Check this out: Graph of the XP table

[Acinonyx]

Ok, so I used the info from the Tip.It XP Table available at http://tip.it/runescape/?page=xp_table.htm to construct this function graph:

 

 

 

 

 

 

Doesn't it really put into perspective how much you have to train to get to 99? haha, it discouraged me a bit, actually. And it also made me admire those guys who got to 98 construction in a matter of a week. But anyway, that's beside the point.

 

 

 

So I tried to figure out how exactly this graph and table were constructed. It seemed to me like it was exponential at first, but actually, it is not exponential (to the first degree anyway)

 

 

 

A property of an exponential function is that successive terms have the same ratios. By that I mean:

 

 

 

the ratio f(2) / f(1) should be the same as the ratio f(3) / f(2). So when you divide the values corresponding to levels 1, 2, 3 as I just said, you should be getting the same ratio of values. This, however, does not happen.

 

 

 

So then I tried to see if the function was exponential to the second degree, meaning that the ratio of the ratios of successive terms should be the same, and that also is not the case. I don't believe that this graph is exponential to any other degree either (correct me if I'm wrong).

 

 

 

apparently a little bit of entropy has been thrown into this XP table, but i badly want to know how they created it. I also tried looking for software that could take all this information and put into an equation for me, but I couldn't find any.

 

 

 

 

 

So...if anybody has an thoughts, or suggestions as to where I can fit an equation to this curve, please tell me! And of course, tell me your reactions upon seeing this graph.

[Vape]

http://maddogcarter.com/phil/runescape/xpformula.html

 

 

 

[homer806]

I doubt they used an equation to find the numbers. I think they just picked them. but you can find the equation with a graphing calc, hang on a sec and i'll do it.

[E_D_G_E_1039]

I doubt they used an equation to find the numbers. I think they just picked them. but you can find the equation with a graphing calc, hang on a sec and i'll do it.

 

 

 

Im almost positive they used some sort of formula.

[homer806]

Well.... nevermind then.

 

I guess i'm just an incompetant fool. or however you spell that big word.

[Vape]

incompetent, fool ;)

[grogcollins]

it's a simply exponential function.

 

where's your grade 12 math?

[Google90]

if someone wanted to make a table on a TI 82 83 84 89..etc and was willing to do a table 1-99 listing each XP for each level, we could find the 5 number summary(minimum value, lower quartile (Q1), median value (Q2), upper quartile (Q3), maximum value.) And the avearge difference between each XP

[Acinonyx]

it's a simply exponential function.

 

where's your grade 12 math?

 

 

 

Like I clearly explained in my original post, it is CLEARLY not an exponential function. Check my post.

 

 

 

And I'm not in grade 12 yet. Sophomores FTW!

[piman1053]

u should make one that goes to like 60, cuz i can fell the curve even at 30. :roll:

[Socc]

AHHHHHH MATH!!!!! it hurts my brain! 0.0 -.- :evil: no math when im around

[Kerdz]

Is it just me or is this graph so insanely easy to see how it was made?

 

 

 

0-14mill on the Y-Axis

 

 

 

1-99 on the X-Axis

 

 

 

Than plot the points..

[Acinonyx]

Is it just me or is this graph so insanely easy to see how it was made?

 

 

 

0-14mill on the Y-Axis

 

 

 

1-99 on the X-Axis

 

 

 

Than plot the points..

 

 

 

well...obviously. I just took the values from the XP table and put them into Excel, which generated a graph.

 

 

 

Why would it seem complicated to make a graph like this?

[Bubsa]

Well, if I ever needed discouragement not to return to RuneScape :shock:

[Utopianflame]

it's a simply exponential function.

 

where's your grade 12 math?

 

 

 

Like I clearly explained in my original post, it is CLEARLY not an exponential function. Check my post.

 

 

 

And I'm not in grade 12 yet. Sophomores FTW!

 

 

 

According to the formula as we know it, the function is a sum of exponentials, which is also exponential (the first time you're likely to come accross this result is in statistics, with regard to the normal distribution).

[pro28]

Even the freshman here knows that that's a geometric sequence.

[Goobore]

...Like I clearly explained in my original post,

 

it is CLEARLY not an exponential function...

 

Here's a link to a post that takes the original function and "connects" the dots and

 

gives the exact same values for the levels as well as all points in between any 2 levels.

 

 

 

And that function is an exponential function plus a polynomial.

[g0geta]

ouch, thats a little discouraging

[council_tax]

somebody was bored...i knew it looked something like that anyway and why the hell am i on runescape forums, i don't even have an active account!

[Goobore]

Even the freshman here knows that that's a geometric sequence.

 

Not exactly right, but it is close to one with r=2^(1/7)

[slayercool66]

Here's the derivation of the total skill experience formula. The formula is an approximation, but a very accurate one (less than 1% error). Keep in mind it only works for high levels (60+), as the low levels follow a different formula.

 

 

 

Let x(n) be a function c*an, where n is the level, x(n) is the total experience, and c and a are real numbers. By looking at an experience chart, if you take any x(n+1) and divide it by x(n), the result is always close to 1.1041. For example, take level 71 experience as 814,445 and divide it by level 70 experience as 737,627; so 814,445/737,627=1.1041. So, you have an equation c*an+1 divided by c*an = 1.1.041. Because only an "a" term is left (c*an+1 divided by c*an = a), we conclude a must be 1.1041. Now take any level, say 71, and substitute into the equation x(n) = c*(1.1041)n. By direct substitution, 814,445 = c*(1.1041)71, so c = 719.98. Thus, the formula for total experience, given a level n greater than 60, is:

 

 

 

x(n) = 719.98*(1.1041)n

 

 

 

Woot I'm a genious ^_^

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Ok, ok it's isnt mine, actually it's taken from N0valye's site, so cred to him

[pro28]

Here's the derivation of the total skill experience formula. The formula is an approximation, but a very accurate one (less than 1% error). Keep in mind it only works for high levels (60+), as the low levels follow a different formula.

 

 

 

Let x(n) be a function c*an, where n is the level, x(n) is the total experience, and c and a are real numbers. By looking at an experience chart, if you take any x(n+1) and divide it by x(n), the result is always close to 1.1041. For example, take level 71 experience as 814,445 and divide it by level 70 experience as 737,627; so 814,445/737,627=1.1041. So, you have an equation c*an+1 divided by c*an = 1.1.041. Because only an "a" term is left (c*an+1 divided by c*an = a), we conclude a must be 1.1041. Now take any level, say 71, and substitute into the equation x(n) = c*(1.1041)n. By direct substitution, 814,445 = c*(1.1041)71, so c = 719.98. Thus, the formula for total experience, given a level n greater than 60, is:

 

 

 

x(n) = 719.98*(1.1041)n

 

 

 

Woot I'm a genious ^_^

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Ok, ok it's isnt mine, actually it's taken from N0valye's site, so cred to him

 

 

 

 

 

Hmmm, I think that equation is wrong...

 

 

 

I got f(x)=719.89(1.1041^X).

 

 

 

Or I could be stupid and I could be totally wrong.

[glademering]

using linear algebra you can create a formula to model the experience, but it could end up being a polynomial to the 100th degree, and it doesn't interest me enough to do it, plus i highly doubt that jagex pulled a formula out of their nether regions that involved terms to the 100th degree, so even though you stated that it isn't explicitly an exponential function, it most probably has a component that is, as well as some other function, be it polynomial or logarithmic or whatever that makes it so that the entire function cannot be modeled by one exponential function.

[Goobore]

Hmmm, I think that equation is wrong...

 

I got f(x)=719.89(1.1041^X).

 

Or I could be stupid and I could be totally wrong.

 

Hmmm, I guess that no one clicked on the link that I provided earlier...

 

 

 

There are 2 100% correct formulas for Experience as a function of Level.

 

First, there is "Phil's" discrete version

 

 

 

 

and then there is Wally's continuous version

 

 

 

I have modified the continuous form of the skill experience formula

 

to exactly match Phil's formula up to level 132.

 

(Btw, level 132 is about 342 million experience for a single skill)

 

 

 

The modified formula is:

 

 

 

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

 

 

 

This matches 100% with the 100 known Runescape exp values,

 

and matches Phil's values for levels 101 to 132.

 

 

 

So, a very crude approximation of the function

 

would be to take the first term of Wally's version.

 

 

 

That would be 720.5*2^(L/7) = 720.5*1.10409^L,

 

which is very similar to N0valye's.

[bjbj1991]

Someone needs to add this formula to another that gives the xp/hour/level, it takes the same amount of time as it does to cook shrimp at level 1 as it does to good a shark at level 99.