Energy Rates

[Lore]

So I just finished crafting 90k essence on an f2p world, and it occurred to me that I should probably have worked out whether it was more effective to stop and rest, instead of just walking and running.

A bit late perhaps, but why not |^_^|

 

After a little work, i realised that there was alot more potential in this, and that the ultimate goal of this should be to develop a formula, relating Agility Level and Weight to Run Energy times. With this we can do:

*

Calculation of a breakeven weight on F2P

*

Calculation of a breakeven weight given an agility level

*

Run Restore times given an agility level

*

Running Time given an agility level and weight

 

I've put everything in here, but just skip to the bottom if you're not interested in helping/understanding this.

 

Hypotheses

 

For resting to be effective, you have to cover more extra distance running with the energy you gain(as opposed to walking) than you lose during the time spent resting.

The two factors that affect your energy are

weight

and your

agility level

The two important concepts for determining efficiency are your

Energy Restore Rate

and your

Energy Depletion Rate

There are three types of energy restore:

Natural Restore

,

Resting Restore

, and

Musician Resting Restore

 

Running speed is exactly double that of walking speed

Weight has no effect on your energy restore rate

 

Weight affects your energy depletion rate, and is not a linear function.

Agility affects your energy restore rate, and should be a linear function.

 

Data

In my measurements, I can only be accurate to the nearest second, so the shorter times are going to be noticeably less accurate.

 

Energy Depletion

Time to use 100% energy (1 agility)

		1kg		64.5 seconds	2 e/s
	15kg		49 seconds	2.49 e/s
	25kg		44 seconds	2.72 e/s
	51kg		33.5 Seconds	3.43 e/s	
	140kg		31.5 Seconds	3.61 e/s
	280kg		30 seconds	3.78 e/s

 

Base Restore

Time to restore 100% Energy

Sixthplumber (1 agility)

			Natural Restore:		225 seconds			4/9 		e/s	0.45
		Rest With Musician:		26 seconds			+177/52		e/s	3.4
		Rest Without Musician:		34 Seconds			+382/153	e/s	2.5

 

 

Lorexvath (80 agility)

			Natural Restore:		109 seconds			100/109		e/s	0.92
		Rest With Musician:		18 seconds			+167/36		e/s	4.64
		Rest Without Musician:		28 Seconds			+2025/763	e/s	2.6

 

Fraggl3s (20 agility)

			Natural Restore:		191 seconds			100/191		e/s 0.52
		Rest With Musician:		26 seconds			
		Rest Without Musician:		34 Seconds

 

Pieman371 (56 Agility)

			Natural Restore:		136 seconds			25/34		e/s 0.74
		Rest With Musician:		21 seconds			
		Rest Without Musician:		31 Seconds

 

Calculations

 

Formula:

	Average Walking Speed = (Time Running * 2 + Time Walking)/(Time Running + Time Walking)
Average Resting Speed = (Time Running * 2)/(Time Running + Time Resting)

Time Running = 100 / (Energy Depletion - Base Restore)
Time Walking = 100 / (Natural Restore)
Time Resting = 100 / (Base Restore + {Rest Restore | mRest Restore})

Energy / Second = (100 +- (Time * Natural Restore))/ Time

 

 

 

F2P Average Speeds

Natural:
	225 seconds walking		
for every	64.5 seconds running	

Sa = (225 + 64.5*2)/289.5
Sa = 354/289.5
Sa = 1.22798

Resting (normal):
	35 seconds resting		
for every	64.5 seconds running

Sa = (35*0 + 64.5*2)/(35+64.5)
Sa = 129/99.5
Sa = 1.296482

Resting (musician):
	26 seconds resting
for every	64.5 seconds runnning

Sa = (26*0 + 64.5*2)/(26+64.5)
Sa = 129/90.5
Sa = 1.425414

 

F2P Breakeven Weight

Given:

Natural Restore = Time Walking = 225 seconds = 0.45 e/s

Rest Restore = 34 Seconds = 2.5 e/s

Time Running = x

Using:

Average Walking Speed = Average Resting Speed

(Time Running * 2 + Time Walking) / (Time Running + Time Walking) = (Time Running * 2) / (Time Running + Time Resting)

(2x+225)/(x+225) = (2x)/(x+34)

 

 

X = 48.726

 

 

Time Running = 100 / (Energy Depletion - Base Restore)

48.73 = 100 / (Energy Depletion - 0.45)

Energy Depletion = 100/48.73 + 0.45 = 2.49

 

By the data I collected with sixth, 2.49 e/s equates 15kg

 

P2P Equations

 

None Yet.

 

Results

 

F2P

 

If you are carrying more than 15kg, it is faster to keep walking, and run when it recharges naturally.

If you are carrying less than 15kg, it is faster to stop and rest, when you run out of energy.

 

Carrying 1kg, average speeds are:

(1 is walking speed)

Walking - 1.23

Resting - 1.29

Resting at a Musician - 1.42

 

P2P

None Yet.

:'(

 

 

How You Can Help

 

To take this any further, we need two equations. One for the Energy Depletion Rate, and one for the Restore Rates.

I'm not sure if I have enough data at the moment to work either out, let alone do it reliably. Once we have them, simply substituting these into the equations for Walking and Running speed will make them work for P2P :)

 

I need more data sets to work with. If you have some spare time, time how long it takes your energy to recharge from 0:

While standing still

While resting

While Resting at a musician.

 

I would very much appreciate it if you could help me out and submit your results in this format. You will be credited for helping.

	Username:
Agility Level:

Standing:
Resting:
Musician Resting:

Also, if anyone is aware of any F2P items heavier than a Rune Platebody, I would like to know (to help with energy depletion).

[Cptbaker08]

I'm sure that Agility doesn't, or shouldn't, affect you restoration as they changed that when they updated agility a few months ago. But that's only in F2P, it still affects P2P.

 

I can't tell if you used agility for doing F2P or not. And if you're a P2P member on a F2P world idk if agility affects that either.

 

Just something i was thinking about when reading it.

[Lore]

Agility no longer has any effect on F2P servers, they updated that a little while ago.

 

I'm not sure what you mean by 'restoration weight'

[Cptbaker08]

Fixed it. And i know they updated it. Since you said in the beginning that it was in F2P, i thought you were meaning all test were F2P. Didn't notice when u changed from F2P to P2P.

[Gandalf14141]

Once you get the P2P selection finished, can you please PM me? As I am intrigued about this now lol.

[Hogi]

Username: The_Hogi

Agility Level: 73

 

Standing: 1 min, 52.4 sec

Resting: 29.8 sec

Musician Resting: 18.1 sec

[CowLayEgg]

Wow that's a lot of data.

All I know is that if you have a musician on your route to the altar, use it.

 

 

[Sinkhan]

This has been stuck in the back of my head for a really long time, but realized it would be a huge undertaking.

 

Glad to see someone with enough initiative to actually do this :thumbup:

 

I'll post some data at some point.

[Lets_3ekout]

That's some nice maths there. I don't have any statistics myself yet, but was interested to see the relation between weight and run time. I can't find if you got the formula but my studies involve this very same type of data analysis, so I decided to count it :razz:

 

Anyway, this is all based on your 5 data samples (3 is a bare minimum, so 5 is actually more than enough). Time ran - Independant variable (X) Weight - Dependant variable (Y). As you said, these do not share a linear relationship. Possible transformations are log(x), log(y), 1/x and 1/y. The only transformation that really works for this data is log(y) =x, the rest leave too big of a pattern.

With a correlation coefficient of ~0.95597 (meaning it's roughly 96% accurate based on the actual data), the formula is "log(weight) = 4.1459 - (0.0634 * time running)". Since most people would use this formula to find time running, I think it might be more handy to put it this way "time running = (log(weight) - 4.1459) / -0.0634". Using this formula for values above 280 or below 1 is extrapolation and accuracy can't be guaranteed (infact, it simply doesn't work with a value of 0 or lower. ).

 

This probably won't help you since you've already covered the maths, but I just find it interesting to see the formulas that jagex devises. Maybe someone else will have a use for the formula some day :-D

[Lore]

I've got my hands on a timer now, so I'm going to redo the times for my accounts. Hopefully it'll be a bit more accurate..

 

(I had been using the windows clock before)

 

Still looking for more datasets, if anyone has a spare minute or two

 

 

Thanks for the input Phillip =)

I hadn't gotten around to looking at that yet, my sister has my graphics calculator now that I finished VCE, so I've been looking for a decent online graph plotting tool.

 

As for the general formula, it looks as it's going to be either a log(x) function [ as log(y) is really just an exponential and doesn't really fit], or an inverted inverse function (1/x, I just wanted to say 'inverted inverse' ^.^).

 

Either graph will have to be shifted left, to accomodate times (when I get some) for negative weight.