The morning coffee is a sacred drink. Get it right and you’re set for the day, but if it’s wrong the hours stretch ahead of you. If your drink of choice is an espresso, you’re probably used to variation between your brews.

However, a study published in the journal Matter by a multi-disciplinary team from four countries has used mathematical modeling to help produce a more consistent espresso. The answer? Fewer coffee beans, ground more coarsely, and less water use.

As Dr Jamie Foster, a mathematician from the University of Portsmouth and co-author of the research, explained: “The conventional wisdom is that if you want a stronger cup of coffee, you should grind your coffee finer. This makes sense because the finer the grounds mean that more surface area of coffee bean is exposed to water, which should mean a stronger coffee.”

Not only are coffee beans ground finely, but current brewing techniques rely on a relatively large mass of coffee beans, around 20 grams (0.7 ounces), to make an espresso shot.

In practice, the team found that this method resulted in clogging of the coffee bed – what you find in the basket of an espresso machine – inhibiting the water’s passage. This spells bad news for a multitude of reasons. The amount of coffee dissolved in the water (extraction yield) is reduced, leading to a waste of raw material and a variation in taste.

To find a solution, the team started by creating a mathematical model for a single grain of coffee. The extraction yield for the whole brew relies on modeling the extraction of millions of individual grains, which are placed irregularly on the coffee bed. Add to that the variability in the water pressure as it flows through the coffee, and the team had a real problem on their hands.

In fact, Foster remarked that “you would need more computing power than Google has to accurately solve the physics and transport equations of brewing on a geometry as intricate as a coffee bed.” To simplify the equations, the researchers borrowed modeling methodologies from electrochemistry. Likening how caffeine dissolves out of coffee beans to how lithium ions are transported between the electrodes of a battery proved successful for the team.

Coupling the maths with many shots of espresso, the researchers reached their conclusion. “One way to optimize extraction and achieve reproducibility is to grind coarser and use a little less water, while another is to simply reduce the mass of coffee," said Dr Chris Hendon (aka Dr Coffee), a computational chemist at the University of Oregon and co-author of the paper.

When the findings were put into practice at a small US coffee shop, the new recipe was found to save them thousands of dollars every year. If applied to the whole of the US coffee industry, the total savings could stand at $1.1 billion each year.

“A good espresso beverage can be made in a multitude of ways,” Hendon concluded. “The point of this paper was to give people a map for making an espresso beverage that they like and then be able to make it 100 times in a row.”