Measuring Vertical Leap at a NBA Slam Dunk Contest

The Slam Dunk contest at the NBA All Star event is usually spectacular. Dwight Howard flying with his Superman cape is a great highlight. Slam dunks are all about getting up high and we want to know how high they jump?

Recently a reader of this website asked whether he could measure the vertical leap of winners of past slam dunk contests from NBA footage of the event, including Michael Jordan's leap from the free throw line in 1987. Unfortunately in a basketball broadcast the camera and usually cameras are often moving, panning or zooming to catch the best view of the player, particularly during a dunk. Analyzing the vertical leap from this footage can be tricky.

The answer to the readers question depends a lot on the video footage that is analyzed, but here are a few basics of video analysis and some ideas of how the vertical leap height may be measured from the footage.

1. Camera angle and view needs to be good to make useful measures of heights (see Video Analysis 101 ). Most footage of the slam dunk contests used multiple cameras and they were often zoomed in at just the wrong time, making this difficult.
2. We only need one image of the player at the peak of his jump to measure vertical leap, but we will also require some scaling so that we can convert the pixels in the image into a real measurement of height. To do this we need to have a single image that includes the player, the bottom of the backboard, the rim and the floor directly underneath the backboard. With all these in one frame of the footage we can make a measure.
3. We will also want to know the height of the player so that we can use this height to estimate their vertical leap. We will measure the height of the jump and subtract the players standing height to get a measure of their jump.
4. Even if all the information is available to us to make the measure, it will still be an estimate as the camera angle may be slightly off and this will make our measure less accurate.

Would this method in fact work?  We can try to analyze a slam dunk contest from 2000 and Vince Carter winning with some serious air. Check out the video below:



From this video we can grab a snapshot of the action at 1:44 in the video and do some measures. First we needed to know some standard basketball measures.

1. Width of the backboard is 72 inches
2. Height of the bottom of the backboard is 114 inches above the ground
3. Vince Carter is listed at 6 foot 6 inches or 78 inches
4. Hip height of a standard man is approximately 53% of his total height. Therefore Carter's hip height is about 41.3 inches.

Now we can make some measures of Carters vertical leap height. This footage has a graphic that measures his jump height at 37 inches. We will use this as a measure to see how well we can do at measuring the jump height using our estimates and video analysis. See the image below:

In the image we can see the following measures:

1. We know that the width of the backboard is 72 inches. We have drawn a green line along the bottom margin of the backboard and used this known distance to scale all our other measures.
2. Next we used the blue line to draw a vertical from the bottom of the backboard to the ground. We know this should be 114 inches. Unfortunately as our scale comes from the width of the back board (green line) we couldn't get it to measure exactly 114 inches with our estimates, but we are close at 114.19 inches.
3. Finally we measure Vince Carter's hip height at the top of his jump and with the yellow line. Here we needed the line to go from the floor at the same height as the blue line to Carters hips. We estimate his hip height at 78.9 inches or 6.575 feet which is almost his head height.
4. We can also notice that the camera is not perfectly horizontal with the backboard. We can see that the backboard is not perfectly horizontal accross the screen, although it is close. This angle may reduce the accuracy of our other measures.

Finally we can estimate Carter's maximum vertical leap from this video footage and for this particular dunk. We know his standing hip height is estimated at 41.3 inches and we estimated his hip height at the peak of the jump for the dunk at 78.9 inches. We subtract the standing hip height from the jump height and we get 37.6 inches.

If the measure shown during the broadcast at 37 inches is accurate then our estimate is pretty good and we  can probably try to do the same measures on other broadcast footage of slam dunk contests. All we need is one image with a view of the backboard, the player and the floor below the backboard as well as knowledge of the dimensions of the basketball backboard and height of the player.

We are always interested to hear about your video analysis projects or hear your comments. We are also available to consult to all our readers on their video analysis and biomechanics needs.  

How Fast can Usain Bolt Run?

The IAAF World Championships begins in less than a month and all eyes will be on the 100m and 200m world record holder, Usain Bolt from Jamaica. We all remember the Beijing Olympics in 2008, when Bolt ran the 100m in 9.69 seconds, throwing out his arms and pumping his chest before crossing the line. There has been a lot of speculation about how fast he could have run with some suggesting a time of 9.55 seconds http://sports.espn.go.com/oly/trackandfield/news/story?id=3583692 .

The publishers of the study above, made use of video analysis to estimate this potential world record time. In fact they used video from Beijing Olympics broadcast productions from NBC, BBC and NRK (a Norwegian Channel). If you are a regular reader of our posts you will already know about many of the techniques they used to analyze the video. Lets look at how they did it.

When you or I setup to capture video of a sporting performance, we know how important the position of the camera is. In this case however the researchers did not have access to the stadium and athletes in Beijing and therefore had to make use of broadcast footage. In most cases this footage includes moving cameras and camera angles that are not always conducive to accurate measurement.

The publishers of the article used basic physics to estimate the possible finish time for Usain Bolt had he not celebrated 20 meters before crossing the line. The basic equations are well known:
Velocity (speed) = Distance/Time
Acceleration = Velocity/Time

So if we can find the distance Bolt covered and the time he took to cover that distance we would have his velocity or speed. We could measure that speed, from the video footage, over numerous intervals to determine how it is changing. Likewise, if we know his velocity (speed) we can measure his acceleration and how it changes over the same intervals.
The publishers of the study estimated Bolts speed and acceleration at the interval before he started to celebrate. At this point his speed and acceleration slow. To determine the predicted finishing time, the researchers assumed that Bolts acceleration could be maintained over the last 20 meters of the race, had he not celebrated. In this way they were able to predict a finishing time of 9.55 seconds.

You probably want to know how they were able to determine distance covered and the time it took. This information was all obtained from the broadcast video. The video used was from NBC and can be found at http://www.nbcolympics.com/video/share.html?videoid=0824_HD_ATB_AU_CE552 . Below is similar video of the race :


In the video you will see the camera rail running from the left to the right at the bottom of the image. This camera rail has bolts spaced evenly along it. By knowing the distance between the bolts on the track and that the start line is at 0 meters and the finish line at 100 meters, we can determine Usain Bolts position relative to the rail bolts at numerous intervals.

You will also see the stadium time clock and the broadcast time clock in the video. These clocks can be used to determine the time at which Bolt reached each interval.
We now have all the information we need. Distance covered and the time it took. From this we can determine his speed and acceleration at all intervals and predict his finishing time had he not begun his celebrations early.

We would like to thank the study authors H. K. Eriksen, J. R. Kristiansen, Ø. Langangen and I. K. Wehus for doing this fun study and we look forward to seeing whether Usain Bolt can get anywhere close to this predicted World record at the IAAF World Championships in Berlin in August.

Please let us know if you want more details on this study or just want to leave a comment. We love to hear from you.

Measuring Your Vertical Leap Using Video Analysis

Before Kobe Bryant or Dwight Howard was considered for a contract in the NBA, they likely had to undergo a series of physical tests and exercises. In fact, most if not all professional and college sports programs require prospective players to complete these "combines", so that they can have a quantifiable way to compare the athletes. Some of the commonly used tests include the 40 yard dash, bench press, and vertical leap. For players in the NBA, the vertical leap test is the most crucial.

The vertical leap test demonstrates how high a player can jump and reach. Ideally, the test shows how high the athlete's center of mass (COM) moves. But since a person's COM is often difficult to determine, the test usually estimates the results by measuring the difference between how high a subject can reach from a standing position, and how high the subject can reach when they jump (either from a stationary or running start). One variation of this test is to simply see how high the athlete can jump and reach. While this latter method measures the maximum height the athlete can touch, it doesn't provide us with how high he/she actually jumped. In simple terms a player with an 9' reach, jumping 1' will reach 10'. A player with a 7' reach, jumping 3' will also reach 10', although it is obvious that the 7' player jumped higher. Simply measuring how high the subject can reach from a standing position before they jump, gives us the additional information needed to calculate how high the athlete jumped.

Professional and college organizations often conduct this test by having the athlete stand next to a tall pole that has little plastic flags extending from it, as shown below. The athlete then jumps and swipes the highest flags he can, and the result is recorded.

If you want to measure your own vertical leap but don't have access to one of these testing devices, you can simply film yourself jumping from a standing position. Besides the basic principles of video analysis (see http://videosportsanalysis.blogspot.com/2009/03/video-analysis-of-sports-101.html), there are two important concepts to keep in mind:

1. In your video clip, you must be able to see an object of known height. This object should also be in the same vertical plane the subject is jumping in. If you're jumping next to a wall, marking a known height on the wall should be good enough. The reason you need to have this information is so the analysis software can scale the distance measurement appropriately (this concept will be shown on the video below).
2. The video analysis software you're using must be able to calculate the distance between two points and be able to use the known height of the object to calibrate the measured distance accordingly; otherwise, the distance between the two points will simply be in units of pixels, which isn't very useful. We need to be able to convert the distance to something like inches or centimeters. If you're interested in finding out more about software packages that offer this type of feature, just let us know and we'll be happy to point you in the right direction.

Below we have a video clip of a subject performing the vertical leap test:



As you can see, we have one point identifying the highest point the subject reached while standing, and one point identifying the highest point the subject reached during the jump. As mentioned in the two concepts above, we have also shown the known height of another object (in this case, the distance from the ground to a point marked on the wall is 37"); and the software automatically uses this information to display the distance between the two points the subject reached in units of inches (23.7").

Compare this subject's results with the likes of NBA superstars Kobe Bryant (38") and Dwight Howard (40"), set to meet in the 2009 NBA Finals. Bryant has been vitually unguardable, draining shots while having defenders' hands in his face, and zipping around opponents with his lightning-quick first step. Howard is a physical force to be reckoned with; players move out of his way when he elevates, to avoid getting "posterized" when he throws down one of his thunderous dunks. It's amazing what these athletes are capable of; and using tests such as the vertical leap allows us to have a more complete understanding of how incredible they really are.