Want to Win the NCAA Tournament? Learn Some Physics

03.09.2012 |

It’s March Madness time again, and the fate of millions of NCAA Tournament fans – and bracket sheets – will live and die with gut-wrenching, soul-sapping, last-second three-point shots and rimmed-out free throws.

How can a team increase its chances of winning the Big Dance? A sound knowledge of physics could be a start.

For the love of the game (and science), NC State engineers Chau Tran and Larry Silverberg took millions of basketball shots – OK, they had a computer simulate all the shots; imagine how sore their elbows would have been otherwise – and came up with two really important lessons.

Noonan … Miss it!

First, the engineers quantified the optimal conditions for making a free throw. They say that shooters should launch the shot with about three hertz of back spin, which is a fancy way of saying that the ball should make three complete backspinning revolutions before reaching the hoop. Back spin deadens the ball when it bounces off the rim or backboard, giving the ball a better chance of settling through the net.

Where to aim? The back of the rim, leaving close to 5 centimeters – about 2 inches – between the ball and the back of the rim. Aiming for the center of the basket decreases the probabilities of a successful shot by almost 3 percent.

The engineers say that the ball should be launched at 52 degrees to the horizontal. If you don’t have a protractor in your jersey, that means that the shot should, at the highest point in its arc to the basket, be less than 2 inches below the top of the backboard.

Free-throw shooters should also release the ball as high above the ground as possible, without adversely affecting the consistency of the shot; release the ball so it follows the imaginary line joining the player and the basket; and release the ball with a smooth body motion to get a consistent release speed.

The engineers didn’t include advice on how to stymie the spasms nerve-wracked players get – known in golf as the yips and in other sports as choking – when they’re on the free-throw line with a game hanging in the balance and 20,000 fans screaming at them to miss. But that’s not a physics thing and couldn’t be simulated.

Call the Bank

Bank shots can be up to 20 percent more effective than swish or direct shots from certain areas of the basketball court.

The engineers also came up with some advice on when basketball players should attempt to shoot a bank shot and when to try for a swish.

They found that, from certain areas of the court – at many angles inside 12 feet from the basket and on the “wings” between the three-point line and the free-throw lane – bank shots can be up to 20 percent more effective than swish shots. But forget about banking straight-away shots from more than 12 feet away – free throws, for instance.

They also found the optimal points on the backboard where the simulated baskets were aimed. (Get out your slide rules.) First, you need to imagine a vertical line 3.327 inches behind the backboard that bisects the rectangular “square” on the backboard.

Then, you need to imagine the aim points certified by the computer simulations as the aim points on the backboard. These points make a “V” shape near the top of the “square.”
Then, wherever you are on the court, you find where the vertical line crosses your aim point and aim for that spot. That should increase your chance of making the shot.

As you watch the tournament this season, pay particular attention to good free-throw shooting and bank shots – and the lack thereof. Teams with players who are good at these two fundamentals should have more success – leading to that “One Shining Moment” when they lift the NCAA Tournament trophy.



6 Responses to “Want to Win the NCAA Tournament? Learn Some Physics”

  1. Stephen Norton says:

    This is very interesting work. As a physicist, it seems intuitively clear that a low ball trajectory in a free-throw (which is often seen in college games) will reduce the chances of making the shot since the margin of error goes down. The work of these engineers confirms this. On the other hand, a very high trajectory will also make the shot more difficult. This implies there’s an optimum launch angle which this work also confirms. I wonder how many coaches know this. I’m guessing not too many. I’m a visiting scientist at Duke but I promise not to tell coach K. Here’s hoping NC State does well in the tournament.

  2. Matt Shipman says:

    Cheers — thanks for keeping this under your hat, Stephen. :)

  3. Stephen Norton says:

    Much has been written about the physics of sport, particularly baseball and to a lesser extent golf, but not much on basketball until now as far as I know. One wonders how much, or even whether, players and coaches pay attention to this research to improve performance. Even if the improvement is small, it could make a difference over time. Here’s a very simple example where coaches don’t seem to be paying attention. Every physics student knows that you should launch a projectile at 45 degrees to get maximum range. Strictly speaking, this holds in the absence of air resistance and certainly air resistance can be important for fairly light objects like golf balls and baseballs (where spin can also have an important effect). However, for a 16 pound shot put the effect of air resistance will be essentially negligible. When I watch shot putters at track meets they very often appear to launch at shallower angles than 45 degrees, sometime much shallower. A simple calculation shows that the range dependence on the launch angle, theta, goes as sin(2theta). This implies that the difference between 40 and 45 degrees translates into a difference in distance of about 2 percent. This may seem small, but for a distance of 75 feet (about the men’s world record), it’s more than a foot. Track coaches take note!

  4. [...] an interesting article on NCSU website. NC State engineers Chau Tran and Larry Silverberg simulated millions of basketball shots to find [...]

  5. Jessica Hook says:

    Coaches pay a lot of attention to physics of movement and how it can benefit the results of players they coach. If there is information for use – coaches will use it. Did you do a review of research on physics in sport? Every USTF clinic I’ve attended is completely based on human physiology and physics of movement. It is important to get this information to the journals and professional publications that coaches read. Also please keep in mind there is a significant human element to shooting/playing basketball. Players shooting mechanics, habits, fatigue, game performance stress, practice stress can all have an impact on every shot taken. It would be great to have engineers team up with coaches and athletes (I realize human subjects bring about a challenge in research) in both game and practice situations to generate valid results. Until we start watching computers simulate basketball in the ncaa tournament, human subjects are important to study. For example your results regarding the use of bank shots to increase made shot percentage. Will this really improve that percentage in a game setting….would it truly be beneficial for a player to analyze where he/she is on the floor and think if the right place to bank of go for the swish, identify the point on the backboard where he/she should aim, when a defender is aggressively running with hands up toward that player? Or is it a higher percentage shot to use the same mechanics practiced thousands of times to release the ball aiming for the back of the rim? The bank shot used to be common in basketball, but has gradually fallen away in the current game. Perhaps replicating aspects of your research with human subjects could provide a clear answer as to why. Thanks for conducting research in sport – coaches do appreciate the science behind what makes their athletes as effective as possible.

  6. [...] Basketball. Their research evaluated means of optimizing free throws and bank [...]

Leave a Reply