# Mobile Computing with a Smart Cricket Ball: Discovery of Novel Performance Parameters and Their Practical Application to Performance Analysis, Advanced Profiling, Talent Identification and Training Interventions of Spin Bowlers

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## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

#### 2.1. Development and Specifications of the Smart Cricket Ball

_{y}and ω

_{z}of the angular velocity ω were unequal zero.

_{x}is defined as the reference, then ω

_{y}measured by gyro Y is underestimated by the cosine of |90°–ψ|. An underestimation or error of 1% or ¼% that results from arccos(1–0.01) or arccos(1–0.0025) corresponds to a right angle deviation by 8.11° or 4.05°, respectively. Errors of the angular velocity of 1% do not make a difference in performance and are therefore acceptable. The same is true for further performance parameters calculated from the angular velocity such as the torque (same error as the angular velocity) or the power (twice the error of the angular velocity). The angles of the SCS in the xy–, xz–, and yz–planes of the BCS were 87.87°, 91.69°, 90.03°, respectively, which correspond to errors of 2.13°, 1.69°, 0.03°, respectively.

#### 2.2. Performance Parameters

_{R}of the ball: the spin rate results directly from the x,y,z angular velocities (ω

_{x}, ω

_{y}, ω

_{z}) measured by the three gyros incorporated into the ball,

_{R}will be denoted simply by ω, as in the course of deriving further parameters, new subscripts of ω will be used, e.g., 0 for the initial condition, t for time, min for minimum, etc.

^{2}), the time derivative of the angular velocity,

_{R}(SI unit: Nm) is calculated from Euler’s equations of motions, which are functions of angular velocity and acceleration.

_{x}≈ I

_{y}≈ I

_{z}.

_{R}results from

**T**has two components (Figure 2 and Figure 3), the spin torque

_{R}**T**and the precession torque

_{s}**T**.

_{p}**T**and

_{s}**T**are perpendicular to each other;

_{p}**T**is parallel to the

_{s}**ω**-vector;

**T**is perpendicular to the

_{p}**ω**-vector. All four vectors are located in an instantaneous plane defined by

**T**and

_{R}**ω**.

**T**and

_{R}**ω**

_{p}equals zero if θ = 0. It is evident that only T

_{s}produces the change of spin rate or angular velocity (thereby causing angular acceleration), whereas T

_{p}causes the precession of the spin axis vector

**ω**. The precession torque component

**T**of the resultant torque

_{p}**T**is therefore a lost torque that could otherwise contribute to physical performance in terms of spin rate and angular kinetic energy. However,

_{R}**T**is required to move the spin axis vector

_{p}**ω**into the torque vector

**T**[15], as

_{R}**ω**always follows the (moving)

**T**. This becomes strikingly apparent in fast bowling, where the motion of the arm imparts topspin on the ball, whereas the fingers impart a backspin during the release of the ball. Therefore, the spin axis vector has to change its direction from pointing to the left (topspin) to pointing to the right (backspin) and move from one hemisphere of the ball to the other one (Figure 3), which is enabled by the precession torque T

_{R}_{p}. The torques against the time are shown in Figure 4.

_{n}(SI unit: rad; unit used in this publication: degrees), normalised to T

_{R}and ω, results from solving Equation (10) for θ [18]:

_{n}, expressed as the angle θ, is the angle between the spin vector

**ω**and the torque vector

**T**at the instant when the

_{R}**ω**-vector commences its major move into the

**T**-vector (Figure 2, Figure 3 and Figure 5). This is usually identified from the p

_{R}_{n}-peak before the p-peak. As p

_{n}values can be larger than 90 degrees, it is advisable to calculate p

_{n}directly from the angle between

**T**and

_{R}**ω**-vectors from Equation (9). From Equation (10) it is evident, that the precession p is directly proportional to T

_{R}and the reciprocal of ω. Dividing p by T

_{R}and multiplying it by ω therefore normalises p and yields p

_{n}, as seen in Equation (13).

_{n}), ω, T

_{s}, T

_{p}, and p is explained as follows:

_{s}generates the angular acceleration α of the spinning object, which in turn changes its angular velocity ω.

_{p}generates the precession p of the spinning object, which tilts the

**ω**-vector.

_{R}, dt and I.

_{0}) + log(sin θ

_{0}) = log(ω

_{0}· sin θ

_{0}), C = ω

_{0}· sin(θ

_{0}), the product of the initial conditions.

_{0}= 1 rad/s and θ

_{0}= π/2 rad = 90°, then C = 1 and logC = 0 so that Equation (20) collapses to sin(θ) = 1/ω, a power law relationship with exponent of –1 (reciprocal function).

_{R}, dt, I. If θ → 0, then sin(θ) → 0 and ω → ∞. In other words,

**ω**can never move into, and reach,

**T**entirely [16]. The product ω · sin(θ) corresponds to the distance between

_{R}**T**and a line parallel to

_{R}**ω**where the endpoints of consecutive

**ω**-vectors are located (Figure 2).

_{1}≤ π/2 ≤ θ

_{2}≤ π, the two solutions of Equation (23); sin (θ

_{1}) = sin (π − θ

_{1}); θ

_{2}= π − θ

_{1}. As the argument of the sine function of Equation (23) cannot be greater than 1 (C/ω ≤ 1), C equals the minimum angular velocity ω

_{min}. If θ

_{0}≤ π/2, then ω

_{0}is increasing as θ

_{1}is decreasing. If π/2 < θ

_{0}≤ π, then ω

_{0}decreases first until it reaches ω

_{min}at θ = π/2, followed by increasing ω. However, θ only decreases from θ

_{0}, first as θ

_{2}and from θ = π/2 as θ

_{1}. In a numerical context, this condition is only satisfied when obeying the rule that dθ/dt < 0; i.e., calculating both θ

_{1}and θ

_{2}and select only consecutive θ-pairs whose dθ/dt is negative.

_{0}= 0

_{R}has a constant value. If θ

_{0}= 0 then C = 0 and ω = t T

_{R}/I + ω

_{0}= t α + ω

_{0}. The ‘±’ sign in front of the square root takes care of different θ

_{0}-conditions (not θ!): positive sign if θ

_{0}< π/2 (Figure 3a), negative sign if θ

_{0}> π/2 (Figure 3b). Equation (28) can be rewritten as:

_{0}.

_{R}is constant); and Equation (23) provides the analytic solutions of θ, as a function of ω but independent of T

_{R}(be it constant or a function of time).

_{R}, as described by Equations (20)–(22), defines the unique dynamics of precession. It is explained from the left side of Equations (15) and (16), namely by the term dt·T

_{R}/I: if T

_{R}increases, then dt decreases and any instantaneous pair of ω and sin(θ), whose product is constant at all times, simply happens earlier and faster, i.e., at smaller times.

_{0}> 0. At the same magnitude of

**T**, the difference between θ

_{R}_{0}= 0 and θ

_{0}> 0 is that, in the former case, all energy produced by

**T**changes the magnitude of

_{R}**ω**; whereas in the latter case, a certain percentage of this energy is wasted for precession. If θ

_{0}= 90°, then at this moment, the percentage is 100%, as T

_{R}= T

_{p}, and T

_{s}= 0. In general, the angular kinetic energy E

_{kin}is calculated from:

^{2}is spinning at ω

_{0}= 1 rad/s. A constant torque T

_{R}of 1 Nm is imparted on the sphere with a rectangular impulse of a duration of 1 s, whereby the initial angle θ

_{0}between

**ω**and

_{0}**T**is 1.12 rad (64.16°; sinθ

_{R}_{0}= 0.9). The initial angular kinetic energy E

_{0}of the sphere before imparting the torque is 0.5 J from Equation (31). At t = 1 s after the T

_{R}was imparted, from Equations (28,29), ω = 1.695 rad/s. The actual E

_{kin}is therefore 1.436 J. Let us assume the ideal condition that θ

_{0}= 0, i.e., all energy that can be potentially produced by T

_{R}accelerating ω. Then, from Equations (28,29), ω = 2 rad/s. The ideal E

_{kin}is therefore 2 J. Subtracting E

_{0}from the two E

_{kin}provides the energies supplied by the torque, for actual and ideal conditions: E

_{actual}= 0.936 J, and E

_{ideal}= 1.5 J. Both E

_{actual}and E

_{ideal}represent a

**change**(Δ) in energy, produced by the torque imparted on the sphere.

_{actual}and E

_{ideal}were calculated from two angular velocities (more precise: from changes in velocity squared), namely ω

_{actual}, identical to ω

_{R}(the vector sum of ω

_{xyz}) of Equation (2), and ω

_{ideal},

**ω**,

_{ideal}**α**, and

_{R}**T**, are stationary and collinear, and that the angle θ between

_{R}**ω**and

_{ideal}**T**is 0.

_{R}_{0}and its energy E

_{0}) and the terminal kinetic energy at release of the ball (terminal spin rate ω

_{t}and its energy, E

_{t}):

^{2}avoids any influence of energy produced by a source other than the actual mechanism that is responsible for generating the spin rate of the ball immediately before release. This issue is also seen from the position of the spin axis when rotating the bowling arm and when imparting spin on the ball. This position changes from one action to the other, and thereby causes precession of the spin axis. This is most impressively seen in fast bowling, where the rotation of the arm produces a top spin of the ball, whereas the ball is released with a backspin. Consequently, the spin axis has to move from one side of the ball to the other [15,16], and as a result, the ball is temporarily decelerated (cf. Figure 3b), followed by an acceleration.

_{0}was determined at the time stamp t

_{1}, implemented in Equation (33), when T

_{R}exceeds 0.02 Nm. This threshold was determined empirically as the beginning of the torque spike. ω

_{t}was determined at the time stamp t

_{2}after the T

_{R}-spike when the ratio T

_{p}/T

_{R}exceeds 0.98 (before reaching its maximum at 1). At this point, the aerodynamic torques are greater than 98% of the total torque T

_{R}and have almost entirely taken over the torques acting on the ball, whereas the finger torques (T

_{s}) dropped to negligible values. The fact that the release point of a spinning object happens when T

_{p}/T

_{R}reaches 1 was already suspected earlier but ultimately verified with a smart frisbee [30]. As a frisbee is released faster than a cricket ball, the transition from sub-unity T

_{p}/T

_{R}to unity T

_{p}/T

_{R}happens sharper and more suddenly than in a cricket ball which is characterised by a more gradual transition.

_{max}/ω

_{max}, has the unit s

^{–1}and therefore corresponds to frequency. If ω were half a sine wave

_{max}at t = 0 and ω

_{max}at t = π/2, then

_{max}/ω

_{max}ratio, the longer is the cycle period, and the more spin rate is produced relative to the angular acceleration.

_{n}(θ

_{0}), p, and T

_{p}are peak values that do not occur at the same time, but rather in the order as indicated, all of them before the T

_{R}-peak (Figure 5). All performance parameters, physical and skill, grant a unique and detailed view into the biomechanics of how the spin rate of the ball is generated.

#### 2.3. Applications of the Performance Parameters

#### 2.3.1. Study 1

^{2}value to identify by how much an individual skill parameter is uninfluenced by the remaining four.

#### 2.3.2. Study 2

#### 2.3.3. Study 3

^{2}value of the regression slope and its p-value, as well as in terms of the residual standard deviation and the differential of the predicted values of first and last balls, to identify any improvement (training effect) or decline (e.g., due to fatigue) of the performance parameters.

#### 2.3.4. Study 4

**ω**was negative, whereas the sense of

**ω**was positive in wrist-spin deliveries (but also in fast bowling). Therefore, the flipper delivery was identified as a finger-spin delivery (cf. Study 2 above), in contrast to the common, but incorrect, belief it be a wrist-spin delivery (cf. figure 5.19 of [2]).

## 3. Results

#### 3.1. Study 1

_{R}of 0.26–0.265 Nm produces a spin rate ω of 14 rps in a fast bowler (X in Figure 6a), 21 rps in a finger spinner (F in Figure 6a), and 28 rps in a wrist spinner (W in Figure 6a). The wrist spinner generates two times more spin rate than the fast bowler—but at the same torque expenditure. This striking result is not only predominantly due to the three different deliveries, but also due to the skill of the bowler. When dividing the torque T

_{R}(Nm) by ω (rps), we obtain the bowling potential (BP in Figure 6a), with the rule of the thumb that 0.1 Nm produces a spin rate of 10 rps (BP = 1; [22]). In Figure 6a, the BP in spin bowlers ranges from 0.75 to more than 1.35. The larger the BP, the more potential the bowlers have to improve their skills by reducing, for example, the precession, which had prevented them from producing more energy in the first place. At a small BP, the skill has already reached a high level of proficiency, and the only practical way for improving the spin rate is through muscle training.

_{max}/ω

_{max}does not depend on the other four skill parameters in less than 7% for all data (spin and seam bowling combined, as well as seam bowling alone), this percentage ranges from 15 to 49% in spin bowling for all five skill parameters.

_{n}has a high R

^{2}value and clearly separates the cohorts of the three different deliveries, the smaller the R

^{2}value becomes, the more the three cohorts merge and overlap. In Figure 6b, while the wrist-spin’s precession ranges only from 14 to 16 rad/s, the data range of the normalised precession spans from 24° to 76°. The opposite is true for seam bowling, 84–241 rad/s versus 105°–132°. In short, within a single delivery, there is no evidence of a perfect correlation between two single skill performance parameters, because they represent the performance of different aspects of spin generation.

#### 3.2. Study 2

#### 3.3. Study 3

^{2}value explains by how much the change of a parameter can be explained from how often the ball is bowled. The p-value informs us of the likelihood that the trend observed is due to chance (if p > 0.1 then the likelihood is >10%; alpha = 0.1). The Δ 10-over value provides the change of the dependent parameter, across the spell, estimated from the model (if p < 0.1).

_{R}and T

_{s}(marginally significant), and power P (marginally significant). The effect on power is explained from ω and T

_{s}(i.e., from their product). Participant 1 shows losses in skill performance, namely with the normalised precession p

_{n}and the efficiency η. Realistically, irrespective of any p-value considerations, the authors of this paper consider an increase in p

_{n}of 7° as substantial from experience; whereas, all other changes, particularly the increase in T

_{R}and the decrease of η are considered trivial.

_{R}and α/ω, while a loss in T

_{s}. The effect on α/ω is explained from the gain in ω and the loss in T

_{s}, considering that α = T

_{s}/I. The gain in α/ω is substantial, the trend effect on T

_{R}and T

_{s}is medium, and the effect on ω is low.

_{R}(marginally significant), T

_{s}, and P. (which is the opposite effect seen in participant 1, except for α/ω, not affected in participant 1). The effect on η is considered substantial (very large); on P large; on T

_{s}medium, and on ω low.

_{R}and T

_{s}) and power. These two profiles were different because participant 2 bowled wrist-spin and therefore could generate more spin from a smaller torque. A striking result is the torque distribution of T

_{R}:T

_{s}:T

_{p}= 0.28:0.22:0.20 of participant 2 with a relatively high T

_{p}, in contrast to participant 1 (0.29:0.28:0.11) and participant 3 (0.24:0.22:0.12). This result corresponds to a lower level of skill performance of participant 2. Accordingly, we would be inclined to assume that the remaining four skill parameters of participant 2 correspond to lower skill levels too. However, since participant 2 is a wrist-spinner, it is not surprising that he produces the lowest precession p, the 2nd lowest p

_{n}, the highest η, and the lowest α/ω. This result emphasises the importance of considering a bowler’s performance relative to the type of delivery (Figure 7) to prevent misinterpretations. Furthermore, this result, although extreme, mirrors the data shown in Table 2, namely that approximately 50% of T

_{p}cannot be explained from the other four performance parameters. It has to be emphasised at this point that we are comparing peak values here.

_{n}, as well as T

_{p}and P exhibit a higher RMSE% than the other parameters.

#### 3.4. Study 4

_{p}was unusually high (red arrow in Figure 10a), and the spin torque T

_{s}was even negative (green arrow in Figure 10a) immediately before the main spike. T

_{s}is negative only if θ

_{0}(p

_{n}) is greater than 90°, typical for fast bowlers (Figure 6b–d,f). As expected, the average θ

_{0}was 94.69°. The statistics of the profiling exercise are shown in Table 4.

_{R}and T

_{s}(and thus ω) were smaller when bowling the unusual technique, which was not surprising as the coach was not used to the new unusual bowling movement. The magnitude of the peak T

_{p}was not smaller when bowling the unusual technique, however, when normalising it to the T

_{R}, it was comparatively higher in the unusual technique. The difference in efficiency η was 73% for the traditional technique, and 37% for the unusual one.

_{s}spike became positive, and the average T

_{p}over a 0.123 s window (Figure 10) decreased significantly (T

_{s}

_{_}_{min}: p = 0.0006, effect size r = 0.83/large effect; T

_{p}

_{_}_{avg}: p < 0.0001, effect size r = 1/large). The physical performance parameters decreased significantly (ω, T

_{R}, T

_{s}, α, P; all of them at p < 0.0001, and effect size r = 1/large), as the bowler was not used to the traditional technique (the same effect as seen in the coach’s data; Figure 12). However, in terms of skill performance parameters, efficiency η, normalised precession p

_{n}, precession torque T

_{p}and the ratio α

_{max}/ω

_{max}improved significantly (η from 39% to 59% [p < 0.0001, effect size r = 1/large]; p

_{n}from 95° to 78° [p = 0.0006, effect size r = 0.83/large]; T

_{p}from 0.1405 to 0.1234 Nm [p = 0.0226, r = 0.56/large); α

_{max}/ω

_{max}from 22.93 to 21.91 s

^{–1}[p < 0.0001, r = 1/large]).

_{R}: p = 0.0688, effect size r = 0.44/large; T

_{s}and α: p = 0.0226, effect size r = 0.56/large; P: p = 0.0404, r = 0.5/large); p

_{n}worsened to 90° (not different from p

_{n}before the intervention training), η dropped only slightly to 55% (p < 0.0001, effect size r = 1/large); T

_{s_min}decreased but was still far better than the data before the intervention training, whereas T

_{p}

_{_avg}worsened slightly but was still better than the average before the intervention training (p < 0.0001, effect size r = 1/large). The data in Table 4 are summarised graphically in Figure 13.

## 4. Discussion

_{n}, identical to θ

_{0}, the angle between

**ω**and

**T**. The closer

_{R}**ω**and

**T**are, the smaller is θ

_{R}_{0}, and the more torque is converted to ω and to angular kinetic energy, rather than wasted for precession. θ

_{0}depends on how fluently the movements are executed, but also on the type of the delivery. A striking example of additional but unnecessary movements of a baseball pitcher was given by Doljin et al. [33]. The pitching efficiency of this player was only 5.4%, the spin rate a low 15.7 rps, but the torque was extraordinarily high at 0.396 Nm. A wrist spinner could have easily achieved 40 rps with the same torque.

_{R}but also, even more important, how efficiently the torque is imparted for the purpose of generating the spin rate ω, gauged from the skill parameters. The first step for doing this is consulting the bowling potential (BP, Figure 6a), i.e., 100 T

_{R}(Nm)/ω (rps). The greater it is, the less skilful are the bowlers, but the more potential they have of increasing their spin rate when improving their lacking skill. In other words, the greater the BP, the more scope the bowlers have to improve their spin rate by becoming more technically proficient through training.

_{n}data of the wrist-spin sidespin delivery shown in Figure 7b are 41° on average, the wrist-spinner with the fastest spin rate (36 rps) shown in Figure 6a had a normalised precession p

_{n}of 24°, the smallest of all data shown in Figure 6b.

## 5. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

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**Figure 1.**The smart cricket ball and its components; (

**a**) from left to right: battery, circular PCB, sensor on breakout board; (

**b**) sensor assembly; (

**c**) assembled sensors on carrier; (

**d**) inductive charging dock; (

**e**) smart cricket ball.

**Figure 2.**Basic principle of precession;

**ω**= angular velocity vector (the subscripts refer to different times t, i.e., 0 at t = 0, etc.),

**T**= resultant torque vector,

_{R}**T**= spin torque component (same direction as

_{s}**ω**),

**T**= precession torque component (perpendicular to

_{p}**T**and

_{s}**ω**),

**p**= precession vector (perpendicular to the

**T**-

_{R}**ω**plane); the vectors

**p**,

**ω**, and

**T**are perpendicular to each other and follow the right-hand rule (

_{p}**P-S-T rule**; S denotes the spin rate

**ω**); the curved and dashed grey arrow indicates the movement of the

**ω**-vector into the

**T**-vector, where the

_{R}**ω**-vector’s magnitude increases continuously as it is accelerated by

**T**; note that the vertical dashed grey line connecting the arrow tips of the

_{s}**ω**-vectors is parallel to the

**T**-vector, to satisfy Equation (22).

_{R}**Figure 3.**Principle of the two torque components: the torque vectors

**T**and the angular velocity vector

**ω**are located in the plane of the circle;

**T**is the resultant of the spin torque

_{R}**T**and the precession torque

_{s}**T**;

_{p}**T**is parallel to

_{s}**ω**;

**T**is perpendicular to

_{p}**ω**; θ is the angle between

**T**and

_{R}**ω**; the precession vector

**p**is perpendicular to the plane of the circle (pointing out of this plane); the sequence of the vectors

**p**,

**ω**, and

**T**follows the right-hand rule (comparable to the x,y,z axes of a coordinate system); (

_{p}**a**): θ < 90° so that

**T**increases the magnitude of

_{s}**ω**; (

**b**): θ > 90° (fast bowling) so that

**T**reduces the magnitude of

_{s}**ω**until θ = 90°.

**Figure 4.**Torques against time; T

_{R}= resultant torque, T

_{s}= spin torque, T

_{p}= precession torque; the release point is determined from T

_{p}/T

_{R}reaching unity.

**Figure 5.**Normalised precession p

_{n}(= θ, the angle between the spin rate vector

**ω**and the torque vector

**T**), precession p, and torque T

_{R}_{R}, against time, exemplifying the sequence of peak data; note that p

_{n}(= θ) drops to 3.5° after the T

_{R}peak.

**Figure 6.**Correlation of different performance parameters; red dots (white X): fast bowlers; green dots (white F): finger-spinners; blue dots (white W): wrist-spinners; (

**a**) torque vs spin rate, the yellow isolines indicate the bowling potential BP at three different levels; the dashed horizontal isoline indicates a torque of 0.26–0.265 Nm, corresponding to 14 rps spin rate in fast bowlers, 21 rps in finger-spinners, and 28 rps in wrist-spinners; note that the wrist-spinners generate twice the spin rate than the fast bowlers at this torque level (this subfigure utilises the data shown in figure 1 of Fuss et al. [22], © 2020 by the authors. Licensee MDPI, Basel, Switzerland.); (

**b**) precession vs normalised precession; the two yellow lines separate the three bowler cohorts; (

**c**) efficiency vs normalised precession; the two yellow lines separate the three bowler cohorts; the dashed vertical line at 90° separates the bowlers with θ

_{0}(initial the angle between the spin rate vector

**ω**and the torque vector

**T**) smaller (Figure 3a) and greater (Figure 3b) than 90°; (

_{R}**d**) α

_{max}/ω

_{max}vs. normalised precession; the two yellow lines separate the three bowler cohorts; (

**e**) efficiency vs normalised precession; (

**f**) precession torque vs normalised precession.

**Figure 7.**Skill performance parameters (box plots and averages) vs. type of delivery; the skill performance parameters are: (

**a**) precession; (b) normalised precession; (

**c**) efficiency; (

**d**) ratio α/ω; green: finger-spin; blue: wrist-spin; BS = backspin, BSS = backsidespin, SS = sidespin, TSS = topsidespin, TS = topspin; the transition from BS to TS is continuous; FL = Flipper; DO = Doosra; GO = Googly; the asterisks denote outliers.

**Figure 8.**10-over spell of participant 3 (Table 3; best improvement of all performance parameters across all participants); efficiency vs. number of delivery (bowling of 6 balls = 1 over); linear fit (red) and running average (green, window width of 9 data).

**Figure 9.**RMSE% and RMSE% normalised to the average (avg) RMSE% of each participant (black: participant 1; blue: participant 2; purple; participant 3) and each performance parameter shown in Table 3 (residual standard deviations during the 10-over spells); the dashed lines show the average RMSE% of each participant, used for normalising the RMSE% in the right graph; the green line corresponds to the average of all participants.

**Figure 10.**Torques vs. time before (

**a**) and after (

**b**) intervention training; T

_{R}= resultant torque (black); T

_{s}= spin torque (green), T

_{p}= precession torque (red); the red and green arrows in subfigure (

**a**) indicate the increased T

_{p}and negative T

_{s}; the blue horizontal line indicates the baseline at 0 Nm, black horizontal line indicates the threshold at 0.02 Nm (cf. main text); the yellow double arrow defines the 0.123 s window for calculating the average T

_{p}(ending at last negative T

_{s}peak before the main T

_{R}peak).

**Figure 11.**Different sections of the torque vs time graph of Figure 10a, used for calculating the moving centre of pressure (COP); L = COP movement along the seam; C = COP movement across the seam; X and Y: smart ball coordinate system.

**Figure 12.**Data of the coach bowling a standard topsidespin (

**a**) in the traditional way and re-enacting the bowler’s technique (

**b**) shown in Figure 10a; T

_{R}= resultant torque (black); T

_{s}= spin torque (green), T

_{p}= precession torque (red); the red and green arrows in subfigure (

**b**) indicate the increased T

_{p}and negative T

_{s}; the blue horizontal line indicates the baseline at 0 Nm, black horizontal line indicates the threshold at 0.02 Nm (cf. main text).

**Figure 13.**Data of Table 4 in graphical form; the data before the training intervention are set to 100%, and the data after the intervention are shown relative to the data before the intervention; percentage > 100% = improvement of a skill parameter after intervention; percentage < 100% = decline of all 5 physical performance parameters after intervention; after intervention (

**A**) = immediately after the intervention; after intervention (

**B**) = after several days of self-training; min T

_{s}and avg T

_{p}refer to the yellow double arrow in Figure 10, defining the 0.123 s window for calculating the average T

_{p}, ending at last negative T

_{s}peak before the main T

_{R}peak.

Physical Performance Parameters | Training Target | Skill Performance Parameters | Training Target |
---|---|---|---|

Maximum spin rate ω_{R} | Improve | Maximum precession p (before the torque spike) | Reduce |

Maximum angular acceleration α | Improve | Maximum normalised precession p_{n} = θ (before the torque spike) | Reduce |

Maximum resultant torque T_{R} | Improve | Maximum precession torque T_{p} | Reduce |

Maximum spin torque T_{s} | Improve | Efficiency η | Improve |

Maximum power P | Improve | ‘Frequency’ α_{max}/ω_{max} | Reduce |

**Table 2.**Unaccounted percentage of a specific skill parameter, not explained from the other four skill parameters, calculated from 100 minus 100 · R

^{2}of a multiple regression; e.g., 4.25% means that the magnitude of the decadic logarithm of the precession (dependent parameter) does not depend on the remaining four (independent) skill parameters in 4.25%; F = finger-spinners, W = wrist-spinners, X = fast bowlers; log

_{10}p

_{max}= decadic logarithm of the precession; p

_{n_}

_{max}= normalised precession; T

_{p_}

_{max}= precession torque; η = efficiency; α

_{max}/ω

_{max}= ratio of maximal angular acceleration to maximum angular velocity (spin rate).

Skill Parameter | Log_{10}p_{max} | p_{n_}_{max} | T_{p_}_{max} | η | α_{max}/ω_{max} |
---|---|---|---|---|---|

F + W + X | 4.25% | 18.63% | 32.29% | 23.19% | 6.66% |

F + W | 15.18% | 43.69% | 48.51% | 34.69% | 27.47% |

X | 5.41% | 15.97% | 25.89% | 38.53% | 6.77% |

**Table 3.**Statistical data of physical and skill parameters during a 10-over spell; data in bold font: significant trend if p < alpha (alpha = 0.1); italicised items: marginally significant, 0.1 < p < 0.12; RMSE = root-mean-square error (deviation) = residual standard deviation; RMSE% (= CV

_{RMSD}) = 100 · RMSE/mean; Δ 10-over: differential between predicted values of 1st and last ball; ‘effect on performance’ according to Table 1; ‘%change’ = 100 · (Δ 10-over)/mean.

Spin Rate ω (rps) | Maximum Precession p (rad/s) | Maximum Normalised Precession p_{n} (deg) | Maximum Resultant Torque T_{R} (Nm) | Maximum Spin Torque T_{s} (Nm) | Maximum Precession Torque T_{p} (Nm) | Maximum Power P (W) | Effici-ency η (%) | Ratio α_{max}/ω_{max} (s^{–1}) | |
---|---|---|---|---|---|---|---|---|---|

10-over spell, participant 1 (finger-spin topsidespin) | |||||||||

Mean | 25.95 | 33.40 | 89.29 | 0.2913 | 0.2815 | 0.1142 | 26.83 | 54.76 | 22.20 |

RMSE | 0.73 | 2.02 | 4.93 | 0.0113 | 0.0101 | 0.0062 | 1.60 | 2.10 | 0.36 |

RMSE% (= CV_{RMSD}) | 2.81 | 6.04 | 5.56 | 3.88 | 3.90 | 5.46 | 5.97 | 3.83 | 1.63 |

R^{2} | 0.0402 | 0.0146 | 0.1522 | 0.0466 | 0.0429 | 0.0293 | 0.0402 | 0.0559 | 0.0233 |

p-value (alpha = 0.1) | 0.1171 | 0.3510 | 0.0017 | 0.0924 | 0.1062 | 0.1821 | 0.1194 | 0.0650 | 0.2349 |

Trend of regression | Increase | nil | Increase | Increase | Increase | nil | Increase | Decrease | nil |

Effect on performance | Gain | nil | Loss | Gain | Gain | nil | Gain | Loss | nil |

Δ 10-over | 0.50 | 6.95 | 0.0083 | 0.0077 | 1.09 | −1.70 | |||

%change | 1.91 | 7.79 | 2.85 | 2.74 | 4.06 | −3.11 | |||

10-over spell, participant 2 (wrist-spin sidespin) | |||||||||

Mean | 28.43 | 21.12 | 80.18 | 0.2821 | 0.2238 | 0.1960 | 24.60 | 64.86 | 16.13 |

RMSE | 1.34 | 3.08 | 14.16 | 0.0213 | 0.0173 | 0.0291 | 2.85 | 4.17 | 1.12 |

RMSE% (= CV_{RMSD}) | 4.72 | 14.73 | 17.72 | 7.56 | 7.70 | 15.04 | 11.61 | 6.40 | 6.91 |

R^{2} | 0.0661 | 0.0495 | 0.0178 | 0.0702 | 0.0828 | 0.0531 | 0.043 | 0.0415 | 0.2058 |

p-value (alpha = 0.1) | 0.1008 | 0.1576 | 0.4004 | 0.0895 | 0.0647 | 0.1415 | 0.1878 | 0.1943 | 0.0025 |

Trend of regression | Increase | nil | nil | Increase | Decrease | nil | nil | nil | Decrease |

Effect on performance | Gain | nil | nil | Gain | Loss | nil | nil | nil | Gain |

Δ 10-over | 1.75 | 0.0286 | −0.0254 | −2.80 | |||||

%change | 6.14 | 10.14 | −11.36 | −17.34 | |||||

10-over spell, participant 3 (finger-spin topsidespin) | |||||||||

Mean | 21.23 | 42.35 | 64.55 | 0.2410 | 0.2205 | 0.1200 | 17.75 | 50.92 | 21.22 |

RMSE | 1.54 | 5.03 | 7.04 | 0.0204 | 0.0221 | 0.0115 | 2.89 | 6.04 | 0.83 |

RMSE% (= CV_{RMSD}) | 7.22 | 11.89 | 10.91 | 8.47 | 10.01 | 9.54 | 16.18 | 11.91 | 3.91 |

R^{2} | 0.0534 | 0.013 | 0.0006 | 0.0459 | 0.0732 | 0.0031 | 0.0508 | 0.4316 | 0.0764 |

p-value (alpha = 0.1) | 0.0755 | 0.3879 | 0.8500 | 0.1003 | 0.0366 | 0.6760 | 0.0837 | 0.000 | 0.0326 |

Trend of regression | Decrease | nil | nil | Decrease | Decrease | nil | Decrease | Increase | Decrease |

Effect on performance | Loss | nil | nil | Loss | Loss | nil | Loss | Gain | Gain |

Δ 10-over | −1.26 | −0.0154 | −0.0213 | −2.30 | 18.08 | −0.82 | |||

%change | −5.91 | −6.39 | −9.68 | −12.96 | 35.52 | −3.85 |

**Table 4.**Statistics of performance parameters before and after training intervention; avg = average; std = standard deviation).

Spin Rate ω (rps) | Maximum Precession p (rad/s) | Maximum Normalised Precession p_{n} (deg) | Maximum Resultant Torque T_{R} (Nm) | Maximum Spin Torque T_{s} (Nm) | Maximum Precession Torque T_{p} (Nm) | Maximum Angular Acceleration α (rad/s^{2}) | Maxi-mum Power P (W) | Effici-ency η (%) | Ratio α_{max} / ω_{max} (s^{–1}) | Minimum T_{s} (Nm) Before Peak Datum | Average T_{p} (Nm) of a 0.123 s Window (cf. Figure 10) | |
---|---|---|---|---|---|---|---|---|---|---|---|---|

Profiling, before the training intervention | ||||||||||||

Avg | 28.31 | 40.14 | 94.69 | 0.3309 | 0.3172 | 0.1405 | 4079 | 32.38 | 39.09 | 22.93 | −0.0055 | 0.0428 |

Std | 0.8 | 2.66 | 8.82 | 0.0112 | 0.0091 | 0.0183 | 117.2 | 1.81 | 4.24 | 0.23 | 0.0104 | 0.0065 |

Min | 27.18 | 35.01 | 86.91 | 0.3156 | 0.3052 | 0.1143 | 3925 | 30.23 | 34.13 | 22.64 | −0.0223 | 0.0346 |

Max | 29.23 | 42.51 | 108.51 | 0.3463 | 0.3307 | 0.1601 | 4253 | 34.94 | 45.75 | 23.2 | 0.0033 | 0.0492 |

After the training intervention | ||||||||||||

Avg | 24.97 | 38.3 | 78.26 | 0.2781 | 0.2674 | 0.1234 | 3439 | 24.66 | 58.83 | 21.91 | 0.0092 | 0.027 |

Std | 0.78 | 2.19 | 6.07 | 0.0107 | 0.0111 | 0.0081 | 143.3 | 1.71 | 1.75 | 0.33 | 0.0042 | 0.0032 |

Min | 23.8 | 34.54 | 71.53 | 0.2603 | 0.2488 | 0.1106 | 3200 | 21.96 | 57.02 | 21.4 | 0.0006 | 0.022 |

Max | 25.84 | 40.95 | 89.45 | 0.2911 | 0.2816 | 0.1333 | 3622 | 26.41 | 61.12 | 22.47 | 0.0134 | 0.0307 |

After several days of self-training | ||||||||||||

Avg | 27.59 | 38.33 | 90.39 | 0.3197 | 0.3058 | 0.1339 | 3932 | 30.76 | 55.2 | 22.68 | −0.0003 | 0.0296 |

Std | 0.73 | 1.08 | 4.47 | 0.0139 | 0.014 | 0.0027 | 179.9 | 1.82 | 2.07 | 0.45 | 0.0042 | 0.0015 |

Min | 26.2 | 36.58 | 85.12 | 0.2953 | 0.2806 | 0.1298 | 3608 | 27.4 | 52.12 | 21.92 | −0.0055 | 0.0269 |

Max | 28.38 | 39.49 | 96.3 | 0.3386 | 0.324 | 0.1379 | 4167 | 33.04 | 58.79 | 23.36 | 0.005 | 0.0309 |

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## Share and Cite

**MDPI and ACS Style**

Fuss, F.K.; Doljin, B.; Ferdinands, R.E.D.
Mobile Computing with a Smart Cricket Ball: Discovery of Novel Performance Parameters and Their Practical Application to Performance Analysis, Advanced Profiling, Talent Identification and Training Interventions of Spin Bowlers. *Sensors* **2021**, *21*, 6942.
https://doi.org/10.3390/s21206942

**AMA Style**

Fuss FK, Doljin B, Ferdinands RED.
Mobile Computing with a Smart Cricket Ball: Discovery of Novel Performance Parameters and Their Practical Application to Performance Analysis, Advanced Profiling, Talent Identification and Training Interventions of Spin Bowlers. *Sensors*. 2021; 21(20):6942.
https://doi.org/10.3390/s21206942

**Chicago/Turabian Style**

Fuss, Franz Konstantin, Batdelger Doljin, and René E. D. Ferdinands.
2021. "Mobile Computing with a Smart Cricket Ball: Discovery of Novel Performance Parameters and Their Practical Application to Performance Analysis, Advanced Profiling, Talent Identification and Training Interventions of Spin Bowlers" *Sensors* 21, no. 20: 6942.
https://doi.org/10.3390/s21206942