SOME OF THE RECIPES in “Liquid Intelligence,” the new cocktail book from food-science authority Dave Arnold, require more commitment—or at least more gear—than one would expect from the average home bartender. For instance, Mr. Arnold, who helms high-tech Manhattan bar Booker and Dax for the Momofuku restaurant group, offers advice on clarifying juice with a centrifuge and installing a carbon dioxide tank under your kitchen sink.  But when he turns to the fundamental science of a drink, his observations offer insight to anyone with a cocktail shaker and a few basic ingredients. His most actionable conclusion: All good mixed drinks consist of a balance of basic elements that is wholly predictable, and therefore easy to duplicate—and riff on.  When Mr. Arnold tallied up the quantities for his recipes, he found that drinks made in the same manner call for the same ratios of booze, acid, sugar and dilution. Blender drinks had the lowest alcohol by volume, the highest dilution and a relatively high proportion of acid. “Built” drinks, meanwhile—as in an Old Fashioned served straight over ice—contained twice as much alcohol and no acid at all.  From there, Mr. Arnold found that as long as he stuck to the ratios, he could create new drinks without even tasting them. “Once you calculate what the acid and sugar levels are of all the various ingredients, and how much different methods of making drinks dilute them,” he said, “you can take almost any ingredient list you want and make it conform to a particular style.”  You could make a daiquiri-like quaff using tequila and green chartreuse in place of rum, as long as you conformed to the ratios, balancing the alcohol with optimal amounts of acid and sweetener. Or, turn a stirred Manhattan into a frozen beverage, because you know how much dilution and acid it takes to make a blender drink taste good.  For amateurs looking to get creative with boutique spirits, Mr. Arnold’s data is a blessing. In “Liquid Intelligence,” he provides the formulas not only for the broader drink categories, but also for dozens of individual drinks, classic and new. Crucially, he also provides data on acid, alcohol and sugar content in standard mixers, liquors, bitters and citrus juices—the key to swapping in one ingredient for another and inventing new cocktails ad infinitum.  Yet Mr. Arnold would be the first to tell you that the human touch—not to mention experience behind the bar—is still important. His research “will only give you the backbone of the drink,” he writes in “Liquid Intelligence.” “All the math in the world won’t help you if you can’t put good flavors together.”  How It Works: Drinks in this category are often sours, because the citrus juice in sour drinks promotes frothy texture when shaken. The following drink also employs another of Mr. Arnold’s tricks: using frozen juice instead of liquid to inhibit dilution, which makes for a more intense flavor overall.  18.6% alcohol by volume | 5.9 grams sugar | 0.32% acid  Several hours before you make the drink, freeze two 1¼ ounce cubes of strained coconut water. Combine 1½ ounces peaty Scotch, ½ ounce Cointreau, ¼ ounce strained fresh lemon juice and a pinch of salt in a metal shaker. Add the 2 coconut-water ice cubes and shake until they turn to slush, there are no large particles left and your shaker is very cold. Strain through a cocktail strainer into a chilled coupe. Twist a slice of orange peel over the top of the drink, then wipe the interior rim of the glass with the fruit side of the peel and discard. Garnish with 1 star anise pod.  How It Works: Stirred drinks require less sugar by volume than blended or shaken drinks because they aren’t as cold—the warmer a drink, the sweeter it tastes. In this case, instead of stirring each drink individually, Mr. Arnold stirs a frozen batch of base with ice water.The result is as easy to drink as it is to prepare for a crowd.  26% alcohol by volume | 3.2 grams sugar | 0.12% acid  Combine 14 ounces Rittenhouse rye, 6¼ ounces Carpano Antica Formula vermouth, ¼ ounce Angostura bitters in a clean 1 liter plastic bottle. Squeeze the excess air out of the bottle, cap it, and put it in the freezer for a minimum of 2 hours. To make the drink, in a chilled pitcher combine the cocktail base from the freezer with 10½ ounces waterthat has been chilled with ice. Stir briefly, then pour into chilled coupes and add a garnish of your choice, such as a strip of orange peel.  How It Works: Built drinks—straight spirits and a tiny bit of sweetener poured directly over rocks in the glass—usually contain little acid, said Mr. Arnold. Because dilution affects the way acids and sugars work together, the drink wouldn’t taste balanced once the ice melted. Here he uses a spicy coriander syrup instead to add complexity to what is typically a very straightforward drink.  32% alcohol by volume | 7.7 grams sugar | 0% acid  Make coriander syrup: Blend 1½ cups coriander seed and 2½ cups filtered water until seeds are well broken. Add to a pot with 2⅓ cups granulated sugar and ¾ teaspoon salt and heat to a simmer. Add scant⅛ cup crushed red pepper. Quickly strain syrup through a fine-mesh sieve. Place one large ice cube or 3 smaller ones in a rocks glass. Add 2 dashes Angostura bitters, 2 ounces Elijah Craig 12-year bourbon and 2¼ teaspoons (⅜ ounce) coriander syrup. Give the drink a brief stir. Twist a slice of orange peel over the top of the drink, then wipe the interior rim of the glass with the fruit side of the peel and drop peel into drink.  How It Works: Blender cocktails illustrate Mr. Arnold’s “fundamental law of traditional cocktails”: The colder the drink, the lower the alcohol, because melting ice both cools and dilutes. These slushy vermouth charmers—served side by side—have very low alcohol by volume, around 14%.  14.4% alcohol by volume | 8.4 grams sugar | 0.74% acid  The day before you plan to make the drinks, combine 5½ ounces Carpano Antica Formula vermouth, 1½ ounces vodka that is 40% alcohol by volume, 2½ ounces filtered water, and 2 pinches of salt in Ziploc bag. Squeeze all air from the bag and freeze. To make the drink, put the mix directly from the freezer into a blender and add ¾ ounce strained fresh lemon juice. Blend to a slush, and serve by itself or with the Ivory.  13.9% alcohol by volume | 7.9 grams sugar | 0.81% acid  The day before you plan to make the drinks, combine 5½ ounces Dolin Blanc vermouth, 1 ounce vodka that is 40% alcohol by volume, 2 ounces filtered water, and 2 pinches of salt in a Ziploc bag. Squeeze all air from the bag and freeze. To make the drink, put the mix directly from the freezer into a blender and add ¾ ounce strained fresh lime juice. Blend to a slush, and serve by itself or with Ebony.
Acquire the codes for classic drinks, and you can improvise infinitely (without wasting a drop). Dave Arnold of high-tech Manhattan cocktail bar Booker and Dax provides the standard ratios for shaken, stirred, built and blender drinks—and recipes for each that any home bartender can pull off.