Curves: Relationship between two systems

Curves: Relationship between two systems

In game design, the concept of “curves” generally refers to graphical representations or mathematical functions used to describe various aspects of a game’s mechanics, progression, difficulty, or other relevant parameters in a relatable way. Curves in game design serve as powerful tools for modelling, analysing, and optimizing various aspects of gameplay to create compelling and enjoyable player experiences.

Linear Curves

Super Mario Bros, the rate at which the difficulty increases as players progress through levels can be considered linear. Each level introduces new challenges and obstacles, with the difficulty gradually ramping up as players advance through the game.

Experience Progression: Linear curves can be used for straightforward progression systems where players gain a fixed amount of experience points for each action. For instance, in a game where players earn a constant amount of XP for defeating enemies or completing quests, a linear progression curve may be employed.

Difficulty Scaling: Linear curves can also be used for simple difficulty scaling, where the challenge level increases at a constant rate over time or as the player progresses. This can provide a consistent level of challenge but may lack the dynamic pacing of other curve types.

Exponential Curves

World of Warcraft, the experience required to level up follows an exponential curve. Initially, players can level up relatively quickly, but as they reach higher levels, the amount of experience needed to advance increases dramatically, resulting in a slower progression rate in later stages of the game.

Experience and Leveling: Exponential curves are commonly used for experience and leveling systems in RPGs. With an exponential curve, the amount of experience required to level up increases rapidly as players advance, creating a sense of achievement early on and progressively slowing down the rate of progression.

Resource Growth: in a city-building game, the rate at which a player’s population grows or resources accumulate may follow an exponential curve, encouraging long-term strategic planning.

Logarithmic Curves

Diablo III, the effectiveness of certain character attributes, such as critical hit chance or damage reduction, diminishes logarithmically. Each additional point invested in these attributes provides less of a benefit compared to the previous points, encouraging players to diversify their character builds.

Diminishing Returns: In games where players can increase their character’s attributes or abilities, the benefits gained from each additional point invested may decrease logarithmically. This encourages players to diversify their investments rather than focusing solely on one aspect.

Difficulty Adjustment: Logarithmic curves can also be applied to difficulty adjustment, where the rate of increase in challenge diminishes over time. This can help prevent players from becoming overwhelmed by steep difficulty spikes as they progress through the game.

Logarithmic Curves


The Witcher 3: Wild Hunt, player engagement can be modeled using an S-curve. Initially, players may take some time to become familiar with the game mechanics and story. However, as they delve deeper into the game world, explore its vast landscapes, and uncover its rich narrative, engagement accelerates rapidly until reaching a peak, where players may experience a sense of completion or satisfaction after completing the main storyline and major side quests.

Player Engagement: S-curves, which combine elements of both exponential and logarithmic growth, are often used to model player engagement over time. Initially, engagement may increase slowly, then accelerate rapidly as players become more invested in the game. Eventually, engagement may plateau or decline as players reach a saturation point or complete the game’s content.

Curves help you fine tune your game design elements.