“I know, this all seems like ‘Best in Show,’ ” says Ryan O’Donovan, an owner of Verve, referring to the faux documentary about dog shows. “It seems ridiculous. We’re trying to make it less ridiculous.”

Verve, where Mr. Baca is director of education, devotes 1,500 square feet to training. It’s part of what the cafe considers the “third wave” of the coffee movement — the first being campfire and drip coffee, the second the Starbucks revolution and the next understanding and evoking the complexity of coffee. Training, Mr. O’Donovan says, “is the nucleus of what we do.”

I show Mr. Baca what I’ve learned. He calls my first shot dry. He is being kind.

Mr. Baca asked me to bring my usual brand of coffee and makes a shot with it. It is not good. Lesson No. 1: coffee matters. Just because the bag says “fair trade” or “locally roasted” does not mean the highest-grade beans have been selected and put through meticulous roasting. We toss my $13-a-pound coffee in the trash. Then Mr. Baca provides a math lesson.

The essence of good espresso, of good coffee in general, revolves around three numbers: the amount of quality dry coffee used, the amount of time water flows through it and the amount of coffee that comes out the other end. When the ratio is right, the process extracts the best flavor. If it is wrong, the good flavor never surfaces or is watered down. A mistake in seconds or grams, I am coming to learn, is the difference between something wonderful and awful.

Mr. Baca explains that you have to experiment to find just the right balance of these three elements for each coffee machine and coffee grind, and then replicate them. He has tested the machinery at Sightglass and determined that we want to use 17 grams of high-end coffee and run water for 25 seconds to yield about 30 grams of coffee.