Mastering the Learning Curve: Formula, Theory, and Application

The phrase "learning curve" often describes the difficulty of acquiring a new skill. However, the learning curve is a well-defined theory used by learning and development teams to improve knowledge retention and skill development. The learning curve formula provides a measurable way to understand the time it takes to master a task.

Generalized vs. Measured Learning Curves

The term "learning curve" is used in two different contexts:

Generalized: This refers to the common understanding of the time it takes to learn a challenging task or skill.
Measured: These learning curves use a mathematical formula to calculate proficiency in a task.

A Brief History of the Learning Curve Theory

The concept of the learning curve dates back to the 1880s.

1885: Dr. Hermann Ebbinghaus introduced the idea of a learning curve while developing his forgetting curve theory, which aimed to understand how people retain and lose information. After evaluating his own memory over time, he formulated a graph to demonstrate the rate of lost information. After seven days that figure plunged dramatically to 10%. The foundations of modern microlearning theory are very much based on Ebbinghaus’ memory studies. The principle of repetitive learning in small chunks to maximise retention has to be proven quite effective.
1934: Arthur Bills explored the learning curve in his paper "General Experimental Psychology," describing it as a graphical representation of efficiency improvement rates on a given task.
1936: T.P. Wright developed the basis for the modern learning curve formula, called the "Cumulative Average Model" (or "Wright's Model"), in his paper "Factors Affecting the Cost of Airplanes." Wright observed that the cost of building airplanes decreased as production performance increased. Wright described a basic theory for obtaining cost estimates based on repetitive production of assemblies.

The Core Concept of the Learning Curve Theory

The learning curve theory posits that the more a person practices a task, the better they become at it, leading to lower training costs and higher output over time. The overall theory suggests that as the number of attempts to complete a task increases, the time required to complete the task decreases. It is recognized that repetition of the same operation results in less time or effort expended on that operation. For the Wright learning curve theory, the underlying hypothesis is that the direct labor man-hours necessary to complete a unit of production will decrease by a constant percentage each time the production quantity is doubled. If the rate of improvement is 20% between doubled quantities, then the factor known as the learning percent, would be 80% (100-20=80). While the learning curve emphasizes time, it can be easily extended to cost as well.

However, the relationship between practice and performance is not linear. There will be periods where a small amount of practice yields significant improvement, while other periods may require many hours of work for only minor improvements.

Read also: Understanding PLCs

Types of Learning Curves

There are several types of learning curve models, each representing different patterns of skill acquisition:

Diminishing-Returns Learning Curve: The rate of progression increases rapidly at the start of learning and decreases over time. This describes tasks that are easy to learn and rapidly progressing skills. Once a learner obtains proficiency, the progression levels off (a plateau).
Increasing-Returns Curve: The rate of progression is slow at the start and rises over time until full proficiency is achieved. The initial cost of slow learning is quickly returned upon reaching the high-efficiency phase. Examples of the increasing returns curve include learning to navigate an internal CRM or how to communicate with each of your organisation’s high-value clients.
"S" Curve (Increasing-Decreasing Return Learning Curve): This is the most commonly cited model. Learners initially have slow improvement progression. However, as they complete a task over time, they experience a rapid improvement in proficiency until the skill is acquired, at which point performance flattens. The S-curve is aptly applied to more complex, scalable workplace learning, such as learning to navigate leadership positions, from team leader or supervisor roles to departmental managers, and C-suite positions. Characteristics of this curve are a slow learning process, followed by an increase in proficiency as the learner becomes more knowledgeable and efficient.
Complex Learning Curve: This model is designed to map more complicated learning patterns and requires more detailed progression tracking. The complex learning curve model looks different for each activity, individual, or group. The third stage of the complex learning curve tends to demonstrate that learner knowledge is plateauing. Think about performing medical diagnoses on patients. Procedures and treatments evolve. The learning experience is a journey. One that requires a commitment to continuous improvement.

Benefits of the Learning Curve Model

The learning curve model helps monitor company performance and identify areas for improvement:

Cost Reduction: As employees or processes become more efficient, the time to complete tasks decreases, reducing labor costs. This means less time to complete tasks and an overall reduction in labour costs. But that’s not it. It’ll also optimise valuable resources like time, leading to reduced production costs.
Improved Output Quality: With increased experience, workers better understand their tasks, leading to fewer errors and higher quality products or services.
Skill Development: The learning curve model emphasizes continuous improvement and a culture of learning. As colleagues become more skilled, they become more valuable. The learning curve model supports this, ensuring that everyone can optimise their skills.
Predictable Performance Metrics: The learning curve model helps establish predictable performance improvement patterns, allowing leaders to measure training effectiveness. This predictability is valuable for planning and forecasting. This formula can be used as a prediction matrix to forecast future performance.
Risk Mitigation: Organizations learn to identify and avoid potential risks based on past experiences. These insights allow organisations to better forecast and plan for the future. Why? People learn to anticipate risk, developing strategies and contingency plans based on previous experience. This transcends new process introduction, commercial disruption, and even some market volatility.

Limitations of the Learning Curve Model

Limited Application: The learning curve model is most effective in environments where tasks are repetitive and consistent over time. In industries or job roles where tasks are highly variable or require significant creative or adaptive work, the benefits of the learning curve may be less pronounced.
Additional Analysis Required: If a learning curve model fails to show the expected results, additional analysis might be required.

Applications of the Learning Curve Model

L&D teams can use the learning curve model to determine the time needed for a person (or group of people) to master a new skill or process.

Project Management: Teams become more proficient by processing repeated tasks or similar projects. As the team gains experience, they develop more efficient processes and problem-solving skills. Let’s say that you have a bespoke HR platform that everyone has access to. Experience is the name of the game. If you’ve requested annual leave ten, fifteen, a hundred times before, you’ll be able to request it in seconds. You’re reaching, or have reached, the top of the learning curve.
Manufacturing Costs: The learning curve can track a workforce’s performance with its manufacturing costs by replacing "performance" and "number of attempts" with total production in units or cost per unit. Organizations can predict this reduction in per-unit cost by modeling the change with the learning curve, considering labor costs and employee training. Initially, the product may reach the market at a higher price point because of the high per-unit cost to produce a good.
Employee Onboarding and Training: L&D teams are tasked with accelerating the time-to-productivity for new hires.
New Technology Implementation: Introducing new technology involves multiple learning curves. Initially, employees may struggle using the new systems, reducing productivity. Over time, as they become more familiar with the technology, their proficiency improves.
Medical Procedures: Surgeons may take longer to perform a procedure initially, but their speed and efficiency improve as they repeat it, often leading to better patient outcomes. Think about performing medical diagnoses on patients. Procedures and treatments evolve. The learning experience is a journey. One that requires a commitment to continuous improvement.

Accelerating the Learning Curve

L&D teams and educational instructors can accelerate the learning curve with the right approach:

Set Measurable Outcomes: Set long and short-term measurable outcomes to evaluate employee performance, training effectiveness, and task mastery.
Efficient Onboarding: Create an efficient onboarding process to help new hires acquire competence and remain confident.
Personalized Learning Programs: Create personalized learning programs with training content tailored according to individual job roles and learning types.
Alternative Training Methods: If the data from the learning curve shows that the current training process is not working, explore alternative employee training methods.
Informal Learning: Often, a formal employee training program does not impart all the knowledge and information employees need.
Digital Adoption Platforms (DAPs): A DAP integrates with existing digital tools to provide automated, personalized training in the flow of work. DAPs assign each learner a contextual task list containing interactive walkthroughs. Walkthroughs are step-by-step prompts that guide users through specific tasks or processes.
Microlearning Platforms: Microlearning software provides bite-sized learning experiences for employees. The foundations of modern microlearning theory are very much based on Ebbinghaus’ memory studies. The principle of repetitive learning in small chunks to maximise retention has to be proven quite effective.
Establish a Time Frame: Establish a time frame for achieving the set of desired outcomes to understand whether or not your training methods are providing the expected results.
Continuous Monitoring: Monitor the learning curve year-round, not just during times of change or when training difficulties arise.
Guidance Analytics: Use guidance analytics to track how employees engage with in-app guidance and support.

The Learning Curve Formula: Wright and Crawford Models

In the manufacturing context, the experience curve or learning curve refers to the way in which the efficiency of processes increases over time as the units are produced. The learning rate or learning curve coefficient refers to the amount of money that is saved every time production is doubled.

Read also: Learning Resources Near You

For instance, let's say the time it takes to produce a given number of units falls by 20% for every double in production numbers; as such, the learning curve percentage is 80%.

Two models can be employed to determine how much time it will take to manufacture N units at a given learning rate and the time required to produce the first unit: the Wright Model and the Crawford Model. The equations associated with each model are similar. If A represents the time taken to manufacture the first unit, the learning curve factor is b ( b = ln(learning percentage / 100) / ln(2) ), then the cumulative total time (CTN) required to manufacture N units is as follows:

NASA provided the following guidelines in relation to the learning curve:

If the process involves 75% hand labor and 25% machine labor, the learning percent is in the region of 80%.
If the process requires equal hand labor and machine labor (50% each), the learning percent is in the region of 85%.
If the process involves 75% machine labor and 25% hand labor, the learning percent is in the region of 90%.

The closer the learning percent moves toward 100%, the less significant the effects of experience.

The calculator uses the learning curve to estimate the unit, average, and total effort required to produce a given number of units. Effort can be expressed in terms of cost, man-hours, or any other measure of effort. The learning percent is usually determined by statistical analysis of actual cost data for similar products.

Read also: Learning Civil Procedure

The calculator can be set to compute the Wright learning curve (generally large processes and complicated operations) or the Crawford learning curve (considered as less technical than the Wright model). The user is required to enter the effort in terms of cost or man-hours required to produce the first unit, the total number of units, and the learning percent.

Stages of Competence

This is represented by a simple line graph, which represents the five different competency stages. The theory proposes that a learner’s efficiency improves over time. The more you learn and practice the knowledge acquired, the more competent you become, until you finally reach expert levels.People learn at their own pace and in their own way.The primary learning phase is unconscious incompetence. They may not necessarily recognise the deficit, or even deny the usefulness of the skill. At this stage, the learner is aware of the skill and knowledge gap. And understands the importance of acquiring what they’re lacking. Learning begins at this stage. Schools in session. The learner knows how to perform the task or apply the skill. But, at this stage, this process requires a thoughtful approach and more experience for it to become second nature. The penultimate stage on the learning curve sees the learner able to perform the skill automatically and unconsciously, without thinking too much about it. Upon reaching the pinnacle of the learning curve, people are willing and able to reflect on what they have learned, understand the underlying systems of the skill, and offer constructive feedback to others yet to reach this stage. The student has become the master.

tags: #learning #curve #calculator #formula