XP Curves Are Weird

Musing about the difficulty curves in Wizards of the Coast’s flagship franchise.

While, in a previous entry, I mentioned I have no love for D&D 3.5, there was one thing I did at least Platonically admire: the leveling system.  In order to get to the next level, you required 1000 times your current level in XP.  Getting from Level 1 to 2 required 1000 points, 2 to 3 need 2000 points more, and so on.  It sounds like a mouthful but what comes out is quite elegant.

dd1

The orange curve is Y=(X-1)1.79; the blue one is the 3.5 XP milestones with each value divided by 1000. For the first two incarnations of D&D, characters leveled up based on their class.  3rd edition (and subsequently 3.5) replaced that with with a simple and beautiful exponential curve.

So of course they had to screw it up in later editions.

Now there could be many reasons for Wizards of the Coast to have deviated from the exponential curve for 4th edition–the first to go canonically go to level 30, but it came at with a tradeoff.  Each future level in 3.5 was harder to achieve than the one before and the extent of that increase in difficulty remained constant.  With 4th and 5th editions, that was not the case.

DD2

Here is a comparison of each of the past 3 D&D editions. These are the sum totals of XP required to hit each of the first 20 levels. What’s interesting is that 4th edition is technically the quickest version to get to Level 20, but that’s probably because 4E required one million XP to get to Level 30.  Had 3.5’s curve kept going to Level 30, players would only need 435,000.  You can get to Level 3 in just 900 points with the new D&D, but Level 20 requires about twice as much as either of the other editions.

Take away all the idiosyncracies, though, you’re left with one exponential curve and two that look close enough, right?DD3

This graph is created by taking the Y-value at each X from the previous graph and subtracting the Y-value from the previous X from it.  To put it a 3rd way, this shows how difficult it is to advance one level, and in a way the difficulty curve of D&D.  While 3.5’s curve is a straight upward-sloping line, 4th and 5th have some weird kinks, and here’s where a potential flaw in those systems starts to show.  In any game, tabletop, video, or otherwise, you ideally want the game to be progressively harder as it goes along.  Providing new and bigger challenges helps keeps players engaged and wanting to continue on.  There’s a philosophical debate to be had on how to set a difficulty curve, but I would imagine most would set it as either a continuously upward-sloping line or a line that resembles a staircase, increasing intermittently instead of constantly.  5th edition distinctly has an issue between Levels 11 and 12, which is only more exacerbated in the next graph.

DD4

This is the change of XP needed to go to each level.  If the previous graph was the difficulty curve, this measures how fast that curve changes.  The 3.5 curve here is flat, but I said as much at the start of this article–each level costs 1000 more than the one before.  4th Edition’s curve indicates that difficulty accelerates incrementally over time, but there’s always a positive increase.  5th Edition’s curve is drunk and needs to go home.

So after 500+ words explaining numbers and lines and putting them to potentially abstract concepts, what does it all mean?  To me, it means that every time Wizards revamped D&D, they chose a different approach to character progression and those new approaches ended up affecting the XP Curve in bizarre ways.  In 3rd edition, prestige classes took to the limelight, which could be added on at any time in addition to your starting class, as long as you meet the prerequisites.  Some of them didn’t even require a particular character level or starting class.  Because prestige classes were so fluid and interchangeable, it was likely easiest to treat all character levels equally and create the XP curve from there.  For 4th edition, characters were broken down into three phases: Starter, Paragon, and Epic.  Each phase was 10 levels long, which explains why that difficulty curve spikes going to level 11, but resets a bit for level 12.

4th Edition Character Level

Total XP Milestone

XP Needed To Reach

9

16,500

3,500

10

20,500

4,000

11

26,000

5,500

12

32,000

6,000

13

39,000

7,000

Levels 20-30 are similar to Levels 10-20, and that’s a reasonable way of looking at character progression–unlocking a brand new phase of play mid-game should be relatively harder, but the game should always get harder.  D&D 5th edition, taking the concepts of 4E and making four phases of 5 levels each, executes the concepts poorly and ends up with a result I can’t explain.  The only solace I have is that I’ll likely be in a minority of players who care about such things.

As a postscript, I wanted to see how Pathfinder and its three speeds of character progression fared in comparison to D&D’s level curves.

DD5

Ideally, these three graphs should be the same approximation of an exponential curve, but with the exponent adjusted based on how fast you want to level.

DD6

This curve shows that is not the case.  Even Paizo has leveling quirks