Espresso is the least reproducible common preparation in coffee. Two shots from the same machine, the same beans and the same barista, minutes apart, can taste noticeably different. The industry's answer for decades was craft: better technique, better tamping, better calibration by taste. In 2020 a group of mathematicians, physical chemists and coffee professionals took a different approach and tried to model the thing properly.
What the study did
Cameron and colleagues published the work in Matter[1], a Cell Press materials journal, under the title Systematically Improving Espresso. They built a mathematical model of the extraction process, treating the coffee puck as a porous bed that water is forced through under pressure, and then validated the model against experimental data drawn from on the order of a thousand espresso shots.
The measure they tracked is extraction yield: the percentage of the dry coffee mass that ends up dissolved in the drink. It is the standard quantitative measure of extraction, and the specialty industry has long treated a range of roughly 18 to 22% as the target zone for filter coffee, a convention originating in work done at MIT in the 1950s relating dissolved solids to cup quality. Below the range, coffee tastes sour and underdeveloped; above it, bitter and astringent.
The counterintuitive result
Standard barista reasoning says that a finer grind exposes more surface area, so finer grinding extracts more. The model and the experiments both found that this stops being true past a point.
Why channelling happens at all
It is worth spelling out the physical picture, because it explains several things baristas already know by feel. Water forced through a bed of coffee at nine atmospheres will take the path of least resistance, as any fluid will. If the bed is perfectly uniform, resistance is uniform and flow is even. If any region is slightly less dense, water moves through it faster, which washes away fine particles, which lowers resistance further, which draws still more water.
That is a positive feedback loop, and positive feedback loops amplify small initial differences into large final ones. A barely detectable inconsistency in how the grounds were distributed becomes a channel carrying a disproportionate share of the water.
Fine grinding makes this worse for two reasons. It raises overall resistance, which increases the pressure differential driving flow into any weak point. And it produces more fines, the very small particles that migrate under flow and both clog some regions and evacuate others.
This also explains why distribution technique matters so much, and why practices like stirring the dry grounds before tamping have become standard in specialty cafes. They are attempts to remove the initial non-uniformity before the feedback loop has anything to amplify.
Extraction yield rose as grind got finer, peaked at a middling setting, and then fell off again at the finest settings. The explanation the authors gave is that at fine grinds, flow through the puck becomes inhomogeneous. Instead of water moving evenly through the coffee bed, it finds and widens preferential paths, a phenomenon baristas call channelling. Water races through the channels, over-extracting the coffee immediately around them while barely touching the rest of the bed.
That produces two problems at once. The average extraction yield drops, because most of the coffee is under-extracted. And reproducibility collapses, because exactly where channels form is essentially random from shot to shot. This is the mechanism behind the everyday frustration: the inconsistency is not sloppy technique, it is a fluid dynamics instability that fine grinding makes more likely.
What they recommended instead
The practical conclusions ran against convention on three fronts. Grind coarser than the point where yield peaks would naively be expected. Use less coffee in the basket. And shorten the extraction time substantially, from the conventional 25 to 35 seconds down toward 10 to 15 seconds.
The logic connects: a coarser grind and a smaller dose both reduce resistance and make flow through the bed more even, which raises the average yield and makes it repeatable, and the shot finishes faster because there is less resistance. The authors framed one route as grinding coarser and using slightly less water, and another as simply reducing the mass of dry coffee.
The commercial implication is what made the paper widely read outside academia. A cafe that can pull a repeatable, well-extracted shot from less coffee is buying fewer beans for the same number of drinks. Across a busy shop, that difference is real money, and the paper drew attention from cafe operators for that reason rather than for the mathematics.
How much caffeine is actually in a shot
A question that follows naturally from extraction science, and that people ask constantly, is how much caffeine ends up in the cup. The answer is less intuitive than expected, because caffeine is highly water-soluble and extracts early and almost completely.
That means extraction yield and caffeine content are only loosely related. A short, coarse, fast shot will still have pulled out most of the available caffeine, because caffeine comes out well before the compounds that determine whether the shot tastes balanced or bitter. Changing grind and time changes flavour far more than it changes caffeine.
What does change caffeine is the dose of dry coffee and the species. The FDA[2] puts an 8-ounce cup of brewed coffee at roughly 95 mg and a single espresso shot at roughly 63 mg, which surprises people who assume espresso is the stronger drink. It is more concentrated per millilitre and smaller in total, so a mug of drip coffee usually delivers more caffeine than a single shot.
Robusta roughly doubles the caffeine of Arabica at the same dose, which is why espresso blends containing Robusta hit harder, and why the species question covered in our article on Philippine coffee varieties has a practical dimension beyond flavour.
Reading it with appropriate caution
A few caveats matter. Extraction yield is a measure of how much coffee dissolved, not a measure of whether the result tastes good. Those correlate, which is why the industry uses the metric, but they are not identical, and a highly extracted shot in the target range can still taste unpleasant depending on the bean and roast. The paper is about reproducibility and efficiency, and does not claim to have found the best-tasting espresso.
It is also worth noting how the study was validated, because it is unusual for coffee research. Roughly a thousand shots were pulled and measured, which is a scale of experimental data that the coffee industry rarely generates and almost never publishes. Much of what passes for knowledge in coffee is accumulated craft experience, which is valuable but hard to distinguish from tradition. A model tested against a thousand measured extractions is a different kind of evidence.
There is also a real trade-off in shot style. Shorter, coarser-ground shots produce a different drink from the long, fine, slow shots much of specialty coffee has favoured, with different body and texture. Some of what the model treats as inefficiency is what a particular cafe considers its house style. And a single modelling paper, however well constructed, does not overturn practice on its own.
It is worth noting that the paper's recommendations were framed as a route to reproducibility and efficiency rather than as a claim about the ideal cup. A cafe optimising for consistency across two hundred shots a day and a person optimising for the single best shot on a Sunday morning are solving different problems, and the model speaks more directly to the first.
What is not really in dispute is the diagnosis. Channelling at fine grind settings is a genuine physical phenomenon, it degrades both yield and consistency, and it explains the variability that baristas have worked around by feel for a century.
The other coffee physics result worth knowing
Coffee has contributed one genuinely famous finding to physics, and it has nothing to do with brewing. When a drop of coffee dries on a table, it leaves a dark ring at the edge rather than a uniform stain. Deegan and colleagues explained why in Nature in 1997[3], in a paper that has become one of the more heavily cited in soft matter physics.
The mechanism is contact line pinning. The edge of the drop sticks to the surface and cannot retreat as the drop evaporates. Because evaporation is fastest at the edge, liquid must flow outward from the centre to replace what is lost there, and that outward capillary flow carries suspended particles with it and deposits them at the rim. The team predicted a distinctive power-law growth of the ring mass over time, independent of the particular substrate, carrier fluid or suspended solid, and confirmed it experimentally by tracking colloidal spheres in evaporating droplets.
The result matters well beyond coffee. Anything involving particles deposited from a drying droplet, including inkjet printing, DNA microarrays, medical diagnostic assays and printed electronics, has to contend with the coffee-ring effect, and a substantial literature exists on suppressing it. That a stain on a cafe table produced a general physical law is a reasonable illustration of how ordinary the origins of good science often are.
It is also a nice illustration of how physics finds its problems. Deegan and colleagues were not trying to solve anything about coffee; they were interested in a general question about how particles deposit from evaporating droplets, and coffee provided a convenient and universally familiar example. The resulting paper is one of the most cited in soft matter physics, and the everyday phenomenon it explains is visible on any cafe table that has not been wiped.
What a home brewer can take from this
Three things generalise beyond espresso machines. First, evenness of extraction matters more than intensity of extraction. Most bad coffee is unevenly extracted rather than simply under- or over-extracted, which is why distributing grounds evenly and wetting them uniformly changes the cup so much.
A fourth, less obvious one: consistency of input beats optimisation of technique. A model that says extraction quality collapses when flow becomes uneven implies that the highest-value habits are the boring ones, weighing the dose, keeping water temperature stable, distributing the grounds evenly, rather than the dramatic ones.
Second, finer is not automatically stronger. If your espresso tastes weak and sour despite a very fine grind and a long pull, the likely problem is channelling, and the counterintuitive fix is to grind coarser.
Third, grind consistency is the variable that most rewards spending money. A grinder producing a narrow particle size distribution reduces the fines that clog a puck and create channels. This is why grinder quality is generally considered more consequential than machine quality, and our grinder guide covers what that means in practice. For the wider brewing picture, our brewing method guide compares what each method does to the cup.
This is the single most common piece of advice given to people upgrading their home setup, and the extraction model explains why it is correct rather than merely conventional.
The summary
A mathematical model validated against roughly a thousand shots found that espresso extraction yield peaks at a middling grind and declines at finer settings, because fine grinding induces uneven channelled flow that wastes coffee and destroys consistency. The recommended response was to grind coarser, dose less, and pull shorter shots, which produces repeatable extraction using less coffee. Separately, the coffee-ring effect, explained in a 1997 Nature paper, remains coffee's best-known contribution to physics.
It is a rare case of a mathematical model producing advice a barista can act on the same afternoon.
Whether a given cafe should follow it depends on whether they are optimising for consistency or for a particular house style.
Both are legitimate goals, and the paper is honest that it addresses the first.
Both results share a quality worth admiring: they take something everyone has seen and explain it well enough to predict it.
For a home espresso user, the most useful single sentence is this: if the shot tastes weak and sour despite a fine grind and a long pull, grind coarser rather than finer.