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I am looking for the math behind carrying capacity.

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I am making a character sheet however I am trying to put in an automatic calculation for carrying capacity without needing to rely on an array. Does anyone know the math behind the carrying capacity table?

http://paizo.com/pathfinderRPG/prd/additionalRules.html
Scarab Sages
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It is an exponential scale. The formula can be dervied from two bits of information: the growth is 4x per 10 points, and Strength 10 has a maximum load of 100 lbs. The formula should be...

Max Encumbrance = 100 x 4^(0.1 x Strength - 10)

Medium and heavy encumbrance thresholds are 1/3 and 2/3 of the maximum encumbrance, respectively. Note that very low Strengths have a linear pattern. Up to 10 strength, the maximum encumbrance is 10x strength score. This actually lowers the maximum encumbrance significantly for strength scores below 5.

I don't think that is it either, as the higher your str goes the more it gets off, for example: 100 x 4^(0.1x(29-10))= 1392.8809 on the site the max encumbrance for 29 str is 1,400 lbs. while close it isn't exactly what the devs made.

It is close enough to use, though I do wonder if any algorithm was used to make the carrying capacity scores or not.
Liberty's Edge

I've been using Shoelessinsight's Google Doc sheets, and the forumula he's using is

Quote:
If(Strength < 10, Strength * 10 * CarrySizeMod, Round(20 * (2^0.2)^(Strength - 10) * CarrySizeMod, 0) * 5)

Where CarrySizeMod = 1 for a medium bipedal creature.

But, after checking the outputs against the book, it seems to be another close enough formula.
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I think they used a formula similar to Horselord's, and then made the numbers look nice.
Scarab Sages
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Vod Canockers wrote:
I think they used a formula similar to Horselord's, and then made the numbers look nice.

I think you're right. The numbers are rounded off.

Edit: Can't believe I forgot to put brackets around (Strength -10) in my formula. It should be:

Maximum Encumbrance = 100 x 4^(0.1 x (Strength - 10)) lbs.

If Strength is less than or equal to 10: Maximum Encumbrance = Strength x 10
Liberty's Edge
Horselord wrote:
Vod Canockers wrote:
I think they used a formula similar to Horselord's, and then made the numbers look nice.

I think you're right. The numbers are rounded off.

Edit: Can't believe I forgot to put brackets around (Strength -10) in my formula. It should be:

Maximum Encumbrance = 100 x 4^(0.1 x (Strength - 10)) lbs.

If Strength is less than or equal to 10: Maximum Encumbrance = Strength x 10

Unfortunately, they don't round to the same degree every time. I made a few rounding formulas that work right over small intervals, but nothing that can cover the whole range.

Horselord wrote:
Vod Canockers wrote:
I think they used a formula similar to Horselord's, and then made the numbers look nice.

I think you're right. The numbers are rounded off.

Edit: Can't believe I forgot to put brackets around (Strength -10) in my formula. It should be:

Maximum Encumbrance = 100 x 4^(0.1 x (Strength - 10)) lbs.

If Strength is less than or equal to 10: Maximum Encumbrance = Strength x 10

I was wondering about that...

And the numbers aren't really rounded off, but made to look nice, although why 1040 and not 1050 is beyond me.
Scarab Sages

I suppose the only way to make a formula that is exact is to input a list instead. Not very satisfying...
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Idward Evanhand wrote:

I am making a character sheet however I am trying to put in an automatic calculation for carrying capacity without needing to rely on an array. Does anyone know the math behind the carrying capacity table?

http://paizo.com/pathfinderRPG/prd/additionalRules.html

Here you go:

Formulas are:

  • A1: <strength value>
  • E1: =IF(A1<10,10*A1,CHOOSE(1+A1-10*INT(A1/10),25,28.75,32.5,37.5,43.75,50,57 .5,65,75,87.5)*POWER(4,INT(A1/10)))

Breaking this down, is:


  • Test for low strength
  • <10, use 10*A1
  • else use base lookup and multiply by series
  • base = 1+A1-10*INT(A1/10)
  • base lookup = CHOOSE(base,25,28.75,32.5,37.5,43.75,50,57.5,65,75,87.5)
  • series = POWER(4,INT(A1/10))

Tested for all strength values in the table and it generates the exact value for max carry.

As stated earlier, the other numbers are 1/3 and 2/3 of max.

If you add the following formulas, you can recreate the table exactly:


  • B1: =INT(E1/3)&" lbs. or less"
  • C1: =INT(E1/3)+1&"-"&INT(2*E1/3)&" lbs."
  • D1: =INT(2*E1/3)+1&"-"&E1&" lbs."

/cevah
Cevah wrote:
Idward Evanhand wrote:

I am making a character sheet however I am trying to put in an automatic calculation for carrying capacity without needing to rely on an array. Does anyone know the math behind the carrying capacity table?

http://paizo.com/pathfinderRPG/prd/additionalRules.html

Here you go:

Formulas are:

  • A1: <strength value>
  • E1: =IF(A1<10,10*A1,CHOOSE(1+A1-10*INT(A1/10),25,28.75,32.5,37.5,43.75,50,57 .5,65,75,87.5)*POWER(4,INT(A1/10)))

Breaking this down, is:


  • Test for low strength
  • <10, use 10*A1
  • else use base lookup and multiply by series
  • base = 1+A1-10*INT(A1/10)
  • base lookup = CHOOSE(base,25,28.75,32.5,37.5,43.75,50,57.5,65,75,87.5)
  • series = POWER(4,INT(A1/10))

Tested for all strength values in the table and it generates the exact value for max carry.

As stated earlier, the other numbers are 1/3 and 2/3 of max.

If you add the following formulas, you can recreate the table exactly:


  • B1: =INT(E1/3)&" lbs. or less"
  • C1: =INT(E1/3)+1&"-"&INT(2*E1/3)&" lbs."
  • D1: =INT(2*E1/3)+1&"-"&E1&" lbs."

/cevah

Thank you that is great! Also Horselord thank you for your help as well.

Here's an attempt.

IF( STR < 10 ; STR*10 ; expformula )

expformula = QUOTIENT( 100*POWER(4;0,1*( STR -10)) + 0,2 * MULTIP ; MULTIP ) * MULTIP

MULTIP = POWER(2;QUOTIENT((E32-10);5))*5

This starts from Vod Canockers comment which supposes that Horselords formula comes close, but the numbers need to be made look nice. I've just come up with a way to make them look nice based on the MULTIP variable, which increases also with a power law to reflect the roundoff magnitude, which starts at 5, then 10, then 20, then 40. This also conveniently explains why 1040 and not 1050. It's the power of 2.

All in one line:

expformula = QUOTIENT( 100*POWER(4;0,1*(E32-10)) + 0,5 * POWER(2;QUOTIENT((E32-10);5))*5 ; POWER(2;QUOTIENT((E32-10);5))*5) * POWER(2;QUOTIENT((E32-10);5))*5

Happy encumbrance everyone!

Not sure how many folks need this five years later, but okay.
nib_ wrote:
Here's an attempt.

I think you missed my entry. It even said:

cevah wrote:
you can recreate the table exactly

:-)

/cevah

math tests have no expiration date... lol... this is really about DnD3.0 model or earlier...

If you really must, I find more elegant

If(Str <= 10) MaxCarryingCapacity = 10*Str
If(Str > 10) MaxCarryingCapacity = 5/4 * 2^Floor(Str/5)* Round[20 * 2^(Mod(Str,5)/5)]

which gives the right answer without resorting to a lookup.
Glendwyr wrote:

If you really must, I find more elegant

If(Str <= 10) MaxCarryingCapacity = 10*Str
If(Str > 10) MaxCarryingCapacity = 5/4 * 2^Floor(Str/5)* Round[20 * 2^(Mod(Str,5)/5)]

which gives the right answer without resorting to a lookup.

Nice. As a formula, it looks like:

E1=IF(A1<=10,10*A1,5/4*2^FLOOR(A1/5,1)*ROUND(20*2^(MOD(A1,5)/5),0))

/cevah
Grand Lodge

Thanks for the excellent spreadsheat math, chappies!

And, excuse the necro, but here is a handy spreadsheet that may help:
Encumbrance Tables for Bipeds and Quadrupeds
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