How Hawk-Eye works in cricket, from cameras to margins

The bowler is still appealing when the graphic appears. A red line arrives from behind the bowler's arm, bends off the surface, meets a pad, and then continues as a ghost through the batter's leg to a set of stumps drawn in outline. Everyone in the ground forms an opinion in about a second. Almost nobody watching understands that the line changed status halfway along, from a record of what happened to a calculation of what probably would have.

That change is the whole subject. Cricket ball tracking works by photographing a delivery several hundred times a second from multiple calibrated viewpoints, computing a three-dimensional position for each of those moments, and fitting a physics model through the resulting cloud of points. Everything up to the pad is measurement. Everything after it is extrapolation from that measurement, which is why the system reports a margin rather than a verdict, and why a picture that looks decisive to a crowd is treated as inconclusive by the playing conditions.

This piece is about the machine rather than the procedure. The review protocol, the allowance of reviews and the sequence a third umpire runs through are covered separately in the guide to the Decision Review System. What follows is the engineering, and what the engineering can honestly claim.

• 2001Year ball tracking reached cricket broadcasts
• 2Accredited ball-tracking providers
• 10Cameras in a full rig, upper end
• 3lbw components reported separately

Camera counts are the published upper end of a full installation and vary by venue. Accredited providers are set by the ICC playing conditions.

Who built it, and what the ICC actually accredits

Hawk-Eye was developed in the United Kingdom by Paul Hawkins, working with engineers at Roke Manor Research, and was co-invented in 2001. It arrived in cricket that year as a television toy. Broadcasters used it to draw pretty lines and argue about lbw decisions the umpire had already made and could not unmake. It had no official standing whatsoever, and for most of a decade its role was commentary rather than adjudication.

That history explains a persistent misunderstanding. The system was designed first to be watchable and only later to be authoritative, and the visual language it developed for television, a confident solid line with hard edges, is a poor representation of what the underlying calculation actually produces. The graphic has never shown its own error band. It has always looked more certain than it is, because it was built for an audience before it was built for a judge.

Two systems are accredited for international use, Hawk-Eye and Virtual Eye, and which one appears depends on the competition's playing conditions and the host broadcaster. They are not the same product. They use different camera configurations, different detection software and different models, and there is no reason to expect their outputs on a given delivery to be identical to the last millimetre.

Accreditation is a real hurdle rather than a formality. The ICC has required providers to submit to independent testing by an outside firm before their output can be used to overturn a decision, which is why ball tracking is treated differently from, say, a broadcaster's speed gun. Hawk-Eye Innovations was acquired by Sony in 2011, and the same underlying technology now appears across a range of sports, which has given it a scale of engineering investment that a cricket-only product could never have justified.

The camera rig, and why the cameras sit where they do

A tracking installation is a set of fixed high-speed cameras positioned around the ground, generally high up, often under the roof or on the upper tiers, and pointed at the pitch. A full installation runs to the high single figures or around ten cameras.

Placement follows two rules that pull against each other. Every point on the ball's likely flight has to be visible to at least two cameras at once, because a single view cannot fix a position in space. And the viewpoints have to be far enough apart in angle that the intersection of their sightlines is sharp rather than glancing. Two cameras nearly in line with each other produce a poor solution even when both can see the ball clearly.

In practice that means a spread of positions: behind the bowler's arm at both ends, square of the wicket on both sides, and intermediate angles filling the gaps. The important consequence is that the rig is part of the venue, not part of the broadcast. It has to be installed, surveyed and calibrated for that ground, and it cannot be moved during play. A camera knocked out of alignment by a spectator, a cleaner or a strong wind degrades the solution in a way nobody watching would notice.

The cameras are also not the broadcast cameras. Television cameras pan, zoom and cut, which makes them useless for measurement, because a camera that moves has to be re-calibrated continuously. Tracking cameras are locked in position precisely so that their relationship to the ground never changes.

Frame rate, and why hundreds of pictures a second is the whole trick

A fast bowler releases the ball at something over 140 kilometres an hour, which is roughly forty metres a second. At standard broadcast frame rates the ball travels a metre and a half between one picture and the next, which is why normal footage shows a smear rather than an object.

Tracking cameras run at several hundred frames a second. At that rate the ball moves a few centimetres between frames, and the flight from release to impact yields dozens of separate sightings rather than a handful.

That number of sightings is what makes everything downstream possible. A trajectory fitted through six points is a guess. A trajectory fitted through fifty is a measurement with the noise averaged out. Every source of error in the individual frames, a slightly misjudged ball centre, a compression artefact, a moment of poor contrast, matters much less when there are fifty of them to fit through.

Frame rate also sets a hard limit that no software can escape. Whatever happens between two frames is invisible. For a delivery that pitches and strikes the pad almost immediately, the number of frames between those two events may be small, and no amount of processing can recover information the sensor never captured. This is the physical reason behind the playing condition that retains the original decision when the ball travelled less than forty centimetres between pitching and impact: in that window there is simply not enough measured flight to characterise what the ball was doing after it bounced.

Finding the ball inside a picture

Before anything can be triangulated, the software has to answer a question that sounds trivial and is not. Which of these several million pixels is the ball?

The system works from difference. It holds a model of what each camera sees when nothing is happening, and looks for the compact, roughly circular region that has changed between one frame and the next and is moving in a way consistent with a cricket ball. Size, shape, brightness and the plausibility of the motion between frames all feed the decision.

The awkward cases are the ones a fan would predict. A red ball against a dark sightscreen or a crowd in dark clothing. A white ball against a pale sky at dusk. A ball passing in front of a fielder's white trousers, or through the batter's shadow, or against the moment when floodlights take over from daylight. Rain on a lens. A ball that is briefly hidden behind the batter's front leg from one camera's viewpoint.

When one camera loses the ball for a few frames the solution degrades rather than fails, because others still have it. When several lose it in the same stretch of flight, that portion of the path is reconstructed from what surrounds it rather than from direct observation. This is not visible on the graphic either.

The system also has to establish the exact frame in which the ball met the pad, and that timing is what anchors the whole lbw calculation. Everything the projection does depends on knowing precisely where the ball was at the instant its flight was interrupted.

Calibration, and turning pixels into a place on the ground

A pixel coordinate is meaningless on its own. Turning it into a position in the world requires knowing, very precisely, where each camera is, which way it is pointing, and how its lens distorts the image.

That knowledge comes from a calibration process performed at the venue. Known reference points on the ground, the creases, the stumps, surveyed markers, are used to solve for each camera's position and orientation, and a lens model corrects the barrel distortion that every wide-angle optic introduces. The output is a mathematical mapping from a point in a camera's image to a line in three-dimensional space passing through the real world.

Calibration is where a great deal of the real accuracy lives, and it is the least discussed part of the system. An error in a camera's assumed position propagates into every measurement that camera contributes to, and it does so quietly, producing plausible answers that are consistently slightly wrong. This is the reason installations are surveyed rather than eyeballed, and the reason the same equipment at two grounds is not guaranteed to perform identically.

Triangulation, and building the three-dimensional path

Once each camera's image point becomes a line in space, the geometry is straightforward in principle. Two lines from two cameras that both saw the ball at the same instant intersect at the ball's position. More cameras give more lines, and the system solves for the point that best satisfies all of them at once.

They will not intersect perfectly, and that is expected. Small errors in ball detection, in calibration and in timing mean the lines pass close to each other rather than through a common point. The solver finds the position that minimises the total mismatch, and the size of that residual mismatch is itself information about how much to trust that frame.

Repeat this for every frame and the result is a cloud of three-dimensional positions with timestamps, ordered along the flight. That cloud, not the smooth line on television, is what the system has actually measured. Everything after this stage is interpretation.

1. 1Capture the delivery at high frame rateFixed calibrated cameras around the ground photograph the ball several hundred times a second, giving dozens of separate sightings between release and impact rather than the handful a broadcast camera would produce.
2. 2Locate the ball in each frameSoftware isolates the compact moving region consistent with a cricket ball, working from the difference between successive frames and rejecting candidates whose size, shape or motion does not fit.
3. 3Convert image points into lines in spaceThe venue calibration turns each camera's pixel coordinate into a line through the real world, correcting for lens distortion and for the surveyed position and orientation of that camera.
4. 4Triangulate a position for every instantLines from cameras that saw the ball simultaneously are intersected, and the solver finds the point that best satisfies all of them, producing a timestamped cloud of three-dimensional positions.
5. 5Fit a physics model through the pointsA model of a ball in flight, accounting for gravity, drag, lateral movement and the change of direction at the bounce, is fitted to the measured cloud, which smooths out per-frame noise.
6. 6Extend the model past the point of impactWhere the ball struck the pad, the measured flight ends. The fitted model is run forward to the stumps, and that extension is the section of the graphic that carries the uncertainty.

The processing chain for one delivery. Steps one to four are measurement of what occurred; steps five and six are modelling and inference.

Fitting a trajectory, and what the model assumes

The fitting stage is where physics enters. The system does not join the measured dots. It fits a curve that a cricket ball could actually have followed, given the forces acting on it.

Those forces are known. Gravity acts downwards. Air resistance acts against the direction of travel and scales with the square of the speed. Sideways movement, whether from swing in the air or from seam or spin off the surface, appears as lateral acceleration. The bounce imposes an abrupt change of direction and a loss of speed.

Fitting a physically plausible curve through the measured cloud does two useful things. It suppresses the noise in individual frames, because a single slightly misplaced point cannot pull a whole curve out of shape. And it produces something that can be extended forwards, which a set of disconnected observations cannot.

The assumption inside all of it is that the ball will keep behaving the way a ball behaves. That assumption holds almost always, and the exceptions are exactly the deliveries most likely to be under review.

The bounce, and the hardest moment in the calculation

Everything difficult about cricket tracking is concentrated in the fraction of a second when the ball meets the surface.

At that instant the ball changes direction, loses speed, and may change its lateral movement entirely. How much of each depends on the incoming angle, the seam position, the revolutions on the ball, the hardness of the surface and what the pitch is made of. A ball landing on the seam behaves differently from one landing on the leather. A ball landing in a footmark on the fourth afternoon behaves differently again.

The system observes the bounce rather than predicting it, which helps enormously. It has frames before contact and frames after, and the change between them is measured. What it cannot know is whether the bounce was representative. A delivery that gripped in a rough patch, skidded off a bare area or hit the edge of a crack has already behaved unusually once, and the model has no way of establishing whether that was a property of the ball or a property of that particular square inch of ground. Anyone who has watched a surface deteriorate knows how much the character of the pitch can change what a delivery does from one over to the next.

Post-bounce measurement is also the shortest section of the flight in most lbw appeals, because batters are usually hit on the pad soon after the ball lands. The model therefore has plenty of evidence about the ball before the bounce and comparatively little about it afterwards, and it is the afterwards that the projection has to extend.

Where measurement stops and prediction starts

The ball hits the pad. Its actual journey towards the stumps ends there and never resumes. The question the lbw law requires an answer to concerns a flight that did not take place.

So the fitted model is run forward. It takes the ball's position, speed, direction and observed deviation at the moment of impact, and computes where the ball would have been when it reached the stumps had the leg not been there.

Two things about that extension deserve stating plainly. It is a genuinely sophisticated calculation resting on well-understood physics and a large body of measured data, and it is right far more often than a human eye watching from twenty-two yards. It is also, unavoidably, a statement about a counterfactual, and every counterfactual carries a range rather than a point.

The graphic does not show the range. It shows a line. The line is the centre of a distribution whose width the viewer is never told, and almost every argument about ball tracking traces back to that omission.

Why the error band grows, and the rules built around it

Uncertainty in the projection is not a fixed quantity. It grows with the length of the extrapolation and shrinks with the quality of the measured flight that preceded it.

1. 1Detection resolution in each frameThe ball's centre is located to within some fraction of a pixel, and a pixel at the far end of a pitch covers real distance. Individual frame errors are small and they do not vanish, they average.
2. 2Calibration of the camera positionsEvery measurement inherits any error in the surveyed position and orientation of the cameras that contributed to it. A miscalibrated rig produces confident answers that are consistently displaced.
3. 3How much post-bounce flight was measuredThe projection is anchored on the ball's behaviour after it landed. A short gap between pitching and impact gives the model very little evidence about the state it is being asked to extend.
4. 4How far the ball must be projectedA batter struck well down the pitch leaves a long extrapolation, and a small error in the modelled deviation compounds over that distance. The same output is less reliable from three metres than from one.
5. 5Whether the bounce was conventionalA ball that gripped in rough, skidded off a bare patch or struck a crack has already deviated from the model once, and nothing in the measurement reveals whether it would have done so again.

The sources compound rather than replace one another. A delivery can be affected by all four at once.

The playing conditions respond to this with distance rules rather than with a published tolerance, which is a sensible engineering answer to a problem that has no single number.

If the ball travelled less than forty centimetres between pitching and impact, there was too little measured post-bounce flight, and a not out decision stands. If the impact occurred three metres or more from the stumps, the extrapolation is too long, and a not out decision stands. Both thresholds have been amended more than once since the review system began, which is itself informative: they are calibration settings on the boundary of trust rather than laws of nature.

Overall width of the wicket22.86cm

Height of the stumps above ground71.12cm

Minimum pitching to impact distance40cm

Impact distance at which not out is retained300cm

Wicket dimensions from Law 8. The forty and three hundred centimetre thresholds are playing conditions and have been amended since the review system was introduced.

Show the numbers

The distances lbw geometry turns on, in centimetres

Item	Distance
Overall width of the wicket	22.86cm
Height of the stumps above ground	71.12cm
Minimum pitching to impact distance	40cm
Impact distance at which not out is retained	300cm

Put those numbers together and the scale of the problem becomes obvious. The system is asked to resolve whether a ball would have clipped a target under twenty-three centimetres wide, after an extrapolation that may run to three metres, from evidence that may span less than half a metre of measured post-bounce flight.

Umpire's call read as an uncertainty band

The three components of an lbw review are assessed separately, and each has a zone with a margin around it. Where the ball is clearly inside or clearly outside, the finding is conclusive. Where it straddles the boundary, the finding is umpire's call and the original decision is retained.

For the projection, the current test is whether at least half the ball is shown striking the wicket zone. The zone itself has moved twice in ways worth knowing. In September 2016 its horizontal extent was widened from the centre of off and leg stumps to their outer edges. In April 2021 its vertical extent was raised from the bottom of the bails to the top of the stumps. Each amendment reclassified a whole category of deliveries from marginal to conclusive or the reverse, without changing a single line of tracking code.

Read as engineering rather than as etiquette, umpire's call is straightforward. The system produces an estimate with an error band. Where the band lies entirely on one side of the decision boundary, the output settles the question. Where it straddles the boundary, the output does not settle it, and the playing conditions then need a rule for what happens when the evidence is inconclusive. The rule chosen is that the standing decision survives.

The consequence people find intolerable follows directly. Two identical graphics can produce opposite outcomes, because the two on-field decisions were opposite. That is not the technology contradicting itself. It is the technology declining to claim precision it does not have, twice, in a game that requires a binary answer both times. The alternative designs, giving every marginal case out or every marginal case not out, would apply a systematic bias to precisely the population of deliveries where the evidence is weakest.

What goes wrong, and how you would know

Failures are rarely dramatic. They are quiet degradations, and the on-screen output looks the same either way.

Obstructed or misaligned cameras. A fielder standing in a sightline, a piece of ground equipment, a camera nudged out of its surveyed position. The remaining cameras carry on, with a weaker geometric solution.

Difficult visual conditions. Dusk, floodlights taking over, rain on a lens, a ball the colour of the background behind it. Detection quality falls and the fitted curve rests on fewer good frames.

Very short measured flights. Full deliveries that pitch and strike the pad almost together. The distance rule exists to catch these, and it catches them by refusing to overturn rather than by flagging low confidence.

Genuinely unusual deliveries. Sharp turn out of rough, a ball keeping unexpectedly low on a worn surface, a delivery that struck a crack. The model assumes typical behaviour off the surface, and these are the deliveries where that assumption is least safe.

Human handling of the output. Someone has to operate the system, select the right delivery, mark the frame of impact and present the finding under time pressure. A correct calculation anchored to the wrong frame produces a wrong answer that looks exactly like a right one.

Uneven availability. Full tracking installations are expensive, and a great deal of first-class and domestic cricket is played without them at all. Access to a corrected decision depends partly on the commercial value of the fixture, which is not a technical failure and is a real inequity.

None of this makes the system untrustworthy. It makes it a measuring instrument with characteristics, which is what every measuring instrument is. The people who understand it least are the ones who treat it either as infallible or as a fraud.

What the same cameras produce when nobody has appealed

The lbw projection is the most argued-about output and by volume the smallest. The rig is running on every delivery of a match, and the great majority of what it records is never shown to a third umpire at all.

Each delivery generates a full description: release point, speed at release and at the bounce, the angle and height at which it landed, the exact spot on the surface it hit, lateral movement in the air and off the pitch, and the height and line at which it passed the batter. Aggregate those across an innings and you have a pitch map, a beehive of where deliveries crossed the stumps, and a bowler's movement profile. Aggregate them across a career and you have something considerably more useful than a bowling average.

That data is the reason the installation exists commercially. Broadcasters want the graphics, but analysts want the numbers, and the numbers now drive selection, field settings, match-ups between particular bowlers and particular batters, and the plans a side takes into a series. The wider practice of turning that feed into decisions is set out in the piece on how cricket teams use data.

Two things follow that are worth holding on to. The first is that the tracking model is not exercised only on review appeals; it is validated continuously against tens of thousands of deliveries whose full flight was observed without interruption, which is a large part of why the physics fit is as good as it is. The second is that the outputs used for analysis are almost entirely measurements rather than predictions, and therefore carry none of the uncertainty that makes the lbw projection contentious. A pitch map is a record. A predicted path is an inference. The same equipment produces both, and only one of them is arguable.

It also explains why the system's public reputation is so strange. Ball tracking is quietly accurate about the ninety-nine per cent of its work nobody looks at, and gets shouted at over the one per cent where it is being asked to reason about an event that never took place.

Why cricket's version is harder than tennis's

The comparison is instructive, because the same company's technology answers a fundamentally easier question on a tennis court.

Tennis line calling asks whether a ball touched the ground inside or outside a painted line. That event happened. The system reconstructs a bounce mark from measurements of a real flight, and the answer is a measurement with a small, characterisable error. It is why tennis can display a definitive in or out and move on, as the piece on electronic line calling in tennis sets out.

Cricket asks where a ball would have gone after something stopped it. Nothing about that flight happened. The system has to extend a model beyond the last real observation, and the further it extends, the wider the honest answer becomes.

There is a second difference that gets less attention. A tennis ball bounces on a manufactured, uniform, standardised surface. A cricket ball bounces on a strip of prepared soil that is deliberately different at every ground, that changes over five days, and whose variability is a celebrated feature of the sport. The pitch is the source of both cricket's richness and its tracking system's hardest modelling problem, and that is not a coincidence.

What to watch when the graphic appears

Five habits will make you a better judge of a tracking replay than most commentary boxes.

Look at where the impact was, not where the line ends. A batter struck a long way forward means a long projection, which means a genuinely wider margin than the confident line suggests, whatever the graphic implies.

Check how far the ball travelled between pitching and pad. A very short gap means the model had little post-bounce evidence, and the forty centimetre rule may end the review before the projection is even considered.

Ask whether the bounce looked normal. A ball that gripped, skidded or kept low has already broken the model's assumption once. The projection cannot know that and will draw its line with the same confidence as any other.

Remember which components were measured. Where the ball pitched and where it struck the batter are observations of real events. Only the third component, whether it was going on to hit, is a prediction. Reviews that fail on the first two never reach the interesting part.

Read umpire's call as a statement about evidence. It means the estimate and its uncertainty straddle a line, so the original decision holds. It is the system being honest, not the system being indecisive, and the signal you see in the middle afterwards is covered in the piece on what each umpire signal means.

The review procedure that surrounds all of this, the allowances, the timing and the order the tests are applied in, is set out in the DRS explainer, and the underlying dismissal law it serves is in the guide to the Laws. The rest of the game's mechanics live in the cricket section, with the full archive at the blog index. Watch enough deliveries with the measured section and the modelled section separated in your head, and the line on the screen stops looking like an answer and starts looking like what it is, which is a very good estimate that knows it is an estimate.