How Accurate is the Hawk-Eye System for Tennis Line Calls

The US Open Tennis 2009 is in full swing. Once again the likes of Federer, Nadal and Murray are playing well and the men's championships looks set for an exciting second week.
We know and have seen how video analysis can be used to analyze a tennis players performance, but it can also be used in real time or almost real time to track the ball and even make close line calls. Of course I am talking about the "Shot Spot" or Hawk-Eye system.

If you have watched any Major Tennis since 2006, you will know exactly what Hawk-Eye is. The Hawk-Eye is used to make decisions on line calls that are challenged by the tennis player. Each player (or team if playing doubles) can challenge a line call on any point. They get a maximum of 2 incorrect challenges each set. If the set goes to a tie break an extra challenge is allowed. Basically the Hawk-Eye challenge enables the tennis players to use technology to challenge line calls they think are incorrect.

The technology being used by the Hawk-Eye system is Video Analysis. Here is how it works.

1. Multiple cameras are placed around the court and players. These cameras are usually placed high up, so that there is less chance that a player will be blocking the ball from the camera view.
2. Multiple cameras are used to ensure accuracy of tracking the ball and to account for possible occlusion (the ball being hidden from the camera view by the players body...)
3. The system uses at least 4 high speed video cameras, with a capture rate presumed to be 500 frames per second.
4. The camera position is calibrated to determine its position in space and relative to the other cameras in the system. The lines on the court are also used in calibration and to compensate for any camera movement.
5. The center of the ball is tracked in 2D by each camera. The ball therefore is like a reflective marker or point on the body. Using the information from all the cameras, the Hawk-Eye system then triangulates the 3D position of the ball.
6. This process is done for each captured frame so that a trajectory of the ball can be created and then overlayed on an animated background containing the lines of the tennis court.
7. Finally the skid and compression of the ball is measured by examining the position and trajectory of the ball prior to the bounce and its position and trajectory after the bounce. In this way they can determine how long the ball was on the ground and how it skidded over the ground.
8. The Hawk-Eye system is said to have an accuracy of 3.6 mm.

I believe that the use of video technology in this way is great for the sport of tennis and for the players piece of mind as well as spectator enjoyment. However we have seen a number of controversial calls with the Hawk-Eye system. Take a look at video of 2 big ones here.

In this first video we see a very tight call for Mikhail Youzhny over Rafael Nadal at Dubai in 2007.


This second video is from the Wimbledon final in 2007. Rafael Nadal benefiting from a very close one over Roger Federer.


In both cases we would have to say that the ball likely looked out to the lines judge who made the call. In both cases the player is most likely only challenging the call because it is a crucial point (Yozhny vs Nadal - Set Point, Nadal vs Federer - Break point). The Hawk-Eye system suggests that in both cases these calls were measured as being 1mm IN, meaning the ball was 1mm from being out.

Have a look what the manufacturers of Hawk-Eye have to say about these two controversial calls at here.

Could Hawk-Eye have been wrong in either or both of these calls and what does it mean that it is 2-3 mm accurate but can suggest that the ball was in by only 1mm?

Here are some points that may effect the accuracy of the system.

1. The camera capture rate of 500 frames per second may be too slow for the hard hitting tennis game of today. Andy Roddick has recorded a fastest serve at 155 mph and ground strokes are often hit with a similar speed. Assuming a capture speed of 500 frames per second or 1 frame every 0.002 seconds, the ball will have moved about 139 mm for every video frame. This may not be sufficient data to determine the position of the ball to within 1 mm.
2. The more cameras that are used the better the chance of tracking the ball and the higher the accuracy. However there are possibilities of occlusion by players, tennis rackets and the net, which will lead to reduced accuracy.
3. High speed video capture also needs excellent lighting. We have discussed the importance of lighting for high speed capture in a previous post . Therefore the system will work best under a roof with artificial bright lighting and will possibly have a problem tracking the ball outdoors, particularly when there is cloud cover or as it gets later into the evening.
4. Assuming everything is perfect for capture, the center of the ball has to be identified as accurately as possible too. If a camera sees the ball at a funny angle or partly occluded the center may not be correctly defined by this one camera and the position of the ball will be inaccurate.
5. The skid and compression of the ball is being estimated and extrapolated based on the trajectory of the ball before and after the bounce. Any inaccuracies in tracking the position and flight of the ball will become larger during an extrapolation (estimation of the movement).

The Hawk-Eye system may not be perfect but it is definitely a step up from the eyeball view of a line judge, particularly when the ball is moving at high speed. We believe Hawk-Eye has improved the line calls in Tennis and this is great for the players and spectators alike. However it still leaves room to debate exciting points and close matches. Enjoy the US Open Tennis and hopefully we will not see any controversial Hawk-Eye calls.

Analyzing Usain Bolt's 19.19 Second 200m World Record

The Scientific Research Project at the 2009 IAAF World Athletics Championships has released the data for the 200m final and now we can break down Usain Bolts incredible 200m World Record of 19.19 seconds.

Click on the table below to get a closer look.

Let's pick out the key points for this race and see if we can compare them to his 100m splits.

1. Bolt's reaction time in this race is 0.133 seconds. This is much better than his 0.145 second 100m world record reaction time. However we have already discussed this in a previous post and know that Bolt can start fast too.
2. As expected Bolt runs the second 100m (from 100-200m ) faster than the first 100m. This is expected, as the start and getting up to speed takes time, while the second 100 meters can be run at close to maximum speed. Bolt's first 100m was run in 9.92 secs with the second hundred taking only 9.27 secs (a negative split). Interestingly, Michael Johnson ran the second 100 meters of his then World Record breaking 19.32 sec 200m race in 9.20 secs, which is faster than Bolt's second 100m in this race.
3. Bolt's maximum velocity during the 200 meter race occurs somewhere between the 50 and 100 meter mark. His average velocity over this 50m part of the race is 11.57 m/s (25.88 mph). In comparison his 100m maximum velocity was 12.27 m/s (27.45 mph). Once again this is to be expected, as the 200m athletes needs to have reserves to complete the race and cannot run at the same speed as in the 100m race.
4. Bolt slows down over each of the last two 50 meter splits as he begins to fatigue, covering each of the following 50 meter splits 2 tenths of a second slower. Watching the race, we can see that he is really straining to run fast, but he is still slowing down. It is expected that any athlete will slow down over the last 100 meters as the muscles tire, two hundered meters is a long way to go at full speed. We have mentioned that in this World Championships Bolt had already run four 100m races and three 200m heats before lining up for the 200m final. This has us excited at the prospect of seeing Bolt break this 19.19 second World Record, when he is fresh and has not run seven previous races.

All that is left to say is that we can expect Bolt to go faster in the 200 meter and 100 meter races in optimal conditions.

There is one record he does not hold yet and that is of the fastest 100m relay split. This record is held by his Jamaican team mate Asafa Powell in 8.70 secs. The anchor leg relay split is much faster than any of the other sprint splits, because the athletes have a flying start and are therefore able to reach top speed much sooner in the 100 meter distance. If Bolt anchors the 4X100m relay in Berlin this week, we expect that relay split record to be broken.

Comparing Usain Bolt's 100 meter and 200 meter World Records

Usain Bolt continues to amaze us with every race he runs. In destroying his own 200 meter world record from the Olympics, he has now set 5 world records in five Olympic or World Championship event finals in a row.

Watch video of the 200 meter race from the 2009 IAAF World Athletics Championships below. The final recorded time and the new record stands at 19.19 seconds, an incredible 0.11 seconds faster than his previous world record.



The 200 meter sprint record is usually a faster time than if you had to double the 100 meter record. This can be seen if we compare the more recent (since the use of electronic timers) progression of world records between the 2 events. As an example, when Donovan Baily held the world 100m record of 9.84 in 1996, the 200m record was held by Michael Johnson at 19.32 secs. This 200m time is faster than double the 100m record at the time.

In both the 100 and 200 meter races, the athletes start from the blocks and it usually takes them around 60 meters or more to reach maximum speed. In fact we saw from analysis of Usain Bolts 100m world record that he reached top speed at 65 meters in that race. Now in the 100m, the athletes maintain that speed for 40 or so more meters, while in the 200m they have 140m more to go and therefore maintain their top speed for longer. In fact the 200m race often has negative splits for the top athletes, meaning that they run the second 100 meters faster than the first 100 meters.

It is therefore interesting to note that if we double Usain Bolts 100m time (9.58) we get 19.16 secs, which in this case is faster than his new 200m world record of 19.19 secs. I am not trying to make the case that this 200 meter world record is not extraordinary, but why is this the case?
Watching the 200m race, he seems to be straining at the end, by this stage of the race his muscles must be burning, as he tries to maintain his maximum speed. He also said in an interview after the race that he felt tired and well he should after running all the 100m and 200m heats and finals. It is possible that this fatigue meant he could not run the 200m as fast as he possibly can. Seldom has the 100m and 200m world records been held by the same athlete or even broken by the same athlete at the same event and so this may be a factor in his 200m time.

Examining the splits and his maximum velocity to compare his 200m to his 100m world records, will give us more insight into what we can expect from Bolt in the future. From this past records history we can speculate that his 200m record is going to be smashed again soon and the 19.0 second barrier is not out of the question.

It is fantastic watching such an incredible athlete run and we hope to learn as much as possible about his biomechanics by watching and analyzing the video footage.

Biomechanical Analysis of Usain Bolts 9.58 sec World Record

At the IAAF World Championships in Berlin, the German IAAF Member Federation, DLV, in cooperation with the IAAF is carrying out a major Biomechanics Project.

The project presented the reaction times and splits for all the finalists from the 100 metersemifinals and the final at the 2009 IAAF World Championships in Berlin.
We thought we would present them here and try to predict just how fast Usain Bolt can run.

This table gives us some real insight into Bolt's race. Lets take a look at some crucial points in the race. You can click on the table to see the details.

1. Of the 8 finalists Bolt has the 3rd slowest reaction time to the gun, at 0.146 seconds. Both Asafa Powell with 0.134 secs and Tyson Gay with 0.144 secs react faster.
2. By the 20 meter mark though Bolt has caught up all this time and gone ahead of Powell by 0.03 secs.
3. From the 20 meter mark on, Bolt is away and getting further away over each 20 meter interval. Although we can also see that Tyson Gay is able to hang pretty close between 20 and 80 meters.
4. Bolt reaches his top speed of 12.27 m/s or 27.45 miles per hour at the 65 meter mark. This can be seen in the second graph presented by the IAAF Biomechanics Research paper.
5. From 80 to 100 meters Bolt actually begins to slow down. We can see that his time for the last 20 meters is 0.05 seconds slower than his fastest 20 meter split of 1.61 seconds. We also know that he reached his maximum speed at 65 meters and everything after that was a little slower.
6. One last thing to note is that in this race there is a tail wind of 0.9 m/s. This is legal but it does give the athletes a slight advantage as it pushes them along.

To determine how fast we think he can run, lets look back at the Beijing Olympics and remember how analysis of that race suggested that if Bolt had maintained his speed through the last 20 meters and did not begin celebrations, he could possibly have run the 100 meters in 9.55 seconds.

His current world mark is pretty close to that already, so where can he improve to make up the time. So here are some key factors that are critical to determine how much faster he can go.

1. Firstly look at the table again and at Bolt's reaction time (RT) for his semi-final. In this race he gets out in 0.135 seconds as against the 0.146 seconds in the final. We also see that he completes the first 20 meters in the same time in both the semis and final, while he definitely seemed to be cruising in the semi-final. It has also been suggested that Bolt actually covered the first 20 meters in Beijing faster than he did in Berlin. This is up for debate though, as if you remember from our post on that study, the video analysis was done using broadcast footage where the camera setup was not optimal. In any case, Bolt can definitely get out of the blocks faster and should be able to cover that first 20 meters faster than he did in Berlin.
2. The prediction from the Beijing Olympics was based on the suggestion that Bolt could maintain his speed at 80 meters through to the end of the race. In Berlin however, he is not able to do this and slows down a little over the last 20 meters. We also notice that all the athletes in the final ran slower over the last 20 meters, than in the split between 60-80 meters (which was the fastest for all of them). Therefore it may be impossible for a 100 meter athlete to maintain their speed over the last 20 meters and the Beijing prediction may have been optimistic in this regard.
3. In the last 10 meters in Berlin, Bolt takes a look out of the corner of his eye to check on Gay. We don't believe this could have caused too much of a slow down. In fact if we look at his average velocity at the 90m and the 100m mark from the research, we can see that he does not slow down between those 2 points. But lets assume he could have been 1 or 2 hundredths of a second faster if he had not checked.
4. The 0.9 m/s tail wind in the final in Berlin will definitely have helped Bolt. A tail wind of up to 2.0 m/s is considered legal for a record to stand. Therefore there is an advantage to be gained with the right conditions.

Finally we have some sort of answer. We think Bolt can definitely run faster. If he improves his reaction time and runs hard through the finish in the right conditions, we have no doubt a new world record will be set.
I am sure we would all love to see an athlete challenge the 9.50 second barrier and Bolt may have it in him to do just that. We look forward to watching it all.

Can Usain Bolt Run Any Faster?

In a recent post we asked the question: How fast can Usain Bolt Run? In this post we introduced you to a study that suggested he could have run the 100 meters at the 2008 Beijing Olympics in less than 9.6 seconds.

At the 2009 IAAF World Athletics Championships, today he proved just that, shattering his own World Record by running the race in 9.58 seconds. Even then he still had time to take a look out of the corner of his eye at Tyson Gay, his closest competitor, who ran an impressive 9.71 seconds

If you missed this amazing race, take a look at the video below.



Unbelievable! The only question left is how much faster can he go? Bolt himself believes that he can run the 100 in 9.4 seconds. To us this seems a bit out of reach, although we believe he will go faster than 9.58.

We would love to hear what you think.

Video Analysis of Sprinting: From the Start

In the 100m and 200m track sprinting events, the start can win or lose a race. In the 100m the winning difference is often measured in 100ths of a second, therefore any advantage that can be gained at the start could be crucial.

At the IAAF World Championships next week, Tyson Gay will take on Usain Bolt for the title of worlds fastest man. So far in 2009 both athletes have put up some impressive times and the first meeting between them this year should be fast, close and exciting. Usain Bolt is the Olympic champion and world record holder. We have previously discussed how fast he could possibly run. Tyson Gay is the reigning World Champion and recently ran the 100m in 9.75 seconds at the US Championships.

With both athletes being at the top of their game, victory may be decided by their start. Neither of them is known for their explosive or fast starts. Bolt has an incredibly long stride length and eats up ground with each step while Gay has unmatched leg speed. The start though is crucial and we have therefore decided to look at some video and examine the start.

Below is some front on video of Tyson Gay at the US Championships. We want to focus on his start.


A good start requires that the athlete sets up correctly. Here are some key factors for the set position before the start gun sounds.

1. The hands are set up on the line and the shoulders and upper body should lean forward over the hands. Track coaches suggest an angle of about 15 degrees (The angle between the shoulders and hands and the vertical). Although we cannot see the angle at which Gay is leaning (this would need a side on view of his start), we can see that he is leaning forward and ready to explode from the blocks.
2. The angle of the knees in the start position must allow the athlete to push away from the blocks with as much power as possible while at the same time being able to get their feet through to begin running. The optimal bend of the front knee should be around 90 degrees to provide the biggest lever to produce push off. The back leg needs to be bent less than this at about 60 degree so that it is able to still push off hard but will straighten before the front leg and have time to come through for the first step.
3. Both legs need to push off almost simultaneously at the start of the race. The athlete cannot be sitting back on either his front or back leg at the start.

Tyson Gay sets up well and in this video he explodes from the blocks, pushing off with both legs quickly. Both legs straighten completely, with the rear leg leaving the blocks and starting to drive through before his front leg (left leg) is completely straight.

Gay also uses his arms to explode out of the blocks, as well as maintain good balance. Watch as his right arm drives backward and his left forward. This motion provides extra forward momentum, but it also ensures that as he starts he does not fall over to one side. The arms act as a counter balance to the motion of the legs. In this start his right leg will take the first step on the track and therefore his left arm needs to be forward to balance this motion.

Moving forward to that first right foot step on the track, we can see that Gay's head and chest are still down low. His arms are driving hard and fast. If you pause the video you will see them as a blur. We can also see that his first step is not too long. In fact his head, chest and hips all remain in front of his foot for this first step. This allows him to continue to stay low with his body. If he took a longer first step, it would force his chest up, which would in turn slow down his speed. His chest and head stay down for as many as 16 steps allowing him to lean forward during this start and continue to accelerate.

His start technique looks great here and although we do not know what his reaction time to the gun was, we can see that he was able to accelerate well from the start and this is why he put up such a fast time.

As I looked through more videos on Tyson Gay's start, I came across one from tttjump that suggested that Gay's knee rolls forward at the start. If you study the slow motion of the start in the video above you will see what this means. Gay's front leg (his left) moves forward and down, in fact bends a little more, just after the start and as his hands leave the ground.

The suggestion is that this extra bend of the front knee at the gun, causes a delay in his ability to get off the blocks. On closer examination we can see that his back foot is driving already (straightening) as his front knee "rolls" forward. This may be causing him to push off with less power from his back leg as he may need to slow it down, to give the right leg time to get into a position to start its push off.

From a biomechanical standpoint, this would suggest that Gay's front leg is not bent to the most optimal position to explode out of the blocks. He may be bending it a little more after the start to get more push off power. The split second it takes to bend the knee that little bit more and the small amount of back foot push off power that he may lose, could determine the outcome of the race against a phenom like Usain Bolt.

Once again from the standpoint of biomechanics, this problem could possibly be solved by simply adjusting Tyson Gays starting blocks or position slightly, allowing his front knee to set up in a more optimal position for his starting style.

Of course for this World Championships, it is too late to make any changes and Tyson Gay should provide Usain Bolt some really stiff competition when they hopefully meet in the final in Berlin.

If you will be watching or filming some video of any of the action at the IAAF world championships and would like to share some video for analysis, please let us know.

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.