Learning curve

A learning curve is a graphical representation of the relationship between how proficient people are at a task and the amount of experience they have. Proficiency (measured on the vertical axis) usually increases with increased experience (the horizontal axis), that is to say, the more someone, groups, companies or industries perform a task, the better their performance at the task.

The common expression “a steep learning curve” is a misnomer suggesting that an activity is difficult to learn and that expending much effort does not increase proficiency by much, although a learning curve with a steep start actually represents rapid progress. In fact, the gradient of the curve has nothing to do with the overall difficulty of an activity, but expresses the expected rate of change of learning speed over time. An activity that it is easy to learn the basics of, but difficulty to gain proficiency in, may be described as having “a steep learning curve”.

A learning curve is a mathematical concept that graphically depicts how a process is improved over time due to learning and increased proficiency. The learning curve theory is that tasks will require less time and resources the more they are performed because of proficiencies gained as the process is learned. The learning curve was first described by psychologist Hermann Ebbinghaus in 1885 and is used as a way to measure production efficiency and to forecast costs.

A learning curve is typically described with a percentage that identifies the rate of improvement. In the visual representation of a learning curve, a steeper slope indicates initial learning that translates into higher cost savings, and subsequent learnings result in increasingly slower, more difficult cost savings.

The Learning Curve Theory

Ebbinghaus’ forgetting curve

While the term “learning curve” came into use in the early 20th century, Dr. Hermann Ebbinghaus described this theory as early as 1885.

He mostly was focusing on memory studies and developed a forgetting curve theory. This theory helps us to understand how our memory works, and retains information, relating to specific things people attempt to learn.

The modern Microlearning theory is based on Ebbinghaus memory studies. Nowadays it helps us understand when and why we forget certain information and how we can tackle this.

Wright’s experience curve

This is the basis for the learning curve formula, the “Cumulative Average Model” (or “Wright’s Model”), which was described by T.P. Wright in 1936 in his work “Factors Affecting the Cost of Airplanes“, after realizing that the cost of aircraft production decreased with the increase in production performance. There are currently different variations of the original formula used today in specialized applications, but the idea remains familiar to the original formula.

The experience curve theory states that the effort to complete a task should take less time and effort the more the task is done over time.

If one were to plot the repeated attempts of a learner against the time taken to complete the attempt, a pattern can be identified indicating that the task takes less time as the learner gains more experience via repeated attempts. The theory can also be expressed as a mathematical function that can be used as a prediction tool.

Learning curve formula

Y = aX^b

Where:

Y is the average time over the measured duration

a represents the time to complete the task the first time

X represents the total amount of attempts completed

b represents the slope of the function

Learning curve models and examples

Although the theory states that more attempts = a decrease in time, it does not always work out that way. Many factors can impact the end-results, resulting in a variety of different learning curve shapes.

Here are four common types of a learning curve and what they mean:

1. Diminishing-Returns Learning Curve

The rate of progression increases rapidly at the beginning and then decreases over time.

This describes a situation where the task may be easy to learn and progression of learning is initially fast and rapid.

Progression levels off as the learner obtain full proficiency. This could be described as a plateau, where the individual is no longer progressing. It could signal that the learner has reached a limit in their ability or that a transition may be occurring. It could also mean that the individual has lost motivation or is fatigued.

2. Increasing-Returns Learning Curve

The rate of progression is slow at the beginning and then rises over time until full proficiency is obtained.

This model describes a situation where perhaps a complex task is being learned and the rate of learning is initially slow.

3. Increasing-Decreasing Return Learning Curve (the S-curve)

This model is the most commonly cited learning curve and is known as the “S-curve” model.

It measures an individual who is new to a task. The bottom of the curve indicates slow learning as the learner works to master the skills required and takes more time to do so.

The latter half of the curve indicates that the learner now takes less time to complete the task as they have become proficient in the skills required. Often the end of the curve begins to level off, indicating a plateau or new challenges.

4. Complex Learning Curve

This model represents a more complex pattern of learning and reflects more extensive tracking.

1. The beginning of the curve indicates that learning is initially slow.
2. The second stage of the curve shows an increase, which indicates that the learner is becoming proficient in the skill.
3. The third stage of the curve indicates that the learner is plateauing in his proficiency once the learner feels he has mastered the skill.
4. The fourth stage of the curve represents that the learner is actually still improving the skill.
5. The last stage of the curve represents the point at which the skill becomes automatic, muscle memory for the learner, often termed “over learning”.