I found the EXP/Level Formula!

Ok... If you have read some of my posts in the goals and achievements section, you will know that I am a little bit of a math nerd. Having just bought a TI-84 graphing calc (woot best hundred bucks i ever spent), I decided to learn about and use runescape things as examples. I got into its statistical functions and decided to put one of them to use. I wanted to know the relative amount of exp we would need if Jagex ever raised the level cap. Now, as a mid-level player (96 CB, 1450ish TL) I don't have any 99 stats, but I used the Tip.It SKill Calcs to tell me the amount of exp needed at every level. I then inputted levels 1-99 in a list and exp amounts from levels 1-99 in another list.

This is where the TI-84 shines: I ran a quartic data regression model on my lists to find a formula that is as accurate as possible. Bear in mind that this produces a polynomial expression of degree 4.

I'd like to put a caveat on this formula. It is rather inaccurate between the levels of 1-60. However, at level 60+, the exp is give or take 3% off. The intent of this function is to determine the amount of exp for levels above 99, so take this function with a grain of salt: it's not going to be 100% accurate... more like 88% accurate.

So: Without further ado,

The Formula:

X is level and Y is exp needed

Y = 1.1240002159979X^4 - 169.81098284753X^3 + 8443.2450488426X^2 - 146185.46656323X + 586908.5427719

very nice....too bad almost no one knows what a regression equation is. nerds unite! :D

side-note: and yes the TI-84 is THE GREATEST CALCULATOR CREATED BY MAN AND BETTER THAN SEVERAL MADE BY MONKEYS.

i have to admit i barley understand any thing you just said :lol: but then again im not too big on maths. but it looks significant i guess =D>

I'll do my best to explain a regression equation in under 50 words:

You know how your math teacher gives you a function and says "If X = 15, find the Y value?"? Well, basically, this is the reverse. You start with X values and the corresponding Y values, and run that through a program to find the function that defines those values.

Unfortunately, my calc can only do quartic regressions and not n-power regressions, so I only have four degrees worth of accuracy in the function.

Also wondering if I should add a table listing the purported exp values of levels greater than 99.

:shock: *stares in wonder and amazement*

I haven't tried it yet but I'm not one to argue with you.

BTW. Nerds Own! (just believe it, our logic is infallible(we've spent years on it))

Also wondering if I should add a table listing the purported exp values of levels greater than 99.

go for it, i'm too lazy to find my calculator, it's somewhere in the corner of my closet, and will not see the light of day until september :mrgreen:

i think my iq dropped 10 points by reading this :shock:

Also, just had a thought:

What if I take Duke Freedom's research on the prices of rares and develop a regression algorithm for the prices of rares (i.e. inflation) THAT would be a pretty big acheivement.

Unfortunately, my calc can only do quartic regressions and not n-power regressions, so I only have four degrees worth of accuracy in the function.

I saw this, and I was reminded of a theory I once heard of (forgot its name or who proposed it...sorry). Apperantly, it has been mathematically proven that there is no formula that can solve equations that are to the fifth power or larger...it must be done by guesswork. So I assume that's why your calculator can only go to the fourth power, but I'm not entirely sure of it.

I'm a calculator programmer to a certain extent, but I've never heard of quartic regressions. But your explanation of it makes it perfectly clear. I've always wanted a calculator to do this, but I never knew it could! BTW, do you know how you can make a TI-89 do quartic regressions?

Note on the post above: I doubt there would be a formula that would describe the price of rares, because it is completely dependent on the corrupt minds of merchanters. *Gets mauled by R2Pleasent*

Thats all well and good

A much simpler way to look at it is:

The xp for a skill doubles every 7 levels that you raise.

So level 106 would be around 26mil xp

Someones already done this with calculus. I dunno where its at though, but its 100% accurate at every level. SOmeone linked to it in a similar post a month or two ago.

Ok , here's the table:

For my typing convenience, I will list exp values for every 5 levels over 100.

Level: Exp needed: Rough Value

105: 18369700: 18.3m

110: 25216225: 25.2m

115: 33764557: 33.7m

120: 44266687: 44.2m

125: 56991468: 57m

130: 72224611: 72.2m

135: 90268688: 90.2m

140: 111443132: 111.4m --------------------------> OVER 100M EXP

145: 136084233: 136m

150: 164545144:164.5m

To the guy with the Question about the TI-89:

I didn't have to write this function, it was included in the STAT menu under CALC (i.e. hit STAT, then cursor right to CALC)

The function arguments are QuartReg(List1, List2, Y1) where List1 and List2 are stat lists that correspond to X and Y and Y1 is the output var (i.e. you could hit "Y=" and see your QuartReg equation listed under Y1.

Ok , here's the table:

 

For my typing convenience, I will list exp values for every 5 levels over 100.

 

Level: Exp needed: Rough Value

 

105: 18369700: 18.3m

 

110: 25216225: 25.2m

 

115: 33764557: 33.7m

 

120: 44266687: 44.2m

 

125: 56991468: 57m

 

130: 72224611: 72.2m

 

135: 90268688: 90.2m

 

140: 111443132: 111.4m --------------------------> OVER 100M EXP

 

145: 136084233: 136m

 

150: 164545144:164.5m

Hola crap..A lot of exp for 150 CMB (Even though it don't exist :wink:

We could send this to Jagex..But it would mess up the whole combat formula

=D>

Also, I could find an inflation model for the mask set by basing it on price and time. This would give a rough approximation for the inflation of the overall economy. Maybe party hats would be a better benchmark. I don't know and don't care, as I can write a model for any rare if I have at least 100 points of ordered pairs (price and time)

Those values aren't for combat levels, but rather for individual levels. (think 111m exp for 140 str alone...)

Pounds author with rock.

Yeeeeah, taste my trusty nerd-busting rock!!

Quit double posting!

Noooo! I value my math skills almost as much as I value my clue scrolls!

:?:

:-s

i have NO idea what the heck your talking about

Or:

side-note: and yes the TI-84 is THE GREATEST CALCULATOR CREATED BY MAN AND BETTER THAN SEVERAL MADE BY MONKEYS.

i soo agree, when your in math class and got nothing to do, just play games and tell your teacher your doing some equation :^o

im not sure that quartic would b best, i reccomend exponential or logrithmic

Unfortunately, I don't have the $200.00 plus to buy Mathematica 8.0, and I am too lazy to right a sigma function in C++... Soultar, if you could release some code for that function, I think I could write a program for it for tip.it...

EDIT: Is "floor" the same as calculating the minima of a curve? Sorry, I'm pretty good at math but not with terminology ;-)