for the over 300 pound overhead press.

Yet a body building enthusiast confesses to lifting only 85 pounds in the military press and the responses aren’t much better.

This enthusiast 105 pounds
So hardly 100 pounds = average, if that’s all these enthusiasts can manage unless they are role players after their gym sessions.

One 13 year old says he can do 165 pounds.

Someone else says:
“A human being who has Athletic physical strength can military press the weight of the average human being or greater; roughly 175 lb (80 kg). In the real world, the vast majority of the population isn't capable of military pressing 175 pounds or more.” He then gets shot down by other commentators.

This for the strongest warrior comepetition.
Competitor 135lb Men/65lb women for this event.

I have no idea what the truth is and don't really care. But the randomness for the military press and the range seems huge, though I think the techniques aren’t clearly defined between these reported weights. So it's use as a comparator to D&D strength seems wildly implausible.

From my research I actually think grip strength is a better comparator to D&D strength. I’ll post that another day.

So bringing today’s ramble to a close.
Ability scores, as ordinal data, do not have to be symmetrical in their pluses and minuses, just ordered. Symmetry leads to confusion and the belief that 3, ain’t that bad. It is.
The rules regarding strength are confusing and inconsistent. -15% to hit with strength 3 is not consistent with the inability to lift more than 30 pounds over your head. You are likely much worse and much more debilitated as an adventurer.

Reroll, readd, redo - An ability score of 3 is unplayable


  1. I've just discovered that Daniel Collins who I quote is Delta - don't I feel stupid!

  2. Makes me feel pretty crafty, though! :)

    Good stuff between this & the other post -- I think it's pretty convincing that the deficiency of Int 3 is probably underestimated by lots of players. Int 3 probably really should be drooling-retarded. I don't mind it being in the game as perhaps the far limits of what we might consider playing, but I don't mind it being banned, either. Makes sense.

    Other comments: The Cornell distinction of interval vs. ratio data is new to me, I've never seen that before. I think you may have smooshed the concepts of "discrete vs. continuous" and (new to me) "interval vs. ratio" (and the absolute zero issue) in a way that may not be technically supported. As one example, the Normal Distribution is a continuous distribution that has coverage from negative to positive infinity, and is often used to model mechanical or targeting error.

    One other thing is AD&D DMG p. 15 expands to description of Strength lifting capacity. At Str 18 you lift 180 pounds; at Str 18/00 you lift 470 pounds (capped at twice body weight). 3E has a similar geometric understanding of Strength capacity which I don't think is bad, either.

    Hope that's helpful to think about. :)

  3. Thanks Delta. My stats knowledge is from the Biosciences. My textbook "Basic Statistics and Epidemiology: a practical guide" by Antony Stewart identifies levels (scales) of numerical data: discrete, and continuous consisting of interval and ratio. The book is titled 'basic' not that this should put off a B/X / BECMI fan, but I will happily bow to your greater stats knowledge. Glad you thought my intuitions about an ability score of 3 is correct even if my arguments aren't perfect. Thanks for commenting!