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Topic Subject: Calculating Your Acquisition of Resources
posted 03 December 2011 06:15 PM EDT (US)   
While much of the information found on this website is obsolete because it derives from earlier versions of the game (patches prior to version 1.03), some of it is simply incorrect, regardless of the version to which it is applied. For example, numerous inaccuracies can be found in the section of this website titled How it Works, which addresses the acquisition of a particular resource over a given period of time. The purpose of this post is to update and correct the information presented in this section wherever appropriate. Because this is a work in progress, this post is subject to revision.

Unit Resource Gathering Rates

As originally posted in the guide titled How it Works: Gathering Rates:
One of the key pieces of data used for optimizing your AoM economy, happens to be the resource gathering rates of villagers.
This is true, as the validity of every principle that follows is entirely dependent upon the accuracy of these statistics. The equation used to describe the rate at which a given unit gathers a particular resource is given below.

x2 - x1
r = 
t2 - t1

Where:

r=Unit's gathering rate for a particular resource
t1=Initial time
t2=Terminal time
x1=Initial amount of a particular resource
x2=Terminal amount of a particular resource

While the equation used to calculate the rate at which a given unit gathers a particular resource is mathematically correct, the numerical accuracy of these statistics is somewhat questionable because at least four of the variables included in this equation require experimental observation to obtain. In the guide, the author lists the gathering rates for various units in the game on a table, which is given below.
Villager Resource Gathering
Unit TypeWoodGoldHerdWildFarm


Greek Villager1.08.91.73.73 .69
Egypt Laborer.98.82.65.65.63
Empowered Egypt Laborer1.18.98.78.78.76
Norse Gatherer1.08.90.73.73 .69
Norse Dwarf.801.09.58.58.53
Thor Dwarf1.001.09.73.73.66
Atlantean Citizen2.562.131.641.851.52
 
Unfortunately, the author has neglected to mention the source of these statistics. I am curious of how these statistics were obtained because, as previously mentioned, the validity of every principle that follows is entirely dependent upon their accuracy. To discern the accuracy of these statistics, I will conduct a number of experiments in the editor and then post my results within the near future.

Period of Unit's Gathering Cycle

In the guide titled How it Works: Gathering Rates, the author states:
With this data, you will be able to calculate how many seconds it takes to acquire a certain amount of resources. For example, to gather for 50 seconds, you take the above unit you wish to deal with, and multiply that number by the amount of seconds. It shall give you the amount of resources.
According to the author, this means that, if you want to know how much gold a Laborer will gather in 50 seconds, you merely refer to the chart above and multiply the rate at which a Laborer gathers gold (which, according to the author, is 0.82 gold per second) by the period of time over which it will be gathered (50 seconds), as illustrated below.

0.82 gold50 seconds
x = 
 x 
1 second1

0.82 gold50
x = 
 x 
11

x = 0.82 gold x 50

x = 41 gold

This is incorrect. This information alone does not tell you how many seconds it takes to acquire a certain amount of any particular resource; it only tells you the time it takes for a particular unit to gather a certain amount of it, which is not the same thing. Why? Because, most units can only carry a certain amount of any particular resource at one time. Laborers, for example, have a default maximum carrying capacity of 10 gold, which means that once this amount is reached, they must return to the nearest drop site and drop off what gold they have before they can commence gathering it once more. As a result, your true acquisition of any particular resource is primarily dependent upon the time taken to complete one of these cycles, as the resources a unit carries are useless until they are deposited at a drop site because, until then, they cannot be spent. The equation used to calculate the period of a unit's gathering cycle is given below.

c + c (mc100%)2d
P = 
 + 
r + r (mr100%)v + v (mv100%)

It can be simplified to:

c + c (mc100%)2d
P = 
 + 
r + r (mr100%)v + v (mv100%)

c1 + (c1 (mc100%))2d
P = 
 + 
r1 + (r1 (mr100%))v1 + (v1 (mv100%))

c1 + cmc100%2d
P = 
 + 
r1 + rmr100%v1 + vmv100%

(100%100% (c1)) + (11 (cmc100%))2d
P = 
 + 
(100%100% (r1)) + (11 (rmr100%))(100%100% (v1)) + (11 (vmv100%))

100%c100% + cmc100%2d
P = 
 + 
100%r100% + rmr100%100%v100% + vmv100%

(100%c + cmc)100%2d
P = 
 + 
(100%r + rmr)100%(100%v + vmv)100%

100%c + cmc100%2d100%
P = 
 x 

 + 
 x 
100%100%r + rmr1100%v + vmv

100%c + cmc12d100%
P = 
 x 

 + 
 x 
1100%r + rmr1100%v + vmv

100%c + cmc200%d
P = 
 + 
100%r + rmr100%v + vmv

c (100% + mc)200%d
P = 
 + 
r (100% + mr)v (100% + mv)

Where:

c=Unit's maximum carrying capacity for a particular resource
d=Distance between resource and nearest dropsite
mc=Modifier for unit's maximum carrying capacity for a particular resource
mr=Modifier for unit's gathering rate for a particular resource
mv=Modifier for unit's velocity
p=Period of unit's gathering cycle
r=Unit's gathering rate for a particular resource
v=Unit's velocity

Assuming ideal conditions (a drop site right next to the Laborers currently mining), the only time between each deposit of gold is the time taken to reach the maximum carrying capacity for it, as demonstrated below.

10 gold (100% + 0%)200% (0 meters)
P = 
 + 
0.82 gold/second (100% + 0%)3.80 meters/second (100% + 0%)

10 gold (100%)200% (0 meters)
P = 
 + 
0.82 gold/second (100%)3.80 meters/second (100%)

1,000% gold0% meters
P = 
 + 
82% gold/second380% meters/second

1,000% gold1 second0% meters1 second
P = 
 x 

 + 
 x 
182% gold1380% meters

1,0001 second01 second
P = 
 x 

 + 
 x 
1821380

1,000 seconds0 seconds
P = 
 + 
82380

P = 12.20 seconds + 0 seconds

P = 12.20 seconds

As the distance between the drop site and the resource increases, so too does the period of a single gathering cycle.

The Acquisition of Resources

Thus, to calculate the amount of gold that a Laborer would gather in 50 seconds, you would divide this time by the time taken to complete on gathering cycle and then multiply the number of cycles by the amount of resources delivered each cycle (the maximum carrying capacity). The equation used to describe your acquisition of a particular resource over a given period of time is given below.

cnut
a 
(nmc)200%d
c100% Σ50% (jmc - 1)
jmc = 1

 
(nmr)(nms)
r100% Σ10% (jmr - 1)s100% Σx% (jms - 1)
jmr = 1jms = 1

Where:

a=Acquisition of a particular resource
c=Unit's maximum carrying capacity for a particular resource
d=Distance between resource and nearest dropsite
jmc=Term of modifier in the sequence of modifiers for unit's maximum carrying capacity for a particular resource
jmr=Term of modifier in the sequence of modifiers for unit's gathering rate for a particular resource
jms=Term of modifier in the sequence of modifiers for unit's speed
nmc=Number of modifiers for unit's maximum carrying capacity for a particular resource
nmr=Number of modifiers for unit's gathering rate for a particular resource
nms=Number of modifiers for unit's speed
nu=Number of units gathering a particular resource
r=Unit's gathering rate for a particular resource
s=Unit's speed
t=Period of time over which a unit (or units) will gather a particular resource

If this explanation seems incomplete, that's because it is. I have yet to include the remaining portion of this equation, but will include it within the near future.

[This message has been edited by Sagacious (edited 12-14-2011 @ 02:40 AM).]

Replies:
posted 03 December 2011 06:18 PM EDT (US)     1 / 12  
This is quite a useful guide, and I think scenario designers would use this for triggering purposes (Working out how long it takes to cut a tree down for cinematics etc.)

Leader and Trigger Artist of Mythic Studios
I need players for my Peloponnesian War RPG (Its Semi-Historical)
Now quit being a bitch and quote me in your signature like Yeebaagooon used to. ~Out Reach
posted 03 December 2011 06:32 PM EDT (US)     2 / 12  
Thank you; as I said in the original post, this is not a complete list of all of the equations involved in calculating your acquisition of a particular recourse over a given period of time. I am short on time, and as a result, will complete the original post within the near future.

[This message has been edited by Sagacious (edited 12-13-2011 @ 05:20 PM).]

posted 03 December 2011 07:23 PM EDT (US)     3 / 12  
Wow, that's so amazing... I like your math equations


( σяυɘ ϙυє )﴿

ʸᵒᵘᵗᵘᵇᵉ ˡˡʳʸ
posted 04 December 2011 03:31 PM EDT (US)     4 / 12  
Thank you; also, note that I have updated the original post.

[This message has been edited by Sagacious (edited 12-13-2011 @ 05:21 PM).]

posted 04 December 2011 04:29 PM EDT (US)     5 / 12  
dude, (Sagacious) how the can you understand this?

[This message has been edited by The AoM Expert (edited 12-04-2011 @ 11:44 PM).]

posted 04 December 2011 05:46 PM EDT (US)     6 / 12  
*Tries to read AND understand*



...



*Brain starts to bleed*

Sometimes I like to take screenshots. But only sometimes.
posted 04 December 2011 06:58 PM EDT (US)     7 / 12  
Expert, covering your swears and avoiding the swear filter is a CoC offence... Please express.your opinion without them.

Leader and Trigger Artist of Mythic Studios
I need players for my Peloponnesian War RPG (Its Semi-Historical)
Now quit being a bitch and quote me in your signature like Yeebaagooon used to. ~Out Reach
posted 04 December 2011 10:37 PM EDT (US)     8 / 12  
AoM Expert > Most

"All we have to decide is what to do with the time that is given to us"

Gandalf - JRR Tolkein. The Fellowship of the Ring
posted 04 December 2011 11:43 PM EDT (US)     9 / 12  
Oh sorry, forgot about that

posted 05 December 2011 04:26 AM EDT (US)     10 / 12  
Thanks for editing it out.

PS: how many more calculations are to be done?

Leader and Trigger Artist of Mythic Studios
I need players for my Peloponnesian War RPG (Its Semi-Historical)
Now quit being a bitch and quote me in your signature like Yeebaagooon used to. ~Out Reach
posted 05 December 2011 08:08 AM EDT (US)     11 / 12  
AoM Expert > Most
Yeah.... No.

Sometimes I like to take screenshots. But only sometimes.
posted 05 December 2011 06:27 PM EDT (US)     12 / 12  
(Tries to read)

AAH! CALCULUS!

"Preparation is not prevention. Just because you know what's coming does not mean you can stop it."
--Me

Something to remember: always know where you're going, but never forget where you came from.

The Age of Chivalry is upon us! Visit the only wiki devoted exclusively to Aoc:H by clicking on the preceding link. Oh yeah, and it works with the HD edition, too--just make sure to get this first.
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