# Exploring Levels Again: The Numbers

Posted by on October 12, 2012

Getting back to the leveling discussion and the idea for an RPG without a level cap, I’m putting some numbers together just to see how they feel and to get an idea for the scope of a level range using WoW-style advancement. Let us make the following stipulations:

• We have a leveling system with no true cap.
• Characters and mobs both have levels.
• The XP needed to advance to a new level is calculated as a number of mob kills of a level equal to that of the character. This is how WoW does it, by the way, although of course in practice you have other factors such as rest XP, XP from quests and so on that will need to eventually be figured in.
• Mobs not at the character’s level will of course yield a different amount of XP, but that’s not important for the purposes of this particular calculation.
• The power curve, i. e. just how much a level means in mechanical effect, is not considered here. In a non-levelcapped system I suggest that the power curve be pretty gradual.

Okay, so given those things, we have a basic leveling calculation:

$x=16c^2e^r$

Where x is the number of XP needed to get to the next level, c is the character’s current level, e is the mathematical constant e (equal to approximately 2.718) and r is a scaling factor equal to the character’s level divided by 10 and rounded to one decimal place. Using this forumla some scaling could be done either by moving the constant up or down or adding some number (probably less than 1) to r.

Truncating the actual XP numbers and plugging in some sample figures, wee see that a level 1 character needs 70 XP to reach level 2, while a level 11 character needs 21,890 XP to reach level 12, or 73,790 accumulated total XP. This works out to over a thousand mobs killed. I’ve calculated this up to level 100 (not a cap, just as high as I have taken the numbers) and it seems likely that very, very few players would surpass level 40, which requires you to have gained the equivalent of over 100K worth of at-level mob kills.

Now, as I said before, you would almost certainly have quests as a means to get XP, and those would yield as much XP as a batch of mobs. Plus there might be XP gain rate boosts of some kind, or XP from crafting, exploration, gathering and so forth. So it might not be as slow in practice as these numbers suggest, but hitting level 20 would be something. If the power curve is indeed gradual and as steep as I suggest, you could tailor quests to target a range of, say, seven levels, and have a lot of overlap within the level ranges in which players will tend to cluster, therefore reducing the need for the same kinds of content in multiple level ranges.

On the other hand, many players under such a scheme might feel, say, in the 20s or even the teens that it takes forever to level. So maybe there is some kind of sub-level advancement a la DDO or Vanguard, where you get your benefits for the next level during that level as opposed to only when you hit it. If the net power gain per level in +5%, for example (it’s probably impossible to quantify this so precisely, but there ought to be some kind of target to shoot at,) you might get +1% at 20% of the next level, another +1% at 40% and so on. You might also want level-independent intangibles (reputation might be one example) that players could go for as measures of accomplishment.

Would crafting be dependent on this overall character level? I’m not sure, but my inclination is to say that it would… but there’s also my other notion that level is supposed to be the result of power advancement rather than the cause. In an arrangement like that, a more complicated progression formula would be in order, probably one based on skill ratings. But I’m not sure you’d need to implement both ideas, actually.

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