March Madness — the annual NCAA basketball playoff spectacle in which millions of us, firmly docked in front of the TV screen, consume 1,000 calories an hour while watching young athletes burn 12 calories a minute — begins in earnest this week. If you’re planning to participate in this national sit-in, you can drastically enhance the viewing experience by pondering the parabola.

It’s the elegant arched trajectory naturally formed by any projectile, from an artillery round to a tomato, moving in a gravitational field. Parabolas have been extensively studied since people started throwing stuff at each other, and they shape the outcome of many ballistic sports, such as baseball, golf, football, shot put and more. But they reach their apex in basketball, where field goals and free throws demand precision control of parabolas.

But not just any parabola. Success favors a fairly high arch. The ball must pass through the hoop with a little room to spare, and that limits the possibilities. The hoop is 18 inches in diameter, and the men’s ball is about 9.5 inches wide (women’s about 9.2). So if the men’s ball were thrown straight down from above — that is, at an angle of 90 degrees to the horizontal hoop rim, as in the classic Michael Jordan airborne dunk — there would be 4.25 inches of free space all around, a comfy margin.

But as the angle decreases and approaches the horizontal, the free space for a “nothing but net” shot gets much smaller. At 55 degrees, it’s about 2.5 inches. At 45 degrees, it’s down to 1.5 inches. And at 30 degrees, it’s basically impossible to get the ball straight into the basket, even with a full scholarship and more tattoos than a Hell’s Angels convention.

Not surprisingly, increasing the height at which the player launches the ball not only reduces the distance to the basket but raises the entry angle of the ball’s parabolic arch, allowing more free space. In a classic study in the 1980s, Peter Brancazio, then a physics professor at Brooklyn College, determined that adding 2 feet to the height at which a shot leaves the player’s fingers increases the success rate by a whopping 17 percent. No wonder you see so many jump shots.

But is there a launch angle that gives the maximum probability of a perfect telegenic swish?

Well, there are many different parabolas that will do the job, and the choice varies according to player height, personal preference and position on the court. But one way to decide, Brancazio wrote 25 years ago in Sport Science: Physical Laws and Optimum Performance, is to “consider the amount of force needed to launch the shot. It is to the shooter’s advantage to use as little force as possible,” he reasoned, because the less the force, “the more quickly and effortlessly (the ball) can be released.”