Cocktail Calculus: The Structure Behind Every Recipe

A database of recipes

Dave Arnold built a database of classic cocktails and his own recipes and analysed each for alcohol, sugar, acidity and dilution. He found that every style, built, stirred, shaken, blended and carbonated, has clear and well-defined relationships between these values, whatever the flavours. Given a set of ingredients and a style, he can write a decent recipe by arithmetic without tasting, and he has tested this dozens of times with results that surprise him. He can, for example, take apple juice, bourbon, Cointreau and lemons and build a drink with the feel of a daiquiri by plugging in numbers; it will not taste like a daiquiri. He is unsure how he feels about that. The math does not replace a brain and a palate, bitterness is a wild card that is very hard to quantify, and some drinks are better with more or less sugar or acid than average.

The math will only give you the backbone of the drink—its structure.

The aromatics and flavours you choose are the soul of the drink, but the numbers are very useful for judging recipes and for writing your own.

How the numbers are written

• Sugar is given in grams per 100 ml, roughly the same as a percentage; weight-in-volume is the only sensible way to measure dissolved solids such as sugar.
• Acid is a simple percentage; at the low concentrations in drinks, usually about a tenth of the sugar level, the difference from grams per 100 ml is very small.
• Volumes are in ounces, at 30 ml to the ounce in his book, and in millilitres.
• Dilution is a percentage of the original recipe volume: 50 percent means every 100 ml of recipe is diluted with 50 ml of meltwater, for 150 ml of drink; 25 percent gives 125 ml.

Charts of typical values for classic cocktails are on pages 128 to 135 of the book and a list of the alcohol, sugar and acid of common ingredients on pages 136 and 137.

Why styles end up as they do

Ordered from most to least alcoholic, the styles are built, stirred, shaken, shaken with egg white, and blended and carbonated tied at the bottom. Apart from carbonated and egg-white drinks, the same order runs from warmest to coldest. That seems backwards, since strong drinks seem to need more chilling, and vodka shots are served very cold, but it follows from the Fundamental Law of Traditional Cocktails: a high-alcohol drink has less dilution, and because chilling and dilution are linked, it is also warmer. The nature of each style is built into the physics of chilling with ice, and Arnold notes that it is hard to say whether our tastes or the physics came first.

A drink with higher initial alcohol dilutes more per unit volume and gets colder, and the limiting cases are chilling juice with ice, which hardly dilutes, and chilling pure ethanol, which dilutes enormously and still always ends with more alcohol than diluted water does.

Sugar. Cold dulls sweetness, so colder shaken drinks carry more sugar than warmer stirred ones. Built drinks add the least sugar, but because they are hardly diluted, they often end up with more sugar per volume than stirred drinks.

Acid. Acid perception is less affected by temperature, and acid flavour fades more slowly than sugar as a drink is diluted. Highly diluted cold drinks, like blended drinks, therefore have less acid per unit of sugar than warmer, less diluted shaken drinks. Stirred drinks have less acid mostly because they are not meant to be tart, and built drinks have very little or none. Flavour concentration, how much sugar and acid there is relative to dilution, is lower in diluted drinks such as blended and carbonated ones.

The typical structure of each style

These guidelines come from forty-five classic cocktails plus ten of Arnold’s own carbonated and blender recipes; the numbers are typical ranges, not rules, with outliers ignored.

• Built. Almost entirely liquor, so the alcohol follows the base spirit. Because they must taste good across a range of dilutions, there is no good sugar-to-acid ratio, and they typically have little or no acid. Typical sugar is about 9.5 g/100 ml at the start and 7.6 at the end.
• Stirred. Some acidity but not tart, and the widest range of alcohol, 21 to 29 percent among sixteen drinks, with one outlier, the Widow’s Kiss, at 32 percent. The Negroni is the lowest in alcohol, which may be why it tolerates so many levels of dilution. The numbers assume a lively 15-second stir with 120 grams of 1.25-inch ice.
• Shaken. Often sours with about equal parts syrup and citrus juice. Simple syrup has ten times as much sugar per ounce as juice has acid, so most shaken drinks hold about ten times as much sugar as acid. Finished alcohol mostly floats between 15 and 20 percent, with initial sugar of 8.0 to 13.5 g/100 ml and acid of 1.20 to 1.40 percent. The volumes given are the actual size of the drink made, not what ends up in the glass, since holdback and pouring losses can take a quarter ounce or more. The assumption is a 10-second shake with 120 grams of 1.25-inch cubes.
• Shaken with egg white. A large egg white is about an ounce, so these drinks start an ounce more diluted. Their sugar-to-acid ratio is often higher, though overall sugar and acid are lower; initial sugar is 10.0 to 13.2 g/100 ml and acid 0.73 to 1.00 percent, and dilution 46 to 49 percent, lower than for plain shaken drinks because the starting alcohol is lower.
• Carbonated. Diluted before they are chilled, so there are no before and after numbers. Newer recipes float between 14 and 15 percent alcohol, with slightly lower sugar-to-acid ratios than shaken drinks.
• Blended. Very diluted, so slightly less acid per unit of sugar than shaken drinks; Arnold dissolves sugar into the booze to keep alcohol fairly high despite the dilution. The volumes quoted are the liquid only, and the poured drink also holds about 1.5 ounces of unmelted ice crystals.