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 Post subject: Some BMI Findings
PostPosted: Mon Feb 02, 2015 11:34 am 
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Joined: Tue May 08, 2012 11:08 am
Posts: 51
BMI TESTING RESULTS

Introduction
With the recent release of a pfile in a previous thread, information was obtained to enable us to quantify the mysterious 'BMI' stat. Similar to the real Body Mass Index, a player's BMI stat was determined to be a function of height and weight, as follows:

Naked BMI = (Weight x 10) / (Height x Height)

Research was undertaken to learn more about this number and its uses.

BMI, Stockiness, and Equipped Weight
The 'Consider' command, when used on a player character or mob, gives a relative comparison of height, weight, and 'stockiness'. Consider the following four comparisons with 'a handsome stag', a mob which can be directly measured to a height of 64 inches and a weight of 120.0 lbs.

Your height is 5 feet, 4 inches, and you weigh 120.0 lbs.
You are carrying 0.0 lbs and wearing 40.9 lbs, peanuts.

con stag
Well, he is as tall as you, as heavy as you, and in general about as stocky as you.

Your height is 5 feet, 4 inches, and you weigh 120.0 lbs.
You are carrying 0.0 lbs and wearing 41.0 lbs, peanuts.

con stag
Well, he is as tall as you, as heavy as you, and in general less stocky than you.


We can see here that equipped weight influences the 'stockiness' comparison. Now let's examine inventory weight.

Your height is 5 feet, 4 inches, and you weigh 120.0 lbs.
You are carrying 50.2 lbs and wearing 40.9 lbs, very light.

con stag
Well, he is as tall as you, as heavy as you, and in general about as stocky as you.

Your height is 5 feet, 4 inches, and you weigh 120.0 lbs.
You are carrying 50.1 lbs and wearing 41.0 lbs, very light.

con stag
Well, he is as tall as you, as heavy as you, and in general less stocky than you.


Even with the addition of a substantial amount of weight to inventory, the stockiness comparison remains unaffected.

Can we be sure that 'stockiness' is related to BMI? Yes, we can. By altering the original BMI equation to include equipped weight, we obtain the following:

BMI = (Total_Weight x 10) / (Height x Height)

where Total_Weight is equal to naked weight plus equipped weight.

Now let's compute the BMI of 'a handsome stag', as well as the two BMI's of the character above, in one case wearing 40.9 lbs (call it Light_BMI) and in the other 41.0 lbs (Heavy_BMI).

Stag_BMI = (120 x 10) / (64 x 64) = 0.292969

Light_BMI = ((120 + 40.9) x 10) / (64 x 64) = 0.392822

Heavy_BMI = ((120 + 41.0) x 10) / (64 x 64) = 0.393066

Heavy_BMI - Stag_BMI = 0.100098
Light_BMI - Stag_BMI = 0.099853

We see that the 'Consider' message changes from 'about as stocky as you' to 'less stocky than you' when the difference in BMI is greater than 0.1. A similar rule is found to apply for the reverse, so we can now say the following:

IF Your_BMI - Target_BMI > 0.1 THEN "less stocky than you"
IF Your_BMI - Target_BMI < -0.1 THEN "stockier than you"

BMI difference values in between -0.1 and 0.1 will con as "about as stocky as you"


Using BMI to Determine a Mob's Height and Weight
Now that we know equipped weight influences BMI, we can use some tricks to determine the height and weight of certain types of mobs whose height and weight are either less than or greater than the minimum or maximum values obtainable by a player character.

Humanoid mobs and horses can both be equipped with items which will increase their naked BMI. Beyond leadable mobs, any humanoid mob that is not currently wielding a weapon can be made to do so by giving it one, which it will then wield, adding to its equipped weight. Similalry, horses can be equipped with various pieces of horse gear which will increase their BMI. In certain cases for these types of mob, their BMI will be of a value such that a 'stockiness' message change can be effected via weight changes. This will give two inequalities, allowing us to arrive at a solution for the two unknown variables of height and weight. Let's now consider a horse example.

Horse: a prancing palomino mare

This is a useful mob for starting with, since its height can be directly measured as 79 inches. Let's compare BMI using a character of 67 inches and 163 lbs.

Your height is 5 feet, 7 inches, and you weigh 163.0 lbs.
You are carrying 0.0 lbs and wearing 58.2 lbs, peanuts. (BMI = 0.492760)

con mare
Well, she is taller than you, heavier than you, and in general stockier than you.

Your height is 5 feet, 7 inches, and you weigh 163.0 lbs.
You are carrying 0.0 lbs and wearing 58.3 lbs, peanuts. (BMI = 0.492983)

con mare
Well, she is taller than you, heavier than you, and in general about as stocky as you.


This puts the horse's BMI somewhere between 0.592760 and 0.592983

Now let's add a bridle and shoes to the horse, adding 1.1 lbs.

Your height is 5 feet, 7 inches, and you weigh 163.0 lbs.
You are carrying 0.0 lbs and wearing 59.0 lbs, peanuts. (BMI = 0.494542)

con mare
Well, she is taller than you, heavier than you, and in general stockier than you.

Your height is 5 feet, 7 inches, and you weigh 163.0 lbs.
You are carrying 0.0 lbs and wearing 59.1 lbs, peanuts. (BMI = 0.494765)

con mare
Well, she is taller than you, heavier than you, and in general about as stocky as you.


This puts the horse's BMI (with an extra 1.1 lbs) somewhere between 0.594542 and 0.594765.

Now, since we are given inequalities rather than equations, solving for the unknown height and weight could give a number of valid values, but we are helped by the fact that a horse's stabling cost is a function of its weight, as follows:

Stable_Cost = Floor(Horse_Weight / 25)

(a full listing of horse stabling costs can be provided, if desired)

Initial verification of this can be found by directly measuring the weight of 'a playful colt' to be 150 lbs, with a stabling cost of 6 coppers.

For our purposes, we find that 'a prancing palomino mare' costs 14 coppers to rent, indicating that its weight is in the range of 350-374.9 lbs. We can use this, along with the fact that height must be a whole number of inches, to narrow down possible solutions to the two inequalities to just one:

Height = 79 inches, Weight = 370 lbs, BMI = 0.592854

We can do the same with Illianer steeds, bloodstock stallions, and Domani razors, all of which have BMI values between 0.45 and 0.593. Most other horses seem to have much higher BMI, such that no amount of weight equipped on a player character will change his BMI enough to cause a stockiness message change.

Illianer steed: Height = 100 inches, Weight = 560 lbs, BMI = 0.56
bloodstock: Height = 100 inches, Weight = 550 lbs, BMI = 0.55
Domani razor: Height = 113 inches, Weight = 575 lbs, BMI = 0.450309

Most other horses have been tested and have been found to have BMI values greater than 0.776.

Bash Testing
The Domani razor is unique among horses in that its BMI is in the correct range to enable some player characters to be both stockier and less stocky than it through addition of weight. Some initial testing has been done, using a human female of 64 inches and 130.0 lbs.

You are a 110 year old female human hunter.
Your height is 5 feet, 4 inches, and you weigh 130.0 lbs.
You are carrying 82.1 lbs and wearing 13.4 lbs, fairly light.
Your base abilities are: Str:17 Int:12 Wil:12 Dex:18 Con:18. W:16 T:16 R:14
Offensive bonus: 117, Dodging bonus: 83, Parrying bonus: 130, Defensive Bonus: 213
Your mood is: Wimpy. You will flee below: 70 Hit Points
Your armor absorbs about 5% on average.

con razor
Well, he is taller than you, heavier than you, and in general stockier than you.


You are a 110 year old female human hunter.
Your height is 5 feet, 4 inches, and you weigh 130.0 lbs.
You are carrying 0.0 lbs and wearing 95.5 lbs, fairly light.
Your base abilities are: Str:17 Int:12 Wil:12 Dex:18 Con:18. W:16 T:16 R:14
Offensive bonus: 117, Dodging bonus: 83, Parrying bonus: 130, Defensive Bonus: 213
Your mood is: Wimpy. You will flee below: 70 Hit Points
Your armor absorbs about 5% on average.

con razor
Well, he is taller than you, heavier than you, and in general less stocky than you.


These values were chosen on the assumption that the stockiness message may indicate important setpoints for bash mechanics. The first has a BMI of 0.350098, and the second has a BMI of 0.550537, compared to the razor's BMI of 0.450309. Total weight was kept constant, merely shifted from inventory to worn, thus keeping OB the same in both cases.

Bash testing was undertaken, with 2000 bash attempts at each BMI. The smaller BMI landed 428, and the larger BMI landed 425. Such a small difference is negligible, seeming to indicate that, in this particular case at least, BMI plays no appreciable role in bash.

Questions remain. Does BMI play a role only when the difference in height and weight between basher and target is much smaller? Also, given the fairly low landing rate, could other effects be masking any BMI contribution?

Future testing will first involve a heavier and higher-OB weapon vs the same target, using the same weight setpoints. If no BMI contribution is found in that case, I will try to find a mob with a height and weight closer to that of the test character, to try to determine what effect this may have.


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 Post subject: Re: Some BMI Findings
PostPosted: Mon Feb 02, 2015 11:37 am 
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Joined: Tue May 08, 2012 11:08 am
Posts: 51
It is indeed true that there are 6 possible weights for a given height, 3 each for males and females. Race actually plays no role, since trollocs/fades/dreadlords all follow the same human charts. Races and sexes do have different Height ranges, however.

For any male char, Weight = (6 x Height) - Z, where Z takes values of 254, 248, or 239.
For any female char, Weight = (5 x Height) - Z, where Z takes values of 200, 195, or 190.

With the interaction of the equations for BMI and Weight, as more weight is worn, the height at which BMI is maxed becomes lower. So when wearing 0 lbs, max BMI is found on male chars 81 inches tall and weighing 241 lbs. Wearing 50 lbs, max BMI is found on male chars 63 inches tall and weighing 139 lbs.

Up to a certain worn weight, males generally have higher BMI than females. Past a certain weight, the max possible BMI occurs on short female chars, since while a male char of the same height would have a higher BMI than a female, females can achieve shorter heights.

Some graphs to illustrate:
Naked Male BMI
Naked Female BMI
Male BMI w/ 25 lbs
Male BMI w/ 85 lbs


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