Hawk-Eye is a computer system that uses multiple high-speed cameras to track the trajectory of balls in sports like tennis, cricket, and soccer. It was developed in 2001 by Paul Hawkins and is now owned by Sony. It works by analyzing video feeds from 6-10 cameras positioned around the field of play and using triangulation to create a 3D representation of the ball's path. Hawk-Eye provides predictions of where a ball would have landed that are generally accurate to within a few millimeters. It is used in sports to review decisions like line calls in tennis or lbw decisions in cricket.

1. Introduction
Hawk-Eye is a complex computer system used officially in numerous sports such
as cricket, tennis, Gaelic football, badminton, hurling, Rugby Union, association
football and volleyball, to visually track the trajectory of the ball and display a record of its
statistically most likely path as a moving image.[1]
Hawk-Eye was developed in the United Kingdom by Paul Hawkins. The system was originally
implemented in 2001 for television purposes in cricket. The system works via six (sometimes
seven) high-performance cameras, normally positioned on the underside of the stadium roof,
which track the ball from different angles. The video from the six cameras is
then triangulated and combined to create a three-dimensional representation of the trajectory of
the ball. Hawk-Eye is not infallible and is accurate to within 5 millimetres (0.19 inch) but is
generally trusted as an impartial second opinion in sports.
It has been accepted by governing bodies in tennis, cricket and association football as a
technological means of adjudication. Hawk-Eye is used for the Challenge System since
2006 in tennis and Umpire Decision Review System in cricket since 2009. The system was
rolled out for the 2013-14 Premier League season as a means of goal-line technology.[3] In
December 2014 the clubs of the first division of Bundesliga decided to adopt this system for
the 2015-16 season.

2. Method of Operation
All Hawk-Eye systems are based on the principles of triangulation using the visual images and
timing data provided by a number of high-speed video cameras located at different locations and
angles around the area of play.[5] For tennis there are ten cameras. The system rapidly processes
the video feeds by a high-speed camera and ball tracker. A data store contains a predefined
model of the playing area and includes data on the rules of the game.
In each frame sent from each camera, the system identifies the group of pixels which
corresponds to the image of the ball. It then calculates for each frame the 3D position of the ball
by comparing its position on at least two of the physically separate cameras at the same instant in
time. A succession of frames builds up a record of the path along which the ball has traveled. It
also "predicts" the future flight path of the ball and where it will interact with any of the playing
area features already programmed into the database. The system can also interpret these
interactions to decide infringements of the rules of the game.[5]
The system generates a graphic image of the ball path and playing area, which means that
information can be provided to judges, television viewers or coaching staff in near real-time.
The pure tracking system is combined with a back end database and archiving capabilities so that
it is possible to extract and analyse trends and statistics about individual players, games, ball-to-
ball comparisons, etc.
I don't trust the data. Don't worry, this isn't another Peter Moores thinkpiece. It's Hawk-Eye or
ball-tracker or whatever you want to call it. I don't trust it. I don't trust the readings it gives.
This isn't a flat-earth theory, though flat earth does come into it, I suppose. How can six cameras
really predict the movement of a ball (a non-perfect sphere prone to going out of shape at that)
off a surface that is neither flat nor stable? A ball that is influenced by constantly changing
amounts of torque, grip, flight, speed and spin, not to mention moisture.
When Hawk-Eye, a prediction system with a known and well-publicised propensity for minor
error (2.2 millimetres is the most recent publicly available figure) shows a fraction less than a
half of the ball clipping leg stump after an lbw appeal, can we take that information at face value
and make a decision based upon it?
During Tuesday's World Cup semi-final, my long-held conspiracy theory bubbled over. How, I
wondered, could the ball that Imran Tahir bowled to Martin Guptill in the sixth over - the turned-
down lbw shout from which the bowler called for a review - have passed as far above the stumps
as the TV ball-tracker indicated? To the naked eye it looked wrong. The predicted bounce on the
Hawk-Eye reading looked far too extravagant.
Worse, why upon seeing that projection did every single person in the pub I was in "ooh" and
"aah" as though what they were seeing was as definitive and irrefutable as a ball sticking in a

3. fielder's hands, or the literal rattle of ball on stumps? Have we just completely stopped
questioning the authority of the technology and the data?
Later I checked the ball-by-ball commentary on ESPNcricinfo. Here's what it said:
"This is a flighted legbreak, he looks to sweep it, and is beaten. Umpire Rod Tucker thinks it
might be turning past the off stump. This has pitched leg, turned past the bat, hit him in front of
middle, but is bouncing over, according to the Hawkeye. That has surprised everybody. That
height has come into play here. It stays not-out."
Why don't we question the authority of a technology that has a well-publicised margin of error?
© Getty Images
It surprised me, but did it surprise everybody? Probably not. More TV viewers seemed to accept
the call than question it. When you've watched enough cricket, though, some things just look a
little off. To me this one didn't add up. Guptill made another 28 runs, not a trifling matter in the
context of the game.
A disclaimer: though I distrust it for lbw decisions, I'm not saying that Hawk-Eye is all bad. It's
great for "grouping" maps to show you where certain bowlers are pitching the ball, because
tracking where a ball lands is simple. What happens next I'm not so sure on, particularly when
the spinners are bowling.
To be fair, Hawk-Eye's inventor Paul Hawkins was a true pioneer and has arguably made a
greater contribution to the entertainment of watching cricket on TV than many actual players

4. manage. That's the thing, though: it's entertainment. In 2001, barely two years after Hawkins had
developed the idea, it had won a BAFTA for its use in Channel 4's Ashes coverage that year. It
wasn't until 2008 - seven years later - that it was added as a component of the Decision Review
System. Quite a lag, that.
On its website, admittedly not the place to look for frank and fearless appraisal of the
technology, Hawk-Eye (now owned by Sony) claims that the fact TV viewers now expect a
reading on every lbw shout is "a testimony to Hawk-Eye's reputation for accuracy and
reliability". But it's not, is it? All that really tells us is that we are lemmings who have been
conditioned to accept the reading as irrefutable fact upon which an umpiring decision can be
made. But it's a prediction.
Not even Hawk-Eye itself would call it a faultless system. Last December the company admitted
it had got a reading completely wrong when Pakistan's Shan Masood was dismissed by Trent
Boult during the Dubai Test. In this instance, the use of only four cameras at the ground (Hawk-
Eye requires six) resulted in the operator making an input error. Why it was even being used
under those conditions is more a question for the ICC, I suppose.
It's not all bad: Hawke-Eye gives great insight into where bowlers are pitching their deliveries ©
Hawk-Eye
The Masood debacle highlights an interesting issue with regards to the cameras though.
Understandably, given the pay cheques at stake and that Hawk-Eye is a valuable component of
their coverage, TV commentators rarely question the readings even in cases as puzzling as the

5. Masood verdict. Mike Haysman is one who stuck his neck out in a 2011 Supersport article.
Firstly, Haysman echoed my earlier thought: "The entertainment factor was the exact reason they
were originally introduced. Precise decision-making was not part of the initial creative
masterplan." The technology has doubtless improved since, but the point remains.
More worryingly, though, Haysman shone a light on the issue with the cameras upon which
Hawk-Eye depends. At that point an Ashes Test, for instance, might have had bestowed upon it a
battalion of deluxe 250 frame-per-second cameras, whereas a so-called lesser fixture might use
ones that captured as few as 25 frames-per-second. Remember: the higher the frame rate the
more accurate the reading. Put plainly, for the past five years the production budget of the rights
holder for any given game, as well as that game's level of perceived importance, has had an
impact on the reliability of Hawk-Eye readings. Absurd.
As a general rule, the more you researchthe technology used in DRS calls, the more you worry.
In one 2013 interview about his new goal-line technology for football, Paul Hawkins decried the
lack of testing the ICC had done to verify the accuracy of DRS technologies. "What cricket
hasn't done as much as other sports is test anything," he started. "This [football's Goal Decision
System] has been very, very heavily tested whereas cricket's hasn't really undergone any
testing." Any? Then this: "It's almost like it has tested it in live conditions so they are inheriting
broadcast technology rather than developing officiating technology." Does that fill you with
confidence?
Hawkins and science-minded cricket fans might bray at the suggestion that Hawk-Eye can't be
taken as law, but in lieu of any explanation of its formulas, machinations and the way it's
operated (also known as proprietary information) it's hard for some of us to shake the doubt that
what we're seeing with our eyes differs significantly from the reading of a computer.

6. Hawkeye Enovation LTD.
Engineers at Roke Manor Research Limited, a Siemens subsidiary in Romsey, England,
developed the system in 2001. Paul Hawkins and David Sherry submitted a patent for the United
Kingdom but withdrew their request.[ All of the technology and intellectual property was spun
off into a separated company, Hawk-Eye Innovations Ltd, based in Winchester, Hampshire.
On 14 June 2006, a group of investors led by the Wisden Group bought the company,[6] who
included Mark Getty, a member of the wealthy USA family and business dynasty. The
acquisition was intended to strengthen Wisden's presence in cricket, and allow it to enter tennis
and other international sports, with Hawk-Eye working on implementing a system for basketball.
According to Hawk-Eye's website, the system produces much more data than that shown on
television, which could be easily shown on the internet.
Put up for sale in September 2010, it was sold as a complete entity to Japanese electronic giant
Sony in March 2011.
Cricket
The technology was first used by Channel 4 during a Test
match between England and Pakistan on Lord's Cricket Ground, on 21 May 2001. It is used
primarily by the majority of television networks to track the trajectory of balls in flight. In the
winter season of 2008/2009 the ICC trialled a referral system where Hawk-Eye was used for
referring decisions to the third umpire if a team disagreed with an LBW decision. The third
umpire was able to look at what the ball actually did up to the point when it hit the batsman, but
could not look at the predicted flight of the ball after it hit the batsman.
Its major use in cricket broadcasting is in analysing leg before wicket decisions, where the likely
path of the ball can be projected forward, through the batsman's legs, to see if it would have hit
the stumps. Consultation of the third umpire, for conventional slow motion or Hawk-Eye, on leg

7. before wicket decisions, is currently sanctioned in international cricket even though doubts
remain about its accuracy in cricket.[
The Hawk-eye referral for LBW decision is based on three criteria:
 Where the ball pitched
 The location of impact with the leg of the batsman
 The projected path of the ball past the batsman
In all three cases, marginal calls result in the on-field call being maintained.
Due to its realtime coverage of bowling speed, the systems are also used to show delivery
patterns of bowler's behaviour such as line and length, or swing/turn information. At the end of
an over, all six deliveries are often shown simultaneously to show a bowler's variations, such as
slower deliveries, bouncers and leg-cutters. A complete record of a bowler can also be shown
over the course of a match.
Batsmen also benefit from the analysis of Hawk-Eye, as a record can be brought up of the
deliveries batsmen scored from. These are often shown as a 2-D silhouetted figure of a batsmen
and colour-coded dots of the balls faced by the batsman. Information such as the exact spot
where the ball pitches or speed of the ball from the bowler's hand (to gauge batsman reaction
time) can also help in post-match analysis.
Tennis
In Serena Williams's quarterfinal loss to Jennifer Capriati at the 2004 US Open, three line calls
went against Williams in the final set, and Auto-Ref system was being tested during the match.
Though the calls were not reversed, there was one overrule of a clearly correct call and the chair
umpire Mariana Alves, that the TV replay showed to be good. She was removed from
consideration for further matches at that year's U.S. Open. These errors prompted talks about line
calling assistance especially as the Auto-Ref system was being tested by the U.S. Open at that
time and was shown to be very accurate.[11]

8. In late 2005 Hawk-Eye was tested by the International Tennis Federation (ITF) in New York
City and was passed for professional use. Hawk-Eye reported that the New York tests involved
80 shots being measured by the ITF's high speed camera, a device similar to MacCAM. During
an early test of the system at an exhibition tennis tournament in Australia (seen on local TV),
there was an instance when the tennis ball was shown as "Out", but the accompanying word was
"In".[citation needed]This was explained to be an error in the way the tennis ball was shown on the
graphical display as a circle, rather than as an ellipse.[citation needed] This was immediately
corrected.
Hawk-Eye has been used in television coverage of several major tennis tournaments,
including Wimbledon, the Queen's Club Championships, the Australian Open, the Davis
Cup and the Tennis Masters Cup. The US Open Tennis Championship announced they would
make official use of the technology for the 2006 US Open where each player receives two
challenges per set.[12] It is also used as part of a larger tennis simulation implemented
by IBM called PointTracker.
The 2006 Hopman Cup in Perth, Western Australia, was the first elite-level tennis tournament
where players were allowed to challenge point-ending line calls, which were then reviewed by
the referees using Hawk-Eye technology. It used 10 cameras feeding information about ball
position to the computers. Michaëlla Krajicek was the first player to challenge a call using the
system.
In March 2006, at the Nasdaq-100 Open in Miami, Hawk-Eye was used officially for the first
time at a tennis tour event. Later that year, the US Open became the first grand-slam event to use
the system during play, allowing players to challenge line calls.
The 2007 Australian Open was the first grand-slam tournament of 2007 to implement Hawk-Eye
in challenges to line calls, where each tennis player on Rod Laver Arena was allowed 2 incorrect
challenges per set and one additional challenge should a tiebreaker be played. In the event of an
advantage final set, challenges were reset to 2 for each player every 12 games, i.e. 6 all, 12 all.
Controversies followed the event as at times Hawk-Eye produced erroneous output. In 2008,
tennis players were allowed 3 incorrect challenges per set instead. Any leftover challenges didn't
carry over to the next set. Once, in one of Amélie Mauresmo's matches, she challenged a ball that
was called in, Hawk-Eye showed the ball was out by less than a millimetre but the call was
allowed to stand. As a result, the point was replayed and Mauresmo did not lose an incorrect
challenge.
Ball compared with impact.

9. The Hawk-Eye technology was used in the 2007 Dubai Tennis Championships with some minor
controversies. Defending champion Rafael Nadal accused the system of incorrectly declaring an
out ball to be in following his exit. The umpire had called a ball out; when Mikhail
Youzhny challenged the decision, Hawk-Eye said it was in by 3 mm.[13] Youzhny said afterwards
that he himself thought the mark may have been wide but then offered that this kind of
technology error could easily have been made by linesmen and umpires. Nadal could only shrug,
saying that had this system been on clay, the mark would have clearly shown Hawk-Eye to be
wrong.[14] The area of the mark left by the ball on a hard court is a portion of the total area that
the ball was in contact with the court (a certain amount of pressure is required to create the
mark)[citation needed].
The 2007 Wimbledon Championships also implemented the Hawk-Eye system as an officiating
aid on Centre Court and Court 1, and each tennis player was allowed 3 incorrect challenges per
set. If the set produced a tiebreaker, each player was given an additional challenge. Additionally,
in the event of a final set (third set in women's or mixed matches, fifth set in men's matches),
where there is no tiebreak, each player's number of challenges was reset to three if the game
score reached 6–6, and again at 12–12. Teymuraz Gabashvili, in his 1st round match
against Roger Federer, made the first ever Hawk-Eye challenge on Centre Court. Additionally,
during the finals of Federer against Rafael Nadal, Nadal challenged a shot which was called out.
Hawk-Eye showed the ball as in, just clipping the line. The reversal agitated Federer enough for
him to request (unsuccessfully) that the umpire turn off the Hawk-Eye technology for the
remainder of the match.
In the 2009 Australian Open fourth round match between Roger Federer and Tomáš Berdych,
Berdych challenged an out call. The Hawk-Eye system was not available when he challenged,
likely due to a particularly pronounced shadow on the court. As a result, the original call stood
In the 2009 Indian Wells Masters quarterfinals match between Ivan Ljubičić and Andy Murray,
Murray challenged an out call. The Hawk-Eye system indicated that the ball landed on the center
of the line despite instant replay images showing that the ball was clearly out. It was later
revealed that the Hawk-Eye system had mistakenly picked up the second bounce, which was on
the line, instead of the first bounce of the ball. Immediately after the match, Murray apologised
to Ljubicic for the call, and acknowledged that the point was out.
The Hawk-Eye system was developed as a replay system, originally for TV broadcast coverage.
As such, it initially could not call ins and outs live, only the Auto-Ref system could produce live
in/out calls as it was developed for instant line calling. Both systems can produce replays.
The Hawk-Eye Innovations website states that the system performs with an average error of 3.6
mm. The standard diameter of a tennis ball is 67 mm, equating to a 5% error relative to ball
diameter. This is roughly equivalent to the fluff on the ball.
Unification of rules

10. Until March 2008, the International Tennis Federation (ITF), Association of Tennis
Professionals (ATP), Women's Tennis Association (WTA), Grand Slam Committee, and several
individual tournaments had conflicting rules on how Hawk-Eye was to be utilised. A key
example of this was the number of challenges a player was permitted per set, which varied
among eventsSome tournaments allowed players a greater margin for error, with players allowed
an unlimited numbers of challenges over the course of a match.[19] In other tournaments players
received two or three per set. On 19 March 2008, the aforementioned organizing bodies
announced a uniform system of rules: three unsuccessful challenges per set, with an additional
challenge if the set reaches a tiebreak. In an advantage set (a set with no tiebreak) players are
allowed three unsuccessful challenges every 12 games. The next scheduled event on the men and
women's tour, the 2008 Sony Ericsson Open, was the first event to implement these new,
standardized rules.[

11. Association football
2011 Hawk-Eye has been proposed for use in Association football but has yet to win general
approval from the major governing bodies of the sport. The Football Association, English
football's governing body, has declared the system as "ready for inspection by FIFA," after tests
suggested that the results of a goal-line incident could be relayed to the match referee within half
a second (IFAB, the governing body for the Laws of the game, insists on goals being signalled
immediately, i.e., within five seconds).[21]
FIFA Secretary General Jérôme Valcke admits Hawk-Eye goal-line technology will be
considered if the system's developers guarantee a 100 percent success rate. Football's governing
body have previously been reluctant to use video technology to settle on-pitch disputes. Testing
of the Hawk-Eye's suitability in football is expected to continue and there could be a trial run in
the English Premier League, according to Paul Hawkins. "We will speak to FIFA over the next
week or so to get the detail, but it looks positive I think," Hawkins said.
On 3 March 2012, Hawk-Eye and another system, GoalRef, were approved by the IFAB and
advanced to a second phase of testing. If either of the two systems meet FIFA's requirements,
they may be approved in time for use in the 2014 FIFA World Cup.[23] Hawk-Eye was tested in
the Hampshire Senior Cup final between Eastleigh and Totton on 16 May 2012
at Southampton's St Mary's Stadium, although only FIFA staff had access to the system readings
and Hawk-Eye was not available to the match officials to assist with refereeing decisions.

12. On 2 June 2012, the system was tested during an international friendly between Belgium and
hosts England at Wembley Stadium. During these tests, the results of the systems will not be
used for the game; the referee will not be informed about the calls from Hawk-Eye.[26] On 5 July
2012 FIFA approved of this technology along with GoalRef to be part of the new goal line
technology system.
On 11 April 2013, Hawk-Eye was approved for use in the English Premier League from the start
of the 2013–14 season. It was officially referred to as the Goal Decision System and was used for
the first time in a game between Liverpool and Stoke City at Anfield on 17 August
2013.[27][28][29] The system uses seven cameras per goal to analyse whether or not the ball has
crossed the line.[30] The first goal to be verified by Hawk-Eye in the Premier League was scored
by Edin Džeko on 18 January 2014 between Manchester City and Cardiff City at the Etihad
Stadium.[31][32]
On 16 December 2013, it was announced that Hawk-Eye will be used in three of the four
quarter-finals and any subsequent matches in the Football League Cup.[33]The system was used
when on the very next day, when in the Sunderland–Chelsea quarter-final, an own-goal from
Sunderland's Lee Cattermole was allowed.
Snooker
At the World Snooker Championship 2007, the BBC used Hawk-Eye for the first time in its
television coverage to show player views, particularly in the incidents of potential snookers.[35] It
has also been used to demonstrate intended shots by players when the actual shot has gone awry.
It is now used by the BBC at every World Championship, as well as some other major
tournaments. The BBC used to use the system sporadically, for instance in the 2009 Masters at
Wembley the Hawk-Eye was at most used once or twice per frame.
[citation needed] Its usage has decreased significantly and is now only used within the World
Championships and very rarely in any other tournament on the snooker tour. In contrast to
tennis, the Hawk-Eye is never used in snooker to assist referees' decisions and is primarily used
to assist viewers in showing what the player is facing.

13. Gaelic games
In Ireland, Hawk-Eye was introduced for all Championship matches at Croke Park in Dublin in
2013. This followed consideration by the Gaelic Athletic Association (GAA) for its use in Gaelic
football and hurling. A trial took place in Croke Park on 2 April 2011. The double-header
featured football between Dublin and Down and hurling between Dublin and Kilkenny. Over the
previous two seasons there had been many calls for the technology to be adopted, especially
from Kildare fans, who saw two high-profile decisions go against their team in important games.
The GAA said it would review the issue after the 2013 Sam Maguire Cup was presented.[36]
Hawk-Eye's use was intended to eliminate contentious scores.[37] It was first used in the
Championship on Saturday 1 June 2013 for the Kildare versus Offaly game, part of a double
header with a second game of Dublin versus Westmeath.[38] It was used to confirm that Offaly
substitute Peter Cunningham's attempted point had gone wide 10 minutes into the second half.[39]
Use of Hawk-Eye was suspended during the 2013 All-Ireland hurling semi-finals on 18 August
due to a human error during an Under-18 hurling game between Limerick and Galway. During
the minor game, Hawk-Eye ruled a point for Limerick as a miss although the graphic showed the
ball passing inside the posts, causing confusion around the stadium - the referee ultimately
waved the valid point wide provoking anger from fans, viewers and TV analysts covering the
game live.[41] The system was subsequently stood down for the senior game which followed,
owing to "an inconsistency in the generation of a graphic".[42] Limerick, who were narrowly
defeated after extra-time, announced they would be appealing over Hawk-Eye's costly
failure. Hawk-Eye apologised for this incident and admitted that it was a result of human error.
There have been no further incidents during the GAA. The incident drew attention from the UK,
where Hawk-Eye had made its debut in English football's Premier League the day before.
Hawk-Eye was introduced to a second venue, Semple Stadium, Thurles, in 2016. There is no TV
screen at Semple: instead, an electronic screen displays a green Tá if a score has been made, and
a red Níl if the shot is wide.[
No official Irish-language term exists, although some publications have used the direct
translation Súil an tSeabhaic.
Australian football
On July 4, 2013, the Australian Football League announced that they would be testing Hawk Eye
technology to be used in the Score Review process. Hawk Eye was used for all matches played at
the MCG during Round 15 of the 2013 AFL Season. The AFL also announced that Hawk Eye
was only being tested, and would not be used in any Score Reviews during the round.
Badminton

14. BWF introduced Hawk-Eye technology in 2014 after testing other instant review technologies
for line call decision in BWF major events.[48] Hawk-Eye's tracking cameras are also used to
provide shuttlecock speed and other insight in badminton matches.[49] Hawk-Eye is formally
introduced in 2014 India Super Series tournament.

15. Doubts
Hawk-Eye is now familiar to sport fans around the world for the views it brings into sports like
cricket and tennis. Although this new technology has for the most part been embraced, it has
been criticised by from some quarters. In the 2007 Wimbledon Championships men's singles
final between Rafael Nadal and Roger Federer, a ball that appeared out was called in by 1 mm, a
distance smaller than the advertised margin of error (3.6 mm).[50] Some commentators have
criticised the system's 3.6 mm statistical margin of error as too large.[51] Others have noted that
while 3.6 mm is extraordinarily accurate, this margin of error is only for the witnessed trajectory
of the ball. In 2008, an article in a peer-reviewed journal[52] consolidated many of these doubts.
The authors acknowledged the value of the system, but noted that it was probably fallible to
some extent, and that its failure to depict a margin of error gave a spurious depiction of events.
The authors also argued that the probable limits to its accuracy were not acknowledged by
players, officials, commentators or spectators. They hypothesised that Hawk-Eye may struggle
with predicting the trajectory of a cricket ball after bouncing: the time between a ball bouncing
and striking the batsman may be too short to generate the three frames (at least) needed to plot a
curve accurately. However, the paper did not attempt to establish the accuracy of the system, and
the only technical information presented was taken from an article on the Cricinfo website.
Novak Djokovic losing his cool over a line call, late in the second set, may have been a pivotal
point of Andy Murray's historic Wimbledon victory yesterday. He believed a ball was out, but
had run out of Hawk-Eye challenges so couldn't formally dispute the call. The BBC coverage
showed Hawk-Eye's analysis of the point in question. Even if Djokovic could have challenged it,
he was wrong: the ball was good.
But how accurate is Hawk-Eye? A paper published in 2008 in a journal called Public
Understanding of Science suggests that the way Hawk-Eye analyses are presented in sport may
lead people to incorrectly assume that its output is definitely what happened. Hawk-Eye presents
a great opportunity to discuss uncertainty, confidence intervals, and the joy of stats, so here's a
Monday morning maths class.
Statistics can be tricky to understand. They're necessary in a lot of science because when testing
hypotheses or ideas, you usually can't test everyone and everything. You take what you hope is a
representative sample, and statistics allow us to make predictions about the underlying
population. They allow for chance differences between the sample and the population, so they
necessarily involve some uncertainty.
All well and good, but what has this got to do with tennis? I'm sure some people will have
clicked on this article purely because it'll have a tennis-related photo and headline, but that's part
of the argument. The Hawk-Eye paper suggests that although stats are tricky to understand (and
it should be pointed out that scientists can fall foul of misunderstanding or misinterpreting them

16. too), it's easier to understand uncertainty when there's a burning interest in being able to do so.
And who has more of a burning interest in Hawk-Eye's output than the sports fans who see it
being used to determine the outcomes of major sporting events?
I know I've shouted "REF! YOU CANNOT BE SERIOUS?!" at the TV watching England play
football (my team, Wycombe Wanderers, are rarely onscreen sadly). Television replays are used
by umpires in rugby matches to assess on-pitch events that were obscured from or missed by
them as they happened. Cricket and tennis use a different system, Hawk-Eye or similar
technology, which predicts either where the ball landed, or the path a ball would have taken.
According to the article, Hawk-Eye works via a number of cameras that capture locations of the
ball as it travels, and a model of the field of play. Cameras cannot record every moment of the
ball's flight, due to frame rate limitations, so between frames the trajectory of the ball must be
estimated. With regards to cricket, where LBW calls are questioned, Hawk-Eye extrapolates
beyond where the ball hits the pad, and predicts whether it would have hit the stumps or not.
A model's ability to predict the future path of a ball depends on a number of factors. The further
a ball travels before it stops, the easier it is to predict where it would have carried on to.
Therefore Hawk-Eye is likely to be less accurate the further towards the batsman the ball
bounces, and the further away the batsman is from his stumps. Though Hawk-Eye technology
takes some uncertainties into account, its purpose is to give a binary outcome: "out" or "not-out".
The article suggests that more information about that uncertainty should be reported to the
television audience, to more honestly show the variation in the possible true paths of a ball. For
example they suggest showing a ball's predicted location, and the confidence intervals that
surround it (if 95% this would mean there's only a 5% chance the ball actually fell outside this
larger area).
This would not only more accurately reflect the limitations of the technology, but it could
potentially teach complex statistical concepts and principles to a huge number of people. Hawk-
Eye could still provide a binary response to an umpire query, but the probability it is the true
answer will also be clear to all.
In tennis, there are differences to cricket that both aid and hinder Hawk-Eye's accuracy. Line
calls are often disputed by players, particularly in serves. This is good for using Hawk-Eye, as
the ball has actually travelled to the position where the call needs to be made (and usually
beyond), so extrapolation beyond the ball's stopping point is not needed.
But tennis balls travel extremely fast (the fastest server at Wimbledon this year was Murray's
semi-final opponent Janowicz, whose serve has clocked 143 miles per hour). A faster ball travels

17. further between each frame on a camera film, meaning more uncertainty as to its trajectory
between frames.
Hawk-Eye is almost certainly going to be correct more often than a human lines-person, but it
can't be perfect, and indeed the makers only claim it is accurate to 5mm (that was in 2008 – it
may be more accurate now with the development of faster frame rate cameras). There have been
a couple of high profile cases where Hawk-Eye appears to have got it wrong in tennis, most
notably in 2007 when Nadal could identify a mark on the court where he claimed the ball landed
(out) that Hawk-Eye reported was good.
If Hawk-Eye could provide a measure of uncertainty around its prediction, it wouldn't make its
decision any more controversial, argues the article. The results could aid the umpire, even if the
margin of error for the technology is reported and explained. They suggest the use of bails in
cricket as another aid to turning the often quick and hard-to-observe live game into a binary "in"
versus "out" decision. For example, a ball could roll slowly and hit the stumps, but not dislodge
the bails, and this would be just "the luck of the game". A close call on Hawk-Eye, which is
likely to be more accurate than a human observer but not completely infallible, is a similar
enhancement to an umpire's decision making.
The paper concludes that Hawk-Eye should be used as an aid to human judgement (their italics),
and that, if used with a little more nuance, it could provide added enjoyment of the games
involved and public understanding of technology, its uses and its limitations. What do you think?
Do you want a simple binary decision in your sports, or would you rather know the accuracy of
Hawk-Eye's output?

18. Conclusion
Hawk-Eye is a complex computer system used officially in numerous sports such
as cricket, tennis, Gaelic football, badminton, hurling, Rugby Union, association
football and volleyball, to visually track the trajectory of the ball and display a record of its
statistically most likely path as a moving image.
Hawk-Eye was developed in the United Kingdom by Paul Hawkins. The system was originally
implemented in 2001 for television purposes in cricket. The system works via six (sometimes
seven) high-performance cameras, normally positioned on the underside of the stadium roof,
which track the ball from different angles. The video from the six cameras is
then triangulated and combined to create a three-dimensional representation of the trajectory of
the ball. Hawk-Eye is not infallible and is accurate to within 5 millimetres (0.19 inch) but is
generally trusted as an impartial second opinion in sports.
It has been accepted by governing bodies in tennis, cricket and association football as a
technological means of adjudication. Hawk-Eye is used for the Challenge System since 2006 in
tennis and Umpire Decision Review System in cricket since 2009. The system was rolled out for
the 2013-14 Premier League season as a means of goal-line technology. In December 2014 the
clubs of the first division of Bundesliga decided to adopt this system for the 2015-16 season.