It's unlikely that mathematical formulas, percentages and laws of physics dance through your head as you rise up and shoot a jumpshot on the basketball court. But like virtually everything else in life, mathematics do play a role when it comes to shooting a basketball. You've probably just never realized it.
Ball-to-Basket Ratio
Anyone who has spent a significant amount of time playing basketball knows that if you're making 50 percent of your shots, you're doing quite well. Likewise, any veteran player has had days when there seems to be a lid on the basket; every shot feels great and looks spot-on when it leaves your hand, yet they continue to rattle out from inside the hoop and carom off of ifs edges.
So it may be difficult to believe that a regulation basket, 18 inches in diameter, is nearly large enough to accommodate two balls -- 9.5 inches -- at once. This fact makes shooting the ball through the basket seem a bit more easy than you would thought.
Arc
It's long been believed that the higher the arc you have on your jumpshot, the better chance it has of going in. And sports physicist Peter Brancazio proved exactly in researching his book, "SportsScience: Physical Laws and Optimum Performance."
Brancazio found that shooting the ball if a more flat-line manner basically eliminates the nearly-double hoop-to-ball size ration, costinh the shooter that advantage. He found that a 45-degree angle is optimal, though shorter players may see better results by adding even more arc to their shots because the shot originates from a lower plane.
Three-Pointers Vs. Two-Pointer
Everyone's played with a "chucker," the guy who does nothing but spot up behind the 3-point arc and lofts long balls at the hoop all day long, barely setting foot in the paint. But perhaps he knows something you don't.
To be awarded 3 points for a shot, a high school, college or rec league player must be standing behind the arc, which sits 19 feet, 9 inches from the hoop at all points. The shot is more difficult than the closer-range two-pointers and even the best jump-shooters tend to hover around a 40 percent success rate. But that's misleading.
If you attempt 10 two-point shots, you would need to make a nearly-impossible 90 percent of them to score 18 points. But if all 10 were 3-pointers, you'd need only to make 60 percent.
Shooting in Volume
Basketball teams have varying styles and strategies. Those with stout defenses but mediocre scoring abilities favor a slow-paced game, with fewer shot attempts. More skilled, speedy offensive teams like to get up as many shots as possible.
Math plays another role here, as players on teams with distinct shooting advantages are best-suited to take rapid shots. The more shots taken in the game, the more the odds favor the more skilled shooting team.
Shot Clock
In college and professional basketball, as well as some high school leagues, there's a shot clock. This limits the amount of time a team can possess the ball before shooting it; otherwise, they turn it over to the opponents.
Though often overlooked, the shot clock can play a crucial role in shooting success. When a player receives the ball late in the shot clock or over-dribbles the ball, wasting time, he's then often forced to take a rushed shot -- which is less likely to go in.
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