Getting everything right all of the time might sound like the ideal scenario, but such a perfect success rate can mean you're not actually learning anything new. 

To make sure you're learning at the optimal rate, new research finds you should be aiming to fail around 15 percent of the time – or 15.87 percent of the time, to be exact.

These findings could have implications for training courses, teaching in classrooms, and everywhere that learning happens. It's that sweet spot between finding something too easy and too difficult.

"These ideas that were out there in the education field – that there is this 'zone of proximal difficulty', in which you ought to be maximising your learning – we've put that on a mathematical footing," says psychologist Robert Wilson from the University of Arizona.

To come up with the 15/85 percent split, Wilson and his colleagues ran a series of machine learning experiments. The experiments were designed to teach computers how to do simple tasks, such as putting patterns into categories, or recognising the difference between odd and even numbers.

The computer systems learnt fastest, the researchers found, when they were making the right call 85 percent of the time. That figure seems to match up with previous studies carried out with animals, too.

According to the team, this sort of split is most likely to apply to humans when it comes to perceptual learning, where we gradually learn through experience and examples (not unlike a machine learning algorithm).

Take a radiologist learning to tell the difference between images of tumors and non-tumors, for example: at a level that's too easy, the radiologist would identify 100 percent of the images correctly. At a level that's too difficult, that might drop to somewhere around 50 percent.

But if the radiologist is correctly identifying 85 percent of the images and making mistakes with the other 15 percent, that could be the spot where the learning rate is the fastest.

Of course, as we gain more knowledge, that difficulty level needs to be adjusted again, to keep the learning task at just the right level in terms of how challenging it is.

The researchers are also keen to point out that their study only covers basic, binary choices – it doesn't necessarily follow that we should all be aiming for an 85 percent grade in our future exams.

More research is going to be needed to figure out how this applies more broadly to education, outside of computer algorithms. For now though, it's a good starting point for finding that balance between something that's so easy we get bored, and so difficult we give up – a quandary that educators have been thinking about for a long time.

"If you are taking classes that are too easy and ace-ing them all the time, then you probably aren't getting as much out of a class as someone who's struggling but managing to keep up," says Wilson.

"The hope is we can expand this work and start to talk about more complicated forms of learning."

The research has been published in Nature Communications.