Graphs for Player Progression Part II

Jiahui Cai
Jun 20, 2016 · 6 min read

This piece continues from Part I where general graphs and their formulae are discussed. In this part, I’ll discuss intention and how to translate that into graphs with case studies.

For me, the first thing I do when thinking about how the various mechanisms of a game system fit together is to consider which variables I want as a basis for comparison. Think of it as currency exchange. Without an exchange rate, it is hard to imagine how different elements compare to each other. Usually, I’d start by thinking about pacing (e.g how long the player takes to gain a level) and rough expectations for the rate of XP gain (ie XP gained / time). From this, I’d derive the curve for XP needed per level gain and then balance and fine-tune with actual figures as they become clearer. Here are some examples of character progression curves and how to think about them.

Neverwinter Nights

Data from: http://nwn.wikia.com/wiki/Level_progression

Key points of note:

  • Level gain at the starting levels should be easier than towards the end
  • The curve seems polynomial in nature with a rather smooth growth in rate of XP required

When thinking about the levelling system here, what would stand out for me is that this game needs to take multiplayer into consideration. With a level cap, it means that after a while, the playing field is levelled and skill will be the differentiating factor. The intention of the levelling system here would be to provide a predictable rate of levelling growth where players can manage their difficulty steepness before allowing for the difficulty to increase organically (ie. after the cap is reached).

Final Fantasy 1

Data from http://www.ign.com/faqs/2003/final-fantasy-experience-table-386613

In contrast, here’s a single-player experience where grinding is expected and the level cap extends beyond what most players would feel compelled to reach — even with grinding.

Here’s the curve in the earlier levels and that in the later levels.

Data from http://www.ign.com/faqs/2003/final-fantasy-experience-table-386613
Data from http://www.ign.com/faqs/2003/final-fantasy-experience-table-386613

Key points of note:

  • The curve in the earlier stages is very similar to that in Neverwinter Nights.
  • In the later levels, the curve is linear.

The intention here would be to have a consistent rate of increase in character growth that the player can intuitively understand like in NWN in the early levels. The non-linear part of the curve is likely to be the amount of growth average players will go through in the course of the game.

Another way of looking at the linear portion of the curve is to consider the entwining of the XP gain/time curve. It is likely that in the early parts of the game, the player will gain XP much quicker than in the later part of the game and that the rate of XP gain becomes stagnant after a while. With the rate of XP gain almost constant, a linear increase in character growth will have the same result as an increasing rate of XP gain and a polynomial increase in character growth.

Clash of Clans

The interesting feature of the levelling system in Clash of Clans and many other social games is that levelling up doesn’t necessarily add to the player becoming stronger in a traditional sense. Instead, levelling up rewards the player with prestige and also more options for gameplay.

Data from http://clashofclans.wikia.com/wiki/Experience
Data from http://clashofclans.wikia.com/wiki/Experience
Data from http://clashofclans.wikia.com/wiki/Experience

Key points of note:

  • Progression is uncharacteristically linear.
  • The increase in XP required gets higher per tier of levels
  • There are a lot of levels.

A game like Clash of Clans wouldn’t work well with a permanent level cap since a consideration is to open up more content in the future to keep users coming back. In a sense, each tier acts as a gigantic level gain and were more tiers to be added, the resultant curve would get closer and closer to a polynomial one.

Before looking at the rationale behind the experience system, it’s also worthwhile to note the rate of XP gain and what this entails. Unlike NWN and FF1, Clash of Clans is a strategy game with a system where building time variations is core to gameplay. The expection of the player would be this -

  • For new players, they will build structures that require minimal building tie. This also forces them to check in often to the game for quick reward gains and drives short term retention.
  • As players become invested from having built many quick-build structures, they are more willing to wait longer to gain bigger rewards. Also, reaping resources from the initial structures will take up a significant amount of game time and starts being a bit of a chore so you don’t want players to occupy their entire game session with just doing that.
  • As players move on to exploring other parts of gameplay, building moves into becoming a more secondary task where players are willing to spend much longer durations waiting for a building to complete while they busy themselves with other tasks.

There are several build duration presets, each with an associated amount of XP gain. Charted, it looks something like this —

Data from http://cocland.com/guides/level-and-experience

Broken down into short build times and longer build times, the curves resemble these -

Data from http://cocland.com/guides/level-and-experience
Data from http://cocland.com/guides/level-and-experience

From the curves, it can be seen that structures with short build times will reap the most rewards (ie. gradient of the curve at that point) but as the build times become longer, the rewards are almost proportionate.

The consequence of this is that new players are better rewarded from building while long-term players with the option of going for structures with long build times and who are are no longer as drawn to the act of building for quick reward gains are rewarded accordingly.

Here’s a plot of the rate of XP gain vs the build times which describes the above.

Data from http://cocland.com/guides/level-and-experience

For longer build times, the rate of XP gain is almost level.

Going back again to progression balancing, how does this relate to a steeper curve necessary for level gains? While in RPGs where tougher enemies reward with higher XP (and take longer to kill), in Clash of Clans, player progression results in the ability to build more concurrent structures. By doing so, even if the rate of XP gain for building one such structure is uniform, the cumulative XP gain increases as the player progresses and player levelling needs to take that as a consideration. The expected cumulative XP gain should mirror the XP gain progression from killing enemies in an RPG.

Conclusions

When designing progression systems, some key points to consider are

  • What should be used as a basis for comparison between the various mechanisms? Usually, all of these map to playtime. When looking at a more micro-level, player level is used to balance when features unlock as well.
  • What is the expectation of the gradient of your graphs? Think of gradient as a rate of increase. Steeper gradients mean a larger increment step.
  • Where are the points of variation? Not all curves need to follow a fixed formula throughout. Most systems utilise different formulae for different ranges of X-axis values like, in the CoC and FF1 examples. This usually corresponds to a point in gameplay where there is a certain expectation of the player.

J’s Game Design and Tech Journal

Notes and Musings About Game Design, Development and Technology.

Jiahui Cai

Written by

Game Designer/Unicyclist. If I had to describe game dev, I’d say it’s tough work but hey, at least I poop rainbows. Personal blog: http://www.ipooprainbows.com

J’s Game Design and Tech Journal

Notes and Musings About Game Design, Development and Technology.

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