How difficult should a task be to maximize learning? If it's too easy, you're not gaining new skills. If it's too hard, you become frustrated and the feedback is too noisy to be useful. This isn't just an intuitive idea; there's a precise mathematical answer.

Research by Wilson, Shenhav, Straccia, and Cohen in 2019 pinpointed a specific sweet spot. They found that for learning systems that improve via gradient descent—a process relevant to both artificial and biological neural networks—the optimal rate of learning occurs when the error rate is just about 15%.

This principle applies specifically to binary classification tasks, where the outcome is either right or wrong. The derivation shows how the amount of information gained from an error, measured using Shannon information, is maximized at this specific difficulty level. Let's dig into why.

Learning is a process of updating an internal model of the world. When you practice a skill, your brain adjusts its neural connections based on the outcome. In machine learning, an algorithm adjusts its parameters. Both use a form of gradient descent, where the system makes small adjustments in the direction that reduces error.

Feedback is the engine of this process. A correct answer reinforces the current model, but an incorrect answer provides a crucial "error signal." This signal tells the system how and how much to change. If your accuracy is 100%, there is no error signal. You aren't learning; you are simply performing. The task is too easy.

Conversely, if the task is too difficult and your error rate is 50% or higher, the feedback becomes random noise. The system can't distinguish between a bad strategy and bad luck. The error signals are too chaotic to provide a clear direction for improvement. The 15% error rate is the point where the error signal is strongest and clearest, providing the maximum amount of useful information to guide the learning process.

This mathematical optimum provides a solid benchmark that complements psychological concepts you might already know. For example, Vygotsky's Zone of Proximal Development (ZPD) describes the space between what a learner can do unaided and what they can do with guidance. The 85% Rule gives us a precise target within that zone.

So, when designing a practice session for yourself or for others, aiming for that 15% error rate is a powerful strategy. It ensures the task is difficult enough to provide new information and drive adaptation, but not so hard that the feedback becomes meaningless. It's the most efficient point for building and refining skills.