Vision and cricket

INVITED REVIEW

Vision and cricketDavid Regan

Department of Psychology, York University, Toronto, Canada

Citation information: Regan D. Vision and cricket. Ophthalmic Physiol Opt 2012, 32, 257–270. doi: 10.1111/j.1475-1313.2012.00909.x

Keywords: cricket, motion in depth,

spatiotemporal prediction, time to collision

Correspondence: David Regan

E-mail address: [email protected]

Received: 14 January 2012; Accepted: 13

March 2012

Abstract

This review discusses the hypothesis that hitting a cricket ball depends on pre-

dicting the instant that the ball will be located in the volume of space within

which it can be successfully hit, and that this prediction is based on retinal

image correlates of the direction of motion in depth and the time to collision

(or time to passage). The performance of top cricket players allows an estima-

tion of their accuracy in this spatio-temporal prediction. The bowler challenges

the batsman’s skill by (1) causing the ball to change direction in flight and/or

after bouncing and (2) causing linked variations in the speed and trajectory of

the ball. I suggest that the linked variations of speed and trajectory exploit a

visual inadequacy of the batsman, namely poor sensitivity to the instantaneous

absolute distance and speed of the ball. Two alternative hypothese are also dis-

cussed, one based on eye movements, the other based on continuous coupling

between perception and action.

The accuracy of predicting the instant at whichthe ball will arrive at the location where it is tobe hit

From the early 1950s to the early 1960s I was a very

enthusiastic cricketer, and from time to time played

against accomplished batsmen. The superiority of their

batting skills was very evident. One reason was that they

seemed to have more time to play the ball than I did. It

almost seemed that they could see a fraction of a second

into the future. This being a seemingly supernatural

explanation I remained baffled. But starting in the early

1970s my research colleagues and I started to gather evi-

dence that retinal image information exists that, in princi-

ple, could allow batsmen to predict when the ball will

arrive in the region of space where it is to be hit and, as

discussed below, develop the ability to translate this

when/where prediction into motor action. This article dis-

cusses the experimental evidence for this when/where

hypothesis, and compares that hypothesis with two alter-

native hypotheses. Finally I discuss how bowlers attempt

to exploit a batsman’s visual weaknesses so as to achieve

his downfall.

The question whether a batsman can visually detect a

given deviation in the trajectory of the ball become irrele-

vant at some instant during the flight of the ball. After

that instant the batsman’s finite reaction time and the

inertia of the bat preclude any significant modification to

the stroke. We and others have suggested that the reac-

tion time for modifying a highly-practiced movement that

is already in progress might be shorter than 230 ms,1 i.e.

less than the laboratory estimates for the reaction time to

an unpredicted event.2 Our argument was based on the

many instances such as, for example, McCabe’s innings of

187 not out facing the ‘bodyline’ bowling of Larwood and

Voce at Sydney in 1932,3,4 where the batsman has repeat-

edly and successfully hit the fastest and most dangerous

bowlers in the World while wearing no head protection.

The laws of cricket still allow occasional use of the tac-

tic of high-speed deliveries aimed at the batsman’s head

or body, and not until the late 1970s was it socially

acceptable to wear any head protection other than the

negligible protection offered by a soft cap. The fast bow-

ler’s intent is to provoke errors by taxing the speed and

accuracy of the batsman’s reactions, while challenging his

determination and nerve. To add to the batsman’s prob-

lems the two halves of the ball’s leather cover are joined

by prominent external stiching that forms a raised seam,

and by aligning the ball’s raised seam asymmetrically with

respect to the ball’s direction of motion, many fast and

medium-paced bowlers cause the ball to swerve while in

the air. The complex aerodynamics that undrlies this kind

Ophthalmic & Physiological Optics ISSN 0275-5408

Ophthalmic & Physiological Optics 32 (2012) 257–270 ª 2012 The College of Optometrists 257

of ‘swing’ bowling has been analysed both mathemati-

cally, and experimentally including the use of wind tun-

nels.5–10 The title of a book written by a captain of the

England team is telling: ‘I Don’t Bruise Easily’.11

As demonstrated by McCabe in 1932, an effective

response to such intimidation is the hook stroke illus-

trated in Figure 1.1,12 The batsman turns to face the bow-

ler and, as illustrated in Figure 1, some batsmen hook

with the head in line with the ball. In cricket the ball

bounces before it reaches the batsman and, depending on

how the raised seam hits the ground, the ball can unpre-

dictably change direction after bouncing.10,13 This allows

an estimate of the upper limit to the accuracy and speed

of the batsman’s spatiotemporal prediction. In particular

Figure 1 shows that, for a 40 m s)1 (90 mph) delivery,

only 230 ms remain for the batsman to adjust for any

change in the ball’s direction.1 The batsman endeavours

to hit the ball with the ‘meat of the bat’ or ‘sweet spot’

(i.e. the centre of percussion)14,15 as illustrated in

Figure 1. If the bat is swung a little too early or a little

too late, the ball may run up the bat and hit the bats-

man’s head, or even impact the head directly. The bat

must contact the ball within a rather limited volume of

space – say a cube of 10–20 cm side length. At a speed of

40 m s)1 the ball passes through the cube in 2.5–

5 ms.12,16 (A cricket bat has a flat front surface some 4.25

inches (10.8 cm) wide, while a baseball bat has a circular

cross section, so the required accuracy of spatiotemporal

prediction is presumably even higher in baseball than in

cricket.)

The performance of a straight drive shows that a top

batsman can make accurate spatiotemporal predictions

for a hitting location that is as far as 2 m from the eyes

(Figure 2).17,18

In an experimental study of batsmen’s reaction times

McLeod19 used high-speed cine-photography to record

the trajectory of the bottom of the bat when interna-

tional-level batsmen executed a hook stroke. He was

unable to find any motor response to a deviation in the

trajectory of the ball until about 0.21 s after the deviation

had occurred. On the other hand he pointed out that the

inertia of the bat may have led to overestimation of reac-

tion time.

Binocular and monocular retinal image correlatesof the direction of motion in depth and the pass-ing distance

Addressing the problem of predicting the approaching

ball’s future location, Beverley and Regan20 showed that,

for the viewing situation depicted in Figure 3, the direc-

tion (b) of the ball’s motion in depth (MID) is a function

of the angular velocities of the ball’s retinal images in the

batsman’s left and right eyes. However, this is only the

case for the component of motion within the horizontal

30 ft0.23 s

90 mph

bounces 4

5

3

2

1

Figure 1. A hook shot viewed from above. From Regan.12 Reprinted

with permission from Pion Ltd., London.

(a) (b)

Figure 2. The straight drive. The photographs show (a) the start of the swing and (b) the end of the follow through after hitting the ball. The

impact between the ball and the bat would have occurred within an imaginary ‘box’ of roughly 10–20 cm side, shown in (a) by the white outline.

The photographs are of the Australian, Victor Trumper, possibly the finest batsman in the history of cricket, at The Oval cricket ground, London in

1902. In 1903, in Sydney, Australia, Trumper drove a ball through a third story window 137 m away in the course of scoring 335 runs in 2.8 h.18

Photographs from Beldam & Fry.17

Vision and cricket D Regan

258 Ophthalmic & Physiological Optics 32 (2012) 257–270 ª 2012 The College of Optometrists

meridian21 (see Figure 4a), and does not distinguish

between directions e, f, g and h in Figure 4ba. In contrast,

Equation 1 is valid for motion within both the horizontal

and the vertical meridians (and any other meridian).

tan b ¼ fIðd/=dtÞ=Dðdd=dtÞg ð1Þ

Where d//dt is the angular velocity of the ball’s binocu-

larly-fused retinal image and dd/dt is the rate of change

of the ball’s horizontal relative disparity and D>>I.22

(Note: A rate of change of absolute disparity does not

produce a sensation of of motion in depth23.)

From Equation 1 we have

L ¼ Iðd/=dtÞ=ðdd=dtÞ ð2Þ

where L, the passing distance, is the distance between C in

Figure 3 and the point of arrival of the ball in the vertical

plane containing the eyes.24,25

Laboratory evidence discussed below supports the con-

clusion that, when predicting the ball’s future location,

observers use binocular information to discriminate trial-

to-trial variations of L (Equation 2) rather than trial-to-

trial variations of angle b (Equation 1).

Although not distinguishing between discriminations of

angle b or of L, direct evidence that observers can utilize

either Equation 1 or Equation 2 was provided by the

finding that observers can discriminate trial-to-trial varia-

tions of the direction of MID for a cyclopean target.26,27

Further evidence is that discrimination thresholds for the

direction of MID are closely similar for motion within

the vertical and horizontal meridians (Figure 4a,b) for

both cyclopean and monocularly-visible targetsb.27,29

Evidence that, when discriminating trial-to-trial varia-

tions in the direction of MID, observers are actually dis-

criminating trial-to-trial variations in passing distance (L

Figure 3. Binocular information about the direction of motion in

depth. A point object located at A is moving at constant speed in the

direction indicated by the arrow. A stationary object is located at

point B. The disparity of A relative to B is d. (Note: A rate of change

of the approaching object’s absolute disparity does not produce a

sensation of motion in depth.23) Point C is midway between the left

eye (LE) and right eye (RE), and I is the interpupillary separation. From

Regan.26 Reprinted with permission from Elsevier.

a

b c

d

e

f

g

h

(a) (b)

Figure 4. Motion in depth contained within the horizontal and verti-

cal meridians. (a) Different directions of motion in depth contained

within the horizontal meridian. (b) Different directions of motion in

depth contained within the vertical meridian. From Portfors-Yeomans

CV & Regan.27 Reprinted with permission from Elsevier.

aThe term ‘meridian’ means the angular orientation of a great

circle of the eye containing the line of sight. For brevity, the

coplanar great circle of the left and right eyes will be called the

‘horizontal meridian’ and the perpendicular meridian the ‘ver-

tical meridian’.21

bSeveral previous papers were written with the assumption that

judgments of the direction of MID were based on a function

of the velocities of the ball’s retinal images in the left and right

eyes, and that the visual system is insensitive to the direction

of MID within the vertical meridian (e.g. Ref.12). In the early

1970s static stereopsis was fairly well understood, and neurons

that were tuned to static disparity had been identified. But the

static disparity mechanism seemed to be too sluggish to allow

for a rate of change of static disparity to explain the rapid pro-

cessing of the direction of MID of an approaching ball demon-

strated by batsmen in their predictions of the ball’s future

location. Our proposed explanation was that the direction of

MID is computed directly from the horizontal velocities of the

ball’s two retinal images rather than being derived from the

prior sluggish computation of relative disparity.1,20,28 As dis-

cussed above, it was found – much later – that this assump-

tion was erroneous.27,29 As well, although ‘blindness’ to

binocular MID that spares sensitivity to relative horizontal dis-

parity is not uncommon,30–32 I have been unable to find any

report of ‘blindness’ to static disparity that spares sensitivity to

binocular MID. In hindsight, our failure to carry out experi-

ments in the 1970s on discrimination thresholds for the direc-

tion of MID within the vertical meridian is regrettable.

D Regan Vision and cricket


in Equation 2) rather than trial-to-trial variations in angle

b in Equation 1 was reported by Portfors-Yeomans and

Regan27 who used prisms to simulate a large change in

viewing distance while holding the retinal images

unchanged. The just-noticeable change in the ratio (d//

dt)/(dd/dt) was not affected by the simulated change in

viewing distance, consistent with the hypothesis that dis-

crimination of the direction of MID was based on dis-

crimination of passing distance. Had discriminations been

based on Equation 1, the just-noticeable change in angle

b should have changed considerably. However, no signifi-

cant change was detected.

To find whether the human visual system contains

multiple binocular mechanisms, each tuned to a different

direction of MID, Beverley and Regan20 compared detec-

tion thresholds for MID before and after adapting to tar-

gets that moved along different directions of MID. They

showed that there are four mechanisms for towards-the-

head motion and four for away-from-the-head motion.

Of the towards-the-head mechanisms, two signaled

‘approaching object will hit the head’, one being most

sensitive for motion directed between the nose and the

right eye, and the other to motion directed between the

nose and the left eye. At half-height the sensitivity curves

of these two mechanisms corresponded to a distance

across the observer’s face of approximately 1.1 cm. The

other two towards-the-head mechanisms dealt with all

other directions of MID. The Beverley and Regan20 exper-

iment was later extended by using a cyclopean target, thus

selecting MID mechanisms tuned to {(d//dt)/(dd/dt)}

and by using MID within both vertical and horizontal

meridians.24 Figure 5 shows sensitivity curves for MID

mechanisms derived from these adaptation data.

Discrimination threshold for trial-to-trial variations in

passing distance was sharpest for a direction of MID

passing midway between the eyesc, and corresponded to

a distance on the observer’s face of approximately

0.2 cm for one observer,28 and 0.15, 0.20, and 0.24 cm

for three observers.29 To explain why these discrimina-

tion thresholds were considerably less than the band-

widths of the most sharply-tuned MID mechanisms,

Beverley and Regan28 proposed an analogy with the

opponent-process theory of colour vision.34 According

to this theory, the first stage of colour processing is car-

ried out by three types of retinal photoreceptors, one of

which is most sensitive to short wavelengths, the second

to medium wavelengths and the third to long wave-

lengths (i.e. the S-, M-, and L-cones). All three types of

cone have very broad sensitivity vs wavelength character-

istics, with full bandwidths at half peak sensitivity

exceeding 70 nm.34 However, the just-noticeable differ-

ence of wavelength is very much narrower than the sen-

sitivity bandwidths of the cones, and falls to minima of

as little as 1–2 nm near wavelengths of about 490 and

590 nm.34 The accepted explanation for this discrepancy

is framed in terms of a second stage of colour process-

ing, namely an opponent-processing stage resulting from

subtraction. The red-green chromatic channel is the

result of subtracting the output of L-cones from the

output of M-cones. The yellow-blue colour channel is

the result of subtracting the summed output of L- and

M-cones from the output of S-cones. This opponent-

processing theory can account for the finding of both

the very low wavelength discrimination thresholds and

the spectral locations of the wavelength discrimination

minima. Beverley and Regan28 proposed that discrimination

1.0(a)

(b)

0.5

0

1.0

0.5

0–2 –1 0 1 2

Sen

sitiv

ity

Direction of motion in depth

Figure 5. Plots of relative sensitivity (ordinate) vs direction for mecha-

nisms tuned to the direction of motion in depth. Abscissae are the

ratio (d//dt)/(dd/dt). From Equation 2, )0.5 and +0.5 on the abscissae

correspond respectively to directions passing through the left eye and

right eye. (a) and (b) respectively are for motion within the horizontal

and vertical meridians. From Regan, Gray, Portfors et al.24 Reprinted

with permission from Cambridge University Press.

cPerhaps this is one reason why batsmen are urged to ‘keep

your head in line with the ball’, even ‘get your nose over the

ball’. But many batsmen need considerable urging before they

consistently play forward with the head over the ball because,

especially on the uneven surfaces sometimes encountered in

the lower grades of cricket, the batsman can be struck in the

face if the ball bounces unexpectedly high. As a young crick-

eter at Cambridge University, Prince Ranjitsihnjhi was suffi-

ciently ambitious to hire professional and even international

fast bowlers to bowl to him in practice, but for some time

found it necessary to tie his right foot to a post-hammered

into the ground before his self control was sufficiently reliable

to allow him to take advantage of the superior visual informa-

tion obtained by placing his unprotected face directly in line

with the speeding ball.33



threshold for the direction of MID is determined by the

difference between the outputs of adjacent MID mecha-

nisms. By analogy with the opponent theory of colour

vision, evidence for opponent processing was that dis-

crimination threshold fell to a minimum at each of the

three directions of MID at which the four overlapping

mechanisms had the greatest difference in the slopes of

their sensitivity curves.

Turning to monocular retinal image correlates of the

direction of MID, for the case of rigid sphere approaching

an observer’s eye, Equation 3 expresses the distance by

which the centre of the sphere will miss the centre of the

eye (i.e. the passing distance) in terms of ns, where n is a

number and s is the sphere’s linear radius,

ns ¼ ðd/=dtÞ=ðdh=dtÞ ð3Þ

and d//dt is the angular velocity of the sphere’s binocu-

larly-fused image, and dh/dt is the rate of expansion of

the sphere’s angular subtense.35,36

Peper et al.37 have reported evidence that passing dis-

tance is indeed encoded in terms of the ball’s radius, at

least in the situation that one eye is occluded.

Retinal image correlates of time to collision andtime to passage

Retinal image correlates of the time to collision (TTC)

with an approaching object can be derived by means of

the geometrical theory of optics. For example a correlate

that is available in monocular vision was derived by the

astrophysicist Fred Hoyle, (Equation 4) and first pub-

lished in 1957 as a footnote in his novel ‘The Black

Cloud’, later republished in Penguin Books.38

TTC ¼ h=ðdh=dtÞ ð4Þ

where TTC is the time to collision with a rigid spherical

object moving at constant speed along a line passing

through the observing eye, and h is the object’s instanta-

neous angular subtense at the eye. (provided that h is

small, though not so small that the rate of expansion is

below detection threshold). For an approaching object

that will pass some small distance to one side of the eye,

equation 4 also gives the approximate time to passaged.

Lee,42 who independently derived equation 4, called the

ratio h/(dh/dt) tau, and suggested that, when driving a

car, humans take advantage of Equation 4 in anticipatory

braking. Though subjected to some criticism43,44 Lee’s

original hypothesis has proved to meet the classical defi-

nition of a fruitful hypothesis, in that it sparked a great

deal of research that led to considerable advances in our

understanding of collision avoidance and interceptive

action.45

There has been much discussion as to whether observ-

ers base monocular judgments of TTC on Equation 4 or

on the ratio (perceived distance)/(perceived absolute

approach speed) (reviewed in Ref. 46). Experimental evi-

dence against the second possibility was published by

Gray and Regan.46 Regan and Hamstra47 proposed that,

rather than being determined by the approaching

object’s actual speed, the perceived speed of motion in

depth is inversely proportional to TTC. According to

this proposal, the stronger the sensation of motion in

depth, the greater the urgency for evasive or interceptive

action.

Equation 5 gives a binocular correlate of TTC for an

object at a straight-ahead location that is approaching a

point midway between the eyes at constant velocity.

TTC ¼ I=Dðdd=dtÞ ð5Þ

where I is the observer’s interpupillary separation, D is

the approaching object’s absolute instantaneous distance

and dd/dt is the object’s rate of change of horizontal rela-

tive disparity.48 For an object that will pass some small

distance wide of the eye, Equation 5 also approximates

the time to passage.

As to the relative importance of the monocular and

binocular correlates of TTC, it may not be intuitively

obvious that it does not depend on the approaching

object’s distance. In particular,

ðdh=dtÞ=ðdd=dtÞ ¼ 2s=I ð6Þ

where I, dh/dt and dd/dt have the same meanings as in

Equations 4 and 5, and s is the linear radius of the

approaching spherical object (e.g., in cm).49 Equation 6

explains why, for any normally-sighted observer, monocu-

lar information about TTC is less effective than binocular

information for approaching objects of small linear size.50

(Binocular information is not affected by the size of the

approaching object.) A second factor in the relative

importance of monocular and binocular information

about TTC is the large intersubject variability in relative

sensitivity to dh/dt and dd/dt.49 Indeed, in some individu-

als a rate of change of relative disparity produces no sen-

sation of motion in depth in some area(s) of the

binocular visual field. Such individuals are said to exhibit

dIf the rate of expansion of an approaching object’s retinal

image is not isotropic, then differing values of TTC are sig-

naled by the rates of expansion of different diameters of the

approaching object. The effect on the visual system of such

simultaneous expansion and shape change is to preclude accu-

rate estimation of absolute TTC based on monocular informa-

tion.1,39,40 However, the addition of binocular information

about TTC allows accurate estimation of absolute TTC.41



stereomotion blindnesse.30–32 In some observers, visual

field areas that are blind to stereomotion can differ for

approaching and receding motion, and for near and far

disparities.32

Many textbooks include a geometrical proof that the

difference in the distances of two points (DD) required to

produce a small constant difference in their relative hori-

zontal disparity (Dd) increases with the square of the

mean distance (D) of the two points. In particular,

Dd ¼ IDD=D2 ð7Þ

where I is the interpupillary separation and D>>DD.

Turning to the perception of MID caused by a rate of

change of disparity, we have from Equation 7

dd=dt ¼ IV=D2 ð8Þ

where dd/dt is the rate of change of relative disparity for

an object at a straight-ahead location that is approaching

the observer at speed V along a line that passes midway

between the eyes. In principle, sensitivity to dd/dt can

extend to further distances than static stereopsis, because

speed is pitted against D2 in Equation 8. From Equa-

tions 4 and 8 we have

dd=dt ¼ I=ðD�TTCÞ ð9Þ

where TTC is time to collision and the velocity of the

approaching object is constant.25 In words: (1) as distance

D increases, the value of dd/dt for an approaching object

will rise above the fixed detection threshold at progres-

sively shorter values of TTC; (2) for any given value of

TTC, the magnitude of the dd/dt signal falls off linearly

with distance.

Equation 5 leaves us with the problem of how the

visual system might encode D (the instantaneous distance

of the approaching object) with sufficient accuracy to

support estimates of TTC based entirely on binocular

information. One hypothesis might be that, when looking

directly at the object, the angle of ocular convergence (I/

D) is used – at least for distances less than a few metres.

This hypothesis, however, is not consistent with the find-

ing that, for a target of constant angular subtense (h), the

effect of large changes of ocular convergence (0–24 prism

dioptres) on the rate of change of binocular disparity

required to cancel the sensation of motion in depth cre-

ated by a fixed oscillation of h was zero for one observer

and only twofold for another observer.49 It is also incon-

sistent with evidence that large changes in vergence do

not change the perceived distance of objects.23,51 A value

for TTC is also given by Equation 10 which, similarly to

Equation 4, does not involve the approaching object’s dis-

tance.

TTC ¼ 2ðdd=dtÞ=ðd2d=dt2Þ ð10Þ

Equation 10 is valid for an object approaching at con-

stant speed from the straight-ahead position along a

straight line that passes midway between the observer’s

eyes, where d is the approaching object’s instantaneous

binocular relative disparity.52 Equation 10 also gives time

to passage for trajectories of small obliquity.

In a laboratory study it was found that, when only

monocular information was available, observers underesti-

mated TTC, and when only binocular information was

available they overestimated TTC, but when both kinds of

information were available observers were more accurate;

absolute error could be as small as 1.3%.50 The experi-

ment just described did not distinguish between an obser-

ver’s use of Equation 5 vs Equation 10, because, as

mentioned earlier, the instantaneous values of dd/dt and

d2d/dt2 were set so as to correspond to an object

approaching at constant linear velocity.

If we assume that a batsman can use visual information

about TTC up to about 230 ms before the ball is hit, a

1.3% error approaches the performance required to

account for the roughly ±2.5 ms accuracy with which a

top batsman can judge the time of arrival of the ball.

However, it is not self-evident that these laboratory find-

ings can be extrapolated to a batsman’s performance. In

particular, from a batsman’s viewpoint the approaching

ball moves simultaneously in the vertical direction, and

possibly sideways also, whereas the simulated approaching

object traveled in a straight line directly towards the

observer’s eyes. Furthermore, a 40 m s)1 (90 mph) deliv-

ery travels the length of a cricket pitch (22 yards) in

0.5 s, and in the laboratory study the shortest TTC was

1.69 s and the shortest presentation duration 0.7 s,

Finally, at 22 yards a cricket ball subtends 0.19�, while the

smallest starting size in the laboratory study was 0.4�.

A model of the early visual processing of a rateof change of size of an approaching object’sretinal images, and the generation of a motion– in – depth signal

Figure 6 shows a model based on psychophysical find-

ings.39,49,53–57 (See also Figures 3, 17, and 18 and pp.

214–218 in Ref. 58).

eThe author is stereomotion-blind in the left visual field,30,31

and was a left-handed batsman though strongly right-handed.

Perhaps left-field stereomotion blindness might explain why

some right-handed individuals bat left-handed: a left-handed

stance presents the stereomotion-sighted visual half-field to the

approaching ball.



Catching the ball

Cricket’s equivalent of the baseball catcher is called the

wicketkeeper, who, like the catcher, wears padded gloves.

In cricket, however, one or more fielders (called slip field-

ers) stand to one or other side of the wicketkeeper, per-

haps 15 m from the batsman when a fast bowler is

operating. Their role is to catch, with their bare hands,

any ball that has been deflected from the edge of the bat

so as to pass wide of the reach of the wicketkeeper The

key point here is that the ball’s trajectory is not deter-

mined until the instant that the ball leaves the edge of the

bat and, since that event is usually unintentional, the

batsman’s body position gives little, if any, predictive

information, so that the visual cues necessary to catch the

ball do not exist before that instant. When a fast bowler

is in action, the ball’s trajectory after leaving the bat is

almost a straight line and may even be rising: travelling at

36–40 m s)1 (80–90 mph) the ball’s remaining time of

flight may be so short (0.38 s in this case) as to test the

fastest reflexes. The most dramatic catches are made when

the rapidly moving ball passes wide of the slip fielder

who completes the catch with his entire body off the

ground in a horizontal position. The demands facing the

slip fielder are highlighted by the fact that, even at inter-

national level, there is a wide gulf between the great slip

fielders and everyone else. Equation 2 indicates where (in

units of I, the interpupillary separation) a catcher’s hand

should be placed to intercept a ball passing over, under

or to the side of the head.

Peper et al.37 investigated one-handed catching perfor-

mance with a real ball rather than a simulated one. Flight

time was 1.6 s, They concluded that their catchers did

not use retinal image information to predict when the ball

would arrive in the region of space where it is to be

caught, even though such information was available.

Rather, their catchers exploited a relation between visual

information and the required movement, i.e. there was a

continuous coupling between perception and action. In

particular, the catcher guided the velocity of the moving

hand in such a way that it was in the right place at the

right time. According to this hypothesis the ‘right place’

is not known until the hand arrives there. It is not clear,

however, that this analysis would apply to the case of slip

catches made off a fast bowler, as the flight time used in

their experiment (1.6 s) was considerably longer than the

approximately 0.38 s flight time from bat to slip fielder

when a fast bowler is in action.

Catching a high lofted ball in both cricket and base-

ball poses quite different problems from those facing a

slip fielder. The catcher may have to run up to 30 m. It

has been proposed that this kind of catch is also

LMRM

a

b

c

d

k1 (a–b)

k2 (c–d)

Rate ofchange ofdisparity

RM

LM

LM

LMMID

Changing-size

Motionin depth

Signal

Changing-size

Signal

Signal

Figure 6. Schematic of the early visual processing of changing-size, changing-disparity and of the encoding of time to collision with an

approaching object. The dashed line depicts the boundaries of a solid untextured rectangular retinal image. LM: Filters that respond to local

motion along the arrowed line. Their outputs (a, b, c, d) assume a magnitude that is linearly proportional to local speed, and a sign that corre-

sponds to the direction of motion. RM: One-dimensional filters whose outputs signal the speed and sign (i e., expansion vs contraction) of relative

motion along some retinal meridian. MID: Motion in depth stage, comprising a two-dimensional nonlinear filter that is most efficiently excited by

expansion of the retinal image when the expansion is isotropic i.e. provided that (in the case of vertical and horizontal meridians) the same time

to collision is signaled by the rates of expansion of the stimulus rectangle’s horizontal and vertical dimensions, i.e. k1 (a–b) = k2 (c–d), where k1 is

inversely proportional to the height of the retinal image and k2 is inversely proportional to its width. The amplitude of the output of the MID

stage is inversely proportional to the time to collision. If the equality does not hold (nonisotropic expansion) the output of the MID stage does not

reliably signal time to collision.41 The MID stage also receives input from a filter whose output is a function of the rate of change of retinal dispar-

ity. From Gray & Regan.41 Reprinted with permission from Elsevier.



achieved by a continuous coupling between perception

and action.Visual cues available to the outfielder and

which might, in principle, be used in practice have been

detailed in a number of theoretical and simulation stud-

ies.59–62 Chapman59 suggested that fielders run along a

path that cancels the acceleration of the ball’s retinal

image. Two limitations of Chapman’s analysis are that it

assumed a parabolic trajectory, and that it required the

fielder to run at constant speed. However, even if rhe

ball’s trajectory deviates somewhat from the parabolic

curve that it would follow in a vacuum, the general

strategy can still work because it is essentially an error-

nulling feedback strategy, in which the changes in the

fielder’s running are driven by the departure of optical

acceleration from zero. Following related lines of

thought, cues that are in practice used by accomplished

outfielders have been investigated in experimental field

studies.63–65

Absolute accuracy of when/where prediction

An assumption in the when/where prediction hypothesis

is that visual perception is accurate. It seems, however,

that this is not necessarily always the case. For example,

estimates of the absolute direction of MID obtained with-

out feedback using a psychophysical technique (button

pressing) showed systematic errors.66 Even with feedback

as to correctness, errors in the perceived direction of

MID remained uncorrected when the observer’s response

was a button-press. But when button pressing was

replaced by a catching task, and feedback was provided,

the absolute accuracy soon improved with practice. This

finding implies that learning was taking place within the

motor system rather than in the perceptual representation

of the direction of MID.

How important is binocular information abouttime to collision and the direction of motion indepth?

Using high speed photography, Alderson et al.67 found

that, when catching a ball with one hand, the temporal

organization of finger flexions occurred only after the ball

was closer than 1.8 m from the hand. These finger flex-

ions are necessary if the ball is to be retained in the

catcher’s grip. They were disrupted when the lights were

switched off 275 ms before the ball arrived. In an intrigu-

ing study, Banister and Blackburn68 ranked 258 Cam-

bridge undergraduates into ‘poor’ and ‘good’ categories

according to their ability at ball games, and found that

the individuals who were ranked ‘good’ had a larger aver-

age interpupillary separation than those who were ranked

‘poor’.

On the other hand it is not necessarily the case that

skilled eye-limb coordination is disrupted when vision in

one eye is lost, even in adulthood. The late Nawab of Pat-

audi was the captain of the Indian cricket team and

scored many centuries in first class and international

cricket before experiencing severe loss of vision in his

right eye as well as double vision following a car accident

in 1961. He found it necessary to counter the double

vision by using the peak of his cap to occlude his right

eye, and continued playing at international level, scoring

many more centuries, and signing off as captain of India

in 1975 by leading his team to victory in two Test

Matches against Clive Lloyd’s very strong West Indies

team.69 It is not clear why (other than some possibly

increased difficulty with slow bowlers) his batting perfor-

mance was so little affected by the loss of binocular

vision. One possible explanation is that there is a very

large intersubject variation in relative sensitivity to chang-

ing-size and changing-disparity49 and the Nawab may

have been much more sensitive to changing-size than to

changing-disparity before his accident.

Colin Milburn, an England international batsman lost

the sight of his left eye in a car accident in 1969. In 1973

and 1974 he returned to first class (County) cricket, but

Wisden found him ‘sadly diminished’-though he did

make 670 runs at an average of 17.2.70 The Nawab of Pat-

audi and Colin Milburn were both right-handed batsmen,

so that losing vision in the left eye might affect perfor-

mance more than losing the use of the right eye. On the

other hand, vision in Milburn’s right eye was also report-

edly affected by his accident.70

Independent visual processing of different kindsof visual information

It has been proposed that the various kinds of visual

information that are important for visually-guided motor

action are processed approximately independently of one

another and approximately independently of all other

kinds of visual information.1,71–73 If the visual system is

organized functionally in this way we can understand

why, once learned, a skill of eye-limb coordination, such

as hitting or catching a ball, transfers readily from one

visual environment to another. A corollary to this

hypothesis is that the degree to which a key kind of infor-

mation is processed independently of other visual infor-

mation would assume greater importance in a complex

visual environment than in a simple one, and might

determine individual differences in task performance in

field conditions such as, for example, piloting high-per-

formance jet aircraft.74,75

Next I describe psychophysical methods for testing

whether a given neural mechanism obeys the ‘independent



processing’ requirement. One technique is to render the

visual variables of interest orthogonal within the entire

stimulus set.47 To illustrate this technique consider binoc-

ular information about MID. Players of ballgames who

use Equation 2 to predict the future location of the ball

must be able to process the ratio (d//dt)/(dd/dt) inde-

pendently of simultaneous variations in d//dt and dd/dt.

In an experiment that addressed this issue the stimulus

was a bright square of 0.5� subtense whose motion simu-

lated different directions and speeds of MID.29 Each of

the 216 test stimuli simulated one of 216 different combi-

nations of direction of MID, speed of MID and excursion

of depth during the test presentation. The reference stim-

ulus had the mean direction, mean speed and mean

excursion of the 216 test stimuli. Each presentation con-

sisted of the reference stimulus paired with one of the test

stimuli.

The 216 test stimuli can be visualized in terms of a

cube of 6*6*6 stimuli. The direction of MID varied

along the x-axis while both speed and excursion were

constant; speed varied along the y-axis while both direc-

tion and excursion were constant; excursion varied along

the z-axis while both direction and speed were constant.

Following each paired presentation of reference and test

stimuli, the observer was instructed to signal three dis-

criminations of the test stimulus with respect to the ref-

erence stimulus: direction, speed and excursion. Three

psychometric functions were obtained for each discrimi-

nation. To the extent that the psychometric functions for

the task-irrelevant variables are flat in Figure 7, the

results show that the observer ignored the two task-irrel-

evant variables while making each of the three discrimi-

nations.

A similar technique was used to show that observers

discriminate trial-to-trial variations of the ratio h/(dh/dt)

(i.e. tau, TTC in Equation 4) approximately indepen-

dently of simultaneous trial-to-trial variations of h, of

dh/dt and of the size change during a presentation,47 it

previously having been shown that an isotropic rate of

change of the size of an object’s retinal image is processed

independently of frontal- plane motion for foveally-

viewed targets of diameter less than about 1.5�.55,56

100

80

60

40

20

0

(a) (b) (c)

(d) (e) (f)

(g) (h) (i)

“Wid

er”

resp

onse

s (%

)“F

aste

r”re

spon

ses

(%)

“Fur

ther

”re

spon

ses

(%)

100

80

60

40

20

0

100

80

60

40

20

00.5 1 1.5 0.8 1 1.2 0.8 1 1.21.4

Direction Speed Excursion

Figure 7. Binocular information about the direction, speed and distance moved in depth by an approaching object are processed independently.

The 216 test stimuli appeared to move in depth at different speeds and in different directions. The reference values of (d//dt)/(dd/dt), dd/dt, and

Dd corresponded respectively to 0.6� wide of a line passing midway between the eyes, 0.4 deg s)1 and 11 arc min (all normalized to 1.0 on the

abscissae). Following each presentation of the reference stimulus and one of the test stimuli the observer signaled three judgments. (a–c): The per-

centage of ‘wider of the head than the reference trajectory’ responses is plotted vs the task-relevant variable (d//dt)/(dd/dt) (in a), against the

task-irrelevant variable dd/dt (in b), and against the task-irrelevant variable Dd (in c); (d–f): The percentage of ‘faster than the reference’ responses

is plotted vs the task-irrelevant variable (d//dt)/(dd/dt) (in d), vs the task-relevant variable dd/dt (in e), and vs the task-irrelevant variable Dd (in f);

(g–i): The percentage of ‘excursion further than the reference’ responses is plotted vs the task-irrelevant variable (d//dt)/(dd/dt) (in g), vs the task

– irrelevant variable dd/dt (in h), and vs the task-relevant variable Dd (in i) From Portfors-Yeomans & Regan.29 Published by the American Psycho-

logical Association. Reprinted with permission.



Observers were able to discriminate trial-to-trial varia-

tions in the ratio (d//dt)/(dh/dt) (Equation 3) approxi-

mately independently of trial-to-trial variations in d//dt

and dh/dt.36

A variant of this technique not only allows more than

three variables to be conveniently assessed, but can also

show whether the observer ignored trial-to-trial variations

in presentation duration and distance moved when dis-

criminating trial-to-trial variations in speed even though

these three variables cannot be rendered orthogonal

within an entire stimulus set.76

The technique just described can also be used to

quantify the amount of crosstalk between responses to

the task-relevant variable and task-irrelevant variables.

This allows the identification of observers whose visual

systems do not obey the ‘independent processing’

requirement.76

Do elite batsmen have superior vision?

I have argued in this paper that sensitivity to the retinal

image variables that allow a batsman to predict when the

ball will arrive in the region of space where it is to be hit,

and the their rapid encoding, are requisites for top class

batting performance. Certainly, cricket coaches emphasize

that a batsman should ‘keep your eye on the ball’ (so as to

monitor the relevant retinal image variables for as long as

possible – though see next section) and should commit to

a stroke as late as possible. However, it does not necessarily

follow that the most successful batsmen will be superior to

the average batsman in these aspects of visual function. For

example, McLeod19 concluded that visual reaction times

for batsmen of international rank are little better than for

casual cricketers, and that the remarkable skill of elite bats-

men lies in their use of visual information to control motor

actions and, in particular, in their ability to minimize the

consequences of finite reaction times. The results of a study

on the flying performance of elite professional pilots flying

telemetry-tracked high-performance jet aircraft is consis-

tent with this conclusion.75 (Batting and piloting may, per-

haps, be comparable in that they both demand rapid and

accurate visual judgments and the translation of visual

information into motor action.) Visual discrimination

thresholds for changing size and for motion correlated with

measures of flying performance. But mean visual thresh-

olds for the pilot group did not significantly differ from the

mean for a group of graduate students who were not pilots,

and were not even particularly athletic.

Eye movements and cricket

Land and McLeod77 monitored the eye movements of

three batsmen playing 25 m s)1 (‘medium paced’ in

professional cricket) deliveries from a bowling machine.

They found that batsmen do not fixate the ball during

much of the period between the instant of delivery and

the ball’s striking the ground a few m from the batsman.

Rather, a batsman fixates the ball at the instant of deliv-

ery and for a short time afterwards, makes a predictive

saccade to the place where he expects it to hit the ground,

waits for it to bounce, and then follows its trajectory for

100–200 ms after the bounce. Land and MacLeod

reported that a short latency for the predictive saccade

distinguished their professional (County cricket) batsman

from the skilled amateur (Minor Counties cricket) and

from the much less skilled club-level batsman. They

showed that this eye movement strategy may allow the

prediction of when the ball will arrive in the region of

space where it is to be hit. They further noted that the

binocular and monocular information about TTC and the

direction of MID discussed earlier in the present review

may be used to refine the prediction during the 100–

200 ms period of tracking the ball after the bounce, and

that their analysis applies more to fast and medium paced

bowling than to slow bowling.

The batsman’s visual weaknesses and theirexploitation by slow bowlers

It is remarkable that some slow bowlers, though they do

not challenge the batsman’s reaction time and nerve, can

be more effective than even the most intimidating of fast

bowler. For example, Rhodes dismissed 4184 batsmen at

a cost of 16.7 runs per-dismissal over his 1898–1930

career in first class cricket.78 Other than A. P. Freeman, C

W. Parker and J. T. Hearne (all slow or medium paced

bowlers) no other bowler has exceeded 3000 wickets.79

No fast bowler has approached such a total, though partly

because the careers of even the most robust are cut short

by physical attrition.

One way in which a slow bowler seeks to remove a

batsman is by spinning the ball, so that on hitting the

ground it changes direction (i.e. ‘breaks’, finds the edge

of the bat, and is caught by one of the fielders. Panel (a)

in Figure 8 depicts an ‘off break’) and panel (b) depicts a

‘leg break’ (see Appendix). A counter to this stratagem is

to hit the ball immediately after hits the ground (Fig-

ure 8c). In this way a slow bowler who relies entirely on

spin can be rendered ineffectual.

To hit the ball as illustrated in Figure 8c, the batsman

must predict where the ball will hit the ground. A bowler

who combines spin with a mastery of the art of flight can

cause the batsman to predict incorrectly where the ball

will hit the ground, so that the batsman’s attempt to

achieve the situation illustrated in Figure 8c finds himself

in the situation illustrated in Figure 8a or 8b. Some skillful



exponents of flight deliberately tempt the batsman to hit

them with their strongest shots, confident that they can

induce a visual misjudgement of where the ball will hit

the ground, so that the ball is mishit and falls into a

fielder’s hands rather than passing far above his head as

the batsman intended.

The art of flight can be understood as follows. Retinal

image information does not include accurate information

about the ball’s instantaneous distance or linear speed.

Consequently, the vertical angular speed of the ball’s reti-

nal image is a poor indicator of where the ball will hit

the ground, quite apart from the fact that humans are

not good at predicting the future location of an accelerat-

ing object. The problem of predicting where the ball will

hit the ground is made even more difficult when the

bowler projects the ball slightly upwards, so that the verti-

cal component of retinal image speed is near zero during

much of the first half of the ball’s trajectory, with the

result that the batsman’s ability to discriminate vertical

speed is poor at a time when he may be forced to commit

to playing forward or back. Many batsmen compensate

for their uncertainty by playing almost ‘blindly’ forward

down the line of the ball for the first few deliveries from

a new slow bowler. This cautious initial stage of an inn-

ings is called ‘playing oneself in’ or ‘getting ones eye in’,

and during this period the batsman learns to predict

where the ball will hit the ground from visual cues picked

up from the bowler’s action and during the early part of

the ball’s trajectory. It is this kind of learning that is

exploited by bowlers skilled in the art of flight as illus-

trated in Figure 9. After several similar deliveries (contin-

uous lines in Figure 9a–c) the batsman learns to predict

where the ball will hit the ground, and confidently hits

the ball just after it leaves the ground. Then the bowler

delivers a ball with the same initial trajectory, but with a

slower speed (broken line, Figure 9a). If the reduction of

speed is artfully concealed the batsman will erroneously

predict that the ball will strike the ground at a rather

than at b, so that instead of being hit immediately after it

leaves the ground (Figure 8c), the ball has time to rise

and change direction (Figure 8a,b) with the result that the

batsman hits the ball with the edge of the bat or with

W

B

a b

R

(a) (b)

(c)

W

B

a b

R

W

B

ab

R

Figure 9. An illustration of the art of flight. The point at which the bowler releases the ball is marked R, the wickets are marked W, and the bat

is marked B. The continuous lines show the path of the ball when the bat strikes the ball just after the ball hits the ground at point a. The broken

lines in (a) and (b) show the path of the ball when a concealed reduction of speed and/or the introduction of top spin causes the ball to hit the

ground further from the bat, at point b, which may result in a mishit. A concealed increase of speed and/or the introduction of back spin, shown

by the broken line in (c), allows the ball to pass underneath the swinging bat and go on to hit the wickets. From Regan.12 Reprinted with permis-

sion from Pion Ltd., London.

W

W

W

B

B

B

X

X

X

BWL

BWL

BWL

(a)

(b)

(c)

Figure 8. (a and b) The ball, released by the bowler at point BWL,

hits the ground at point X in front of the wickets (W) and changes

direction because of its spin. At the moment of impact with the ball,

the bat is so far from point X that the ball hits the edge of the bat

and may be caught by a fielder. (c) The batsman anticipates correctly

the location (X) at which the ball will hit the ground, so that the ball

is hit with the centre of percussion of the bat immediately after it hits

the ground, and is directed where the batsman intends. From

Regan.12 Reprinted with permission from Pion Ltd., London.



some other part of the bat far from the centre of percus-

sion, and the ball may be caught by one of the fielders.

One way in which bowlers conceal a reduction in the

speed of the ball is to hold it more loosely or to flick the

wrist backwards as the ball is released.80 If in addition the

ball is released a little earlier, not only is the ball slower,

but the initial trajectory is higher (Figure 9b). The bats-

man may be even more deceived by this tactic and pre-

dict that the point of impact b will be closer than a

instead of being even further away than in Figure 9a. A

third way of inducing misjudgement is to spin the ball so

that the top of the ball rotates towards the batsman (i.e.

‘top spin’); the resulting Magnus force causes the ball to

‘dip’ and to hit the ground unexpectedly far from the

batsman (see Appendix).

A second art of the flight bowler is to induce the bats-

man to predict that the ball is further away than it really

is. After several similar deliveries (Figure 9c, continuous

line) the bowler delivers a ball with a similar initial tra-

jectory, but with artfully concealed higher speed (broken

line). If the batsman fails to detect this increase in speed

he may mishit the ball with the end of the bat and be

caught. If the visual misjudgement is more severe, the

ball may pass under the bat and hit the wicket, the so-

called ‘Yorker’ (Figure 9c). One way in which bowlers

generate a concealed increase of speed is to flick the

wrist forward at the instant of delivery. A second way of

inducing the same misjudgement is to spin the ball so

the the top of the ball rotates away from the batsman

(i.e. ‘back spin’); the resulting Magnus force causes the

ball to fall less rapidly under gravity (see Appendix).

Cardus81 describes the batsman’s experience when bat-

ting against one of the masters of flight as follows:

‘Rhodes gets his men out before the ball pitches; spin

with him is an accessory after the act of flight – flight

which disguises the ball’s length, draws the batsman for-

ward when he ought to play back, sends him playing

back when he ought to come forward, and generally

keeps him in a state of mind so confused that in time

he begins to feel it might be a mercy to get out. Against

Rhodes, no long innings has ever been played that did

not in the end find the batsman intellectually a little

worn and weary.’

Acknowledgements

I thank Dr Michael Jenkin and Dr Heather Jenkin for

advice and assistance in preparing this paper. I am grate-

ful to Howard Regan for technical help. I thank the two

anonymous referees for insightful comments. This

research was supported by the Natural Sciences and Engi-

neering Research Council of Canada (NSERC Discovery

grant to D. R.)

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David Regan received a BSc in physics from Imperial Col-

lege in 1957 followed by an MSc and PhD, also in physics.

In his PhD thesis he introduced and named the steady-state

evoked potential technique, which is the basis of the sweep

technique and the frequency-tagging technique. He was

awarded a DSc (London) in 1974. He spent 10 years in the

Research Department of Neuroscience at Keele University

before moving to Canada in 1975, where he was I.W. Killam

Research Professor and Professor of Ophthalmology at Dal-

housie University. In 1985 he moved to Toronto where he

was Natural Sciences and Engineering Research Council/

Canadian Aviation Electronics Industrial Research professor

of Vision and Aviation at York University and Professor of

Ophthalmology at the University of Toronto.

David Regan has received several awards including the

Order of Canada, Queen Elizabeth II Medal, Prentice Medal

(American Academy of Optometry), Proctor Medal (ARVO),

Dawson Medal (Royal Society of Canada) and the NSERC

Award of Excellence. He is a Fellow of the Royal Society of

Canada and a Foreign Member of the Netherlands Royal

Academy.



Documents

Vision and cricket