TruthScape.com  9  TruthScape Skill Secrets       9  TruthScape Skill Secrets - A General Guide to RuneScape Skills and Training            9  TruthScape Skill Secrets - General Guide - Overview of RuneScape Skills

An Overview and Summary of RuneScape Skills and the Benefits of Each TruthScape Skill Secrets - General Guide - The Economics of RuneScape Skills and Skill Training

Most RuneScape players know that there is a direct relationship between a skill’s level and the number of experience points in that skill, but beyond that, things get a little murky. How exactly are those XP targets for each level calculated? Why does each level take longer to get to than the one before? And is it true that the number of XP you have doubles every seven levels?

As I’ll show you know, there is indeed some method to what initially seems like madness.

The idea of having skill levels be based on the amount of XP in the skill is common to most RPGs, but each has a different way of determining what the relationship should be. Jagex chose to use a numerical calculation for RuneScape’s XP-level relationship, which is why the number of XP you need to get to each new level isn’t a nice round number.

Here’s the mathematical expression of the formula for calculating the number of XP needed to reach a particular skill level (for level 2 or higher):

Clear as mud, right? J Well, I can’t explain equations in detail here, but I’ll try to give you an idea of what this means. (This is mostly for those who are curious; you don’t need to know how this works, of course!)

First of all, the symbols that look like square brackets (“[ ]”) but with the tops cut off represent the floor function. This means to take the lowest integer value of an expression; for example, floor(3.7) = 3.

Second, the “S” symbol is the Greek letter sigma, and means that you are summing up a series of values. In this case, we compute the equation next to that symbol for each integer from 1 to 1 less than the level we’re calculating, then add them all up. Thus, you can only calculate XP for a particular level by adding up a series of numbers and then doing another computation on them; there is no simple “take the level and divide it by a certain figure” sort of formula.

Last but not least, the expression inside the sigma contains an expression of the form 2^n/7, which means “to the power of” (for example, 2³=8); its presence makes the formula exponential. Functions that contain exponential elements tend to increase in value faster the higher the value itself is. This is why, each time you get to a new level, you need more XP to get to the one after that.

Notice that the exponent is “n/7”? This means that the multiplying factor doubles every time “n” goes up by 7. In turn, this is why the number of XP needed does indeed double every seven levels (at higher levels).

The formula can be used just by plugging in different values for “Level” and computing the results. Level 1 is always 0 XP, so we start with level 2 as follows:

• Level 2: The summation goes from 1 to Level-1 = 2-1 = 1, so there’s just a single term to evaluate: (1+300*2^(1/7))=332.2269. The floor is 332, and dividing by 4 yields a result of 83. The floor of that is of course still 83, and that’s how many XP we need for level 2.
  
  
• Level 3: The summation goes from 1 to Level-1 = 3-1 = 2, so there are two terms to evaluate. We already know the value for n=1, it is 332.2269 as before. When n=2, we evaluate: (2+300*2^(2/7))=367.7041. Then we add 332.2269+367.7041 = 699.931. The floor is 699, divide by 4 and the result is 174.75. Take the floor of that and we need 174 XP for level 3.
  
  
• Level 4: The summation goes from 1 to Level-1 = 4-1 = 3, so there are three terms to evaluate. We already know the values for n=1 (332.2269) and n=2 (367.7041) from above. When n=3, we evaluate: (3+300*2^(3/7))=406.7701. Add the three terms and we get 332.2269+367.7041+406.7701 = 1106.701. The floor is 1106, divide by 4 and the result is 276.5. Take the floor of that and we need 276 XP for level 4.

And so it goes for all 99 levels.

Of course, nobody would really work out all the numbers by hand; the figures are calculated using computer programs. In Table 9 I have done exactly that, showing you how many XP you need for each RuneScape level, along with the amount of incremental XP needed to get to the level after it.

There are two extra columns in the table that you may find interesting. The column second from the right is simply the “XP Needed to Reach Next Level” column divided into “XP Required for Level”. It tells you, after you reach a particular level, what percentage of your XP you will need to add to get to the one after. As you can see, this starts out high but then quickly slows and then settles on the figure of 10.4%. What is this number? Easy: 2^(1/7) - 1 = 10.4%. J The general rule of thumb of needing 10% more XP per level works pretty well starting at about level 40.

The right-most column shows what percentage of the XP needed for level 99 you have earned at each of the other levels. It shows nicely what exponential growth does, and why there’s a good reason that it seems like when you hit level 90, you aren’t even half-way yet to 99—because you aren’t! J I’ve also graphed it in Figure 128, which shows a classic exponential growth curve.

Figure 128: Progress Towards Level 99 by Current Skill Level

This chart shows what percentage of the total XP needed for level 99 in a skill at various skill levels. You can see here the classic result of using an exponential function: most of the early levels require little XP, but then the amount begins to increase, and the last few levels comprise the bulk of the total XP required.

Note that the curve crosses the 50% mark at level 92, and the 25% mark at level 85; XP doubles every seven levels. The red dot marks what is commonly called the knee of the curve (as you can see by its shape). It is significant because in many ways it represents the best reward in terms of level attained for XP gained—this is why so many players stop skills at approximately level 80.

An Overview and Summary of RuneScape Skills and the Benefits of Each TruthScape Skill Secrets - General Guide - The Economics of RuneScape Skills and Skill Training

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