Spreadsheets are at their best when they are helping us solve useful problems. And what could be more useful than getting better at basketball? Perhaps this spreadsheet could help you dominate avoid getting kicked out of your local pickup game..
A couple researchers at North Carolina State showed that in certain locations on a basketball court (near the baseline and near the sidelines), a bank shot is more likely to go in than a direct shot:
http://www.wired.com/2011/03/physics-basketball-shots/
In their paper, they then discuss the optimal aiming strategy, which is where things get a little murky. Basically, you have to imagine a vertical bar 3.326 inches behind the backboard and aim at the point where the “V” on this backboard would intersect with the vertical bar:
Most of us probably can not tape up a “V” on our public court (or play with a backboard that is transparent), but – we could build a spreadsheet to help us visualize where to aim depending on where we are standing on our court. The goal of our spreadsheet will be to input a location on the court, and have the spreadsheet output where on the backboard you should aim at.
First things first – build a representation of a basketball court for the user input. A quick internet search describes the baseline to be 50 feet wide, the key 12 feet wide x 10 feet off the baseline, and the backboard 4 feet from the baseline with the basket in the center. The two blocks on the sides of the key (marked in blue below) – are 3 feet beyond the backboard and one foot long. Row 8 and Column B contain the coordinates of where we are standing on the court – in this case the “X” is at 8 feet deep and 17 feet from the sideline.
Next, we make a representation of the backboard – this part of the spreadsheet is the part which will output where to shoot. We use the same measurements in the picture above – note that each cell denotes 1 inch here versus one foot above – Row 88 converts the cell to a location on the above basketball court (the backboard is between 22 and 29 feet on the court above).
Now comes the hard part – using the coordinates of where the player is standing, how do we figure out where on that “V” line we should aim at, knowing that the coordinate where we are standing needs to intersect the “V” line and then intersect a vertical bar 3.326 inches behind the backboard?
As with many spreadsheets and problem solving situations, there is more than one right way to solve this. Our approach will be to calculate for every point on the “V” on the backboard, how far behind the backboard are we going to intersect the center of the backboard, given our current standing position. We then pick the point on the aiming “V” that has the closest value to 3.326 inches.
For our example we’ll use the (17, 8) point on the court above, and the following point on the backboard, whose location is 24.125 feet, 4 feet:
Now I hope you paid attention on geometry class, because we are going to dust off the old “properties of similar right triangles” lesson. There are two right triangles in the picture that are on top of each other, one has its highest point at the backboard, and the other’s highest point is where a straight line drawn between the current position and the backboard intersection point hits the middle of the backboard.
Zooming in…the properties of similar triangles would say that the ratio of B1/B2 = H1/H2.
- B1 is just the point the backboard we are looking at (24.125) minus our current position of 17.
- B2 is the backboard midpoint, (25) minus our current position (17).
- H1 is our Y position (8) minus the position of the backboard (4).
- H2 is what we are solving for, with a little algebra, H2 = (H1*B2)/B1.
- Then we see whether H2 – H1 is close to 3.326 inches.
For the Formula, we square the difference between (H2-H1) and 3.326 inches, and then we pick the point with the lowest difference.
Now that we put in the formula for each point on the backboard, we get this nice output – note that we should aim close to the greenest area with the 0’s for the court location above.
Check out the spreadsheet by clicking below: note the court location inputs are at locations CA29 and CA30:
Excel Spreadsheet: Basketball bank shot
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Amazing work! A must read for all NBA players!