Maybe they just came up with random numbers. :-$

Maybe they just came up with random numbers. :-$

 

 

 

LOL :XD: All these hardworking peoples genius work gone to waste

ROFL. I understand all that, but could never come up with it.. at least with my current knowledge of math.

 

 

 

 

 

 

 

So more importantly, has anyone seen the algorithms Google uses to determine the order in which sites appear on a search result list?

 

 

 

 

 

 

 

:shock: Those things are nuts. I can't find the link again, though.... :(

I would try to figure it out but I just got back from school so my brain kinda hurts..... :cry:

To all those that wonder how the Level-to-Exp formulas came about...

 

 

 

 

 

 

 

For Phil's formula I suspect that Jagex leaked it long ago.

 

 

 

AFAIK, Phil never said were he got it.

 

 

 

 

 

 

 

For Wally's formula, you can do a search to find some posts

 

 

 

that he made a long time ago explaining the process.

 

 

 

 

 

 

 

IIRC, it's basically

 

 

 

-- convert Phil's formula to a "smooth" function.

 

 

 

This tells you the functional form to use for the formula.

 

 

 

-- use "Least squares" curve fitting (200 year old math, lol)

 

 

 

to find the A, B, etc values that are used in the formula.

 

 

 

(The least squares problem is to find x in the equation A*x=B)

 

 

 

 

 

 

 

For my inverse formula for Exp-to-Level I played around with various functional forms

 

 

 

before I settled on the Log() and ratio of polynomials thing that gave me good results.

 

 

 

I also used the Least Squares technique to generate my numbers.

 

 

 

 

 

 

 

For this kind of problem it helps to know the right Math tool to use...

 

 

 

 

 

 

 

Hope this helps

Maybe they just came up with random numbers. :-$

 

 

 

 

 

 

 

yeah. Andrew was like "hmm... level 99... what exp numbers should that one be?"

 

 

 

Paul: " make it like 13 million :XD: nobody is ever going to reach that!"

 

 

 

*hi five*

 

 

 

Andrew: "good one. Imagine what kind of loser would have 99 in like 5 skills? It's impossible!"

 

 

 

Paul: "ooh, make it even more than 13 just to throw them off!"

 

 

 

*more hi-fives and snickers*

 

 

 

 

 

 

 

This is not meant to offend anybody with 99s in a lot of skills *cough n0valyfe and thehate*, back when runescape was released even 50 anything was crazy.

after level 20, the XP doubles every 7 levels

Yeah I think I agree with the "Hey lets pick random numbers!" theory :P

 

Maybe they just came up with random numbers. :-$

 

 

 

 

 

 

 

yeah. Andrew was like "hmm... level 99... what exp numbers should that one be?"

 

 

 

Paul: " make it like 13 million :XD: nobody is ever going to reach that!"

 

 

 

*hi five*

 

 

 

Andrew: "good one. Imagine what kind of loser would have 99 in like 5 skills? It's impossible!"

 

 

 

Paul: "ooh, make it even more than 13 just to throw them off!"

 

 

 

*more hi-fives and snickers*

 

 

 

 

 

 

 

This is not meant to offend anybody with 99s in a lot of skills *cough n0valyfe and thehate*, back when runescape was released even 50 anything was crazy.

Lmao! :lol: If so then tell me why is it 34431 exp and not some gibberish numbers?

 

 

Maybe they just came up with random numbers. :-$

 

 

 

 

 

 

 

yeah. Andrew was like "hmm... level 99... what exp numbers should that one be?"

 

 

 

Paul: " make it like 13 million :XD: nobody is ever going to reach that!"

 

 

 

*hi five*

 

 

 

Andrew: "good one. Imagine what kind of loser would have 99 in like 5 skills? It's impossible!"

 

 

 

Paul: "ooh, make it even more than 13 just to throw them off!"

 

 

 

*more hi-fives and snickers*

 

 

 

 

 

 

 

This is not meant to offend anybody with 99s in a lot of skills *cough n0valyfe and thehate*, back when runescape was released even 50 anything was crazy.

Lmao! :lol: If so then tell me why is it 34431 exp and not some gibberish numbers?

 

 

 

 

 

 

 

How does 34,431 not look like a gibberish number (without knowing about the formulas of course)?

 

 

 

 

 

 

 

Yeah I've known the formula for a while but never understood it. Maybe I'll ask my math teacher about it all :-$ The floor really threw me off.

 

 

 

 

 

 

 

So the area of the floor (in sq. m.) multiplied by x amount of levels...

That's like a 7th degree function :P . Nothing beats good ol' F(x)=ax+b.

after level 20, the XP doubles every 7 levels

 

 

 

 

 

 

 

That's actually an excellent rule of thumb, that's always what I'd used to remember it.

 

Maybe they just came up with random numbers. :-$

 

 

 

 

 

 

 

yeah. Andrew was like "hmm... level 99... what exp numbers should that one be?"

 

 

 

Paul: " make it like 13 million :XD: nobody is ever going to reach that!"

 

 

 

*hi five*

 

 

 

Andrew: "good one. Imagine what kind of loser would have 99 in like 5 skills? It's impossible!"

 

 

 

Paul: "ooh, make it even more than 13 just to throw them off!"

 

 

 

*more hi-fives and snickers*

 

 

 

 

 

 

 

This is not meant to offend anybody with 99s in a lot of skills *cough n0valyfe and thehate*, back when runescape was released even 50 anything was crazy.

 

 

 

 

 

 

 

More something like this:

 

 

 

 

 

 

 

Andrew - Now, how much xp shall we need each level?

 

 

 

Paul - Easy, let's use this formula:

 

 

 

 

 

 

 

Experience = floor(A*(2^(L/7)-2^(1/7)) + B*L^5 + C*L^4 + D*L^3 + E*L^2 + F*L + G)

 

 

 

 

 

 

 

Where L is the Level.

 

 

 

So now it's an exponential function plus a 5th degree polynomial with

 

 

 

 

 

 

 

A = 720.533673767946

 

 

 

B = 3.54298390625729e-09

 

 

 

C = -1.0176384179772e-06

 

 

 

D = 9.69859806900786e-05

 

 

 

E = 0.121741672963253

 

 

 

F = -0.2074127222877

 

 

 

G = 0.139103528112173

Maybe they just came up with random numbers. :-$

It's what I would of done if I was a game designer -deffinantly :-w

Level 200 - 287416243706 xp

 

 

 

 

 

 

 

thats what I call challence!

Level 200 - 287,416,243,706 xp

 

 

 

Well, sooner or later the Exp value is gonna run into the max value for the type of number Runescape uses.

 

 

 

 

 

 

 

IIRC, Runescape uses a signed 32 bit number so the max integer would be 2^31-1

 

 

 

That's 2,147,483,647 or about level 150

 

 

 

 

 

 

 

Some speculations on my part...

 

 

 

 

 

 

 

If Runescape actually keeps 1 decimal digit to the right of the number

 

 

 

(It does for magic and melee combat. Probably others as well)

 

 

 

Then the max number would be 214,748,364.7

 

 

 

That's about level 127

 

 

 

 

 

 

 

Jagex has placed a displayed exp cap of 200 million.

 

 

 

(Players can earn some exp past 200 million but it's not displayed)

 

 

 

Notice that that is a "nice" number slightly less than the 214 "max"

 

 

 

 

 

 

 

Now, if Jagex decided to take that 200 million cap and "apply" it

 

 

 

towards the combat level formula then you end up with level 126.58

 

 

 

That would be displayed as 126, the known max level.

 

 

 

 

 

 

 

Only Jagex knows the max values for certain but the above speculations are kinda interesting.

Personally, I don't believe there's a nice function behind the (lvl, xp) pairs. I've drawn some mappings with my functional calculator, and the growth seems somewhat exponential, but not completely regular. It could be constructed from a few different functions and then be compiled from those.

 

 

 

 

 

 

 

Of course they may have drawn the mapping f(x) = 1.2x^4 - 184x^3 + 9248x^2 - 161600x + 654933 for example and taken some approximate values from that. Or maybe they just hand-drawed some curve and used a computer program to look up for some values. After all, any set of pairs can be approximated with extreme accurateness if we just add enough terms to the function. I highly doubt the programmer just came up with numbers with more than 10 decimals.

 

 

 

 

 

 

 

My bet is they just hand-drew a curve and took values from that.

 

 

 

We can always search for functions, and there is an infinite amount of 100% accurate functions (since the values are discrete) and none of them are really "better" than the others.

 

 

 

 

 

 

 

I study mathematics at an university so feel free to ask me some questions.

The thing I find interesting is that at 200M xp in a skill (max xp you can have), you would be lvl 126.

 

 

 

 

 

 

 

126 = max combat lvl.

 

 

 

 

 

 

 

Coincidence? :-k

...I study mathematics at an university so feel free to ask me some questions.

 

 

 

What do you think of the 2 Level-to-Exp functions presented earlier?

woah this more intense than maths higher tier GCSE

I know you've all posted nice, smart formulas for this..but have you ever thought about that it might even be like..they just picked some random numbers? =P (With some thinking about them ofcorse)

 

...I study mathematics at an university so feel free to ask me some questions.

 

 

 

What do you think of the 2 Level-to-Exp functions presented earlier?

 

 

 

 

 

 

 

Natural logarithms would be the most logical choice for function, if you ask me. However, because of the discrete, non-infinite nature of the data we have, we can never be sure of the exact function (supposing there even is one).

all I know is that I have 900+ lvls and I only have enough xp to have half of a 99 #-o

 

 

 

I actually don't think there's an equation for it, some guy just plotted an xp line on a graph and that's where it stayed -.-

...Natural logarithms would be the most logical choice for function, if you ask me.

 

 

 

But doesn't the slope of the Natural log function go the wrong way as the level increases?

 

 

 

Namely, the Exp curve looks exponential not logarithmic.

 

 

 

 

 

 

 

However, because of the discrete, non-infinite nature of the data we have,

 

 

 

we can never be sure of the exact function (supposing there even is one).

 

 

 

Yeah, that's why I'm curious as to where Phil's formula came from.

 

 

 

It's such a strange looking thing.

I know you've all posted nice, smart formulas for this..

 

 

 

but have you ever thought about that it might even be like..

 

 

 

they just picked some random numbers? =P

 

 

 

(With some thinking about them ofcorse)

 

 

 

Well, the Exp numbers do have some curious properties.

 

 

 

 

 

 

 

Things like:

 

 

 

the Exp at a level divided by the Exp 7 levels lower

 

 

 

gets very close to 2 as the level increases.

 

 

 

(Example: the exp needed to go from 90 to 91 is 556499

 

 

 

the exp needed to go from 97 to 98 is 1112977

 

 

 

That ratio is 1.99996

 

 

 

If you used 89 and 96 instead, that ratio is 1.99995)

 

 

 

 

 

 

 

or

 

 

 

 

 

 

 

the Exp needed for the next level gets close to 1.104089 times

 

 

 

the present level exp as the level increases.

 

 

 

(Example: the exp from 97 to 98 is 1112977

 

 

 

the exp from 98 to 99 is 1228825

 

 

 

That ratio is 1.104088

 

 

 

If you used 96 to 97 and 97 to 98 then that ratio is 1.104086)

 

 

 

 

 

 

 

So, the Exp vs Level numbers do show some very predictable properties.

 

 

 

 

 

 

 

Finally, one "simple" function (an exponential plus a polynomial) computes the numbers exactly.

 

 

 

 

 

 

 

So, it appears to me that Jagex gave a fair amount of "non-random"

 

 

 

thought as to how they wanted the Exp curve to increase.