# Effect of Ball Weight on Speed, Accuracy, and Mechanics in Cricket Fast Bowling

^{*}

## Abstract

**:**

## 1. Introduction

_{run-up}, which adds directly to the ball release speed. If the initial angular velocity of the arm is zero, the release speed of the ball, v, is given by

_{ball}is the mass of the ball and m

_{arm}is the mass of the bowler’s arm.

## 2. Methods

#### 2.1. Participants

#### 2.2. Modified Balls

#### 2.3. Test Procedures

#### 2.4. Modified-Implement Training Program

#### 2.5. Analysis of the Acute Effects of Ball Weight

_{m}+ c(x–x

_{m})

^{2}) were fitted to the data. The decision about the most appropriate curve was guided by examining the distribution of the residuals [19]. If both curves seemed appropriate for the data, a calculation of Akaike’s Information Criterion (AICc) was used to determine which of the curves gave the best fit [20]. If a straight line was the best fit to the data, the effect of ball weight on the variable was taken as the gradient of the line (a). If the 90% confidence interval of the gradient included zero, ball weight was deemed to have no effect on the variable [21]. If a u-shape was the best fit to the data for the variable, the maximum/minimum value of ball weight was taken as the maxima/minima in the fitted u-shape curve (x

_{m}). If the 90% CI of x

_{m}included 156 g, the standard ball weight was deemed to be the optimum weight. In this study, a less conservative confidence interval (90%) was used so as to give a greater chance of identifying potentially beneficial or detrimental effects [22].

_{run-up}= 5 m/s. We tested two versions of the bowling model; the first version had only one fitted variable (T, with m

_{arm}set to 5% M), and the second version had two fitted variables (T and m

_{arm}). The decision about the best version of the model was guided by examining the distribution of the residuals [19] and with a calculation of Akaike’s Information Criterion [20]. The fit values for shoulder torque were expected to be similar to values measured in adult male fast bowlers [13], and the fit values for arm mass were expected to be about 5% of the participant’s body mass [8].

#### 2.6. Analysis of the Modified-Implement Training Program

## 3. Results

#### 3.1. Acute Effects of Ball Weight

_{arm}) was the most appropriate for two participants. However, for the version with one fitted variable, the distribution of residuals was not uniform for three participants. Therefore, the version with two fitted variables (T and m

_{arm}) was deemed to be a slightly more appropriate model. For both versions of the model the values for the coefficient of variation, root-mean-square deviation, and AICc were similar to those for the linear fit. The three participants (3, 4, and 6) that showed no clear effect of ball weight on ball speed had large uncertainties in the fitted values for shoulder torque and arm mass (Table 3).

#### 3.2. Effects of the Modified-Implement Training Program

## 4. Discussion

#### 4.1. The Acute Effects of Ball Weight

#### 4.2. The Effects of a Modified-Implement Training Program

_{ball}

^{0.15}, where A is a constant [6,35], and so ball release speed decreases at a rate of about 3.6 m/s per 100 g increase in ball weight. Therefore, a modified-implement training program for cricket fast bowling should require a much greater range of ball weight than that for a baseball pitching training program.

## 5. Conclusions

## Supplementary Materials

## Acknowledgments

## Author Contributions

## Conflicts of Interest

## References

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**Figure 1.**These plots show the expected decrease in ball release speed with increasing ball weight in cricket fast bowling; (

**a**) effect of shoulder torque; (

**b**) effect of arm mass (as % of body mass). Calculations are from a simple one-segment model of cricket bowling (equation 1) with body mass M = 80 kg, angular distance ∆θ = 270° (i.e., ¾ of a revolution), and run-up speed v

_{run-up }= 5 m/s [7]. The calculations for the effect of torque are with m

_{arm}= 5% M [8], and the calculations for the effect of arm mass are with T = 100 N·m. The shaded areas indicate the range of ball weight used in modified-implement training studies: dark grey = Petersen et al. [5]; light grey = present study.

**Figure 2.**Locations of the target zones (0, 1, 2, and 3) used to score bowling accuracy (for bowling to a right-handed batsman). Participants were asked to try to hit the top of the off-stump (*) after the bounce.

**Figure 3.**Plot (

**a**) shows the linear decrease in ball speed with increasing ball weight. Data for Participant 2. The solid line is a linear regression fit and the dashed lines show the 90% confidence bands. Plot (

**b**) shows the differences in the rate of decrease in ball speed among the 10 participants. Only the regression lines are shown; data points have been omitted for clarity. The dashed line shows the relationship calculated from the bowling model (Equation (1), with T = 110 N·m, ∆θ = 270°, v

_{run-up }= 5 m/s, m

_{arm}= 5% M, and M = 90 kg).

**Figure 4.**These plots show the effect of ball weight on the ability of a player to bowl a ‘good length’; (

**a**) change in the length of the delivery, (

**b**) change in release angle required to maintain the same length as that achieved with a standard-weight ball (156 g). Calculations are from a 2D aerodynamic model of the flight of a cricket ball [31]. The shaded area indicates the range of ball weight used in the present study.

Training Group | Participant | Age (Years) | Height (m) | Mass (kg) | Bowling Action^{ 1} |
---|---|---|---|---|---|

Intervention | 1 | 27 | 1.77 | 81 | side-on |

(under and overweight balls) | 2 | 26 | 1.84 | 93 | mixed |

3 | 23 | 1.87 | 94 | front-on | |

4 | 26 | 1.80 | 102 | semi-open | |

5 | 18 | 1.82 | 99 | mixed | |

Control | 6 | 19 | 1.91 | 87 | mixed |

(standard-weight balls) | 7 | 20 | 1.80 | 84 | semi-open |

8 | 20 | 1.73 | 88 | mixed | |

9 | 25 | 1.79 | 78 | front-on | |

10 | 34 | 1.71 | 97 | front-on |

**Identification of the participant’s bowling action was based on a visual inspection of the orientation of the back foot, hips, and shoulders during the delivery stride [16].**

^{1}Training Weeks | Session | Total Number of Deliveries | Ball Weight^{ 1} | Number of Deliveries for Each Ball Weight |
---|---|---|---|---|

1–2 | 1 | 36 | C–A–B–A; F–A | 4–8–4–8; 4–8 |

2 | 36 | C–E–C–F; E | 5–10–5–10; 6 | |

3 | 36 | C–A–B–A; F–A | 4–8–4–8; 4–8 | |

3–4 | 1 | 38 | C–A–B–A; A | 5–10–5–10; 8 |

2 | 38 | C–E–C–F; E | 4–8–4–8; 14 | |

3 | 38 | C–A–B–A; A | 5–10–5–10; 8 | |

5–6 | 1 | 40 | B–E–B–F; F | 4–8–4–8; 16 |

2 | 40 | C–A–C–A; F | 6–12–6–12; 4 | |

3 | 40 | B–E–B–F; F | 4–8–4–8; 16 | |

7–8 | 1 | 42 | B–E–B–F; F | 4–8–4–8; 18 |

2 | 42 | C–A–C–A; F–A | 6–3–6–3; 16–8 | |

3 | 42 | B–E–B–F; F | 4–8–4–8; 18 |

**Key to ball weights: A = 71 g, B = 113 g, C = 141 g, D = 156 g (not used), E = 198 g, F = 213 g. A semi colon (;) indicates a 10-minute recovery where the participant performed controlled dynamic stretches before continuing the training program.**

^{1}Linear Fit ^{1} | Cricket Bowling Model ^{2} | ||||
---|---|---|---|---|---|

Participant | Rate of Decrease in Ball Speed (m/s per 100 g) | r^{2} | RMSD (m/s) | Shoulder Torque T (N·m) | Arm Mass m_{arm} (kg) |

1 | 1.8 ± 1.8 | 0.23 | 5.4 | 60 ± 60 | 1.9 ± 2.1 |

2 | 1.0 ± 0.4 | 0.61 | 1.3 | 100 ± 40 | 3.6 ± 1.7 |

3 | 0.5 ± 0.6 | 0.21 | 1.7 | 180 ± 190 | 7.0 ± 7.9 |

4 | 0.0 ± 1.0 | <0.01 | 3.0 | — | — |

5 | 1.2 ± 0.3 | 0.86 | 0.8 | 80 ± 20 | 2.8 ± 0.7 |

6 | 0.5 ± 1.0 | 0.08 | 3.0 | 190 ± 360 | 7.3 ± 14.2 |

7 | 2.1 ± 0.6 | 0.75 | 2.0 | 40 ± 10 | 1.4 ± 0.5 |

8 | 1.1 ± 0.6 | 0.48 | 2.0 | 70 ± 40 | 3.0 ± 2.0 |

9 | 1.4 ± 0.9 | 0.44 | 2.7 | 50 ± 30 | 2.1 ± 1.5 |

10 | 1.2 ± 0.7 | 0.48 | 2.1 | 50 ± 30 | 2.3 ± 1.5 |

**r**

^{1}^{2}= coefficient of variation; RMSD = root-mean-square deviation.

^{2 }Equation (1), with the angular range of the arm set to ∆θ = 270° and the run-up speed set to v

_{run-up }= 5 m/s.

Training Group | Participant | Before (m/s) | After (m/s) | Difference(m/s) | ±90% CI (m/s) | Interpretation |
---|---|---|---|---|---|---|

Intervention | 1 | 32.6 | 34.7 | 2.1 | 0.9 | Probably beneficial |

2 | 32.0 | 31.7 | –0.3 | 0.3 | Probably trivial | |

3 | 30.9 | 32.5 | 1.7 | 0.5 | Probably beneficial | |

4 | 30.8 | 31.6 | 0.8 | 0.6 | Possibly trivial | |

5 | 30.6 | 31.2 | 0.6 | 0.2 | Probably trivial | |

Control | 6 | 31.6 | — | — | — | — |

7 | 31.0 | 30.2 | –0.8 | 0.4 | Possibly trivial | |

8 | 29.5 | — | — | — | — | |

9 | 28.9 | 29.6 | 0.8 | 0.8 | Possibly trivial | |

10 | 27.3 | 27.9 | 0.6 | 0.6 | Probably trivial |

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## Share and Cite

**MDPI and ACS Style**

Wickington, K.L.; Linthorne, N.P. Effect of Ball Weight on Speed, Accuracy, and Mechanics in Cricket Fast Bowling. *Sports* **2017**, *5*, 18.
https://doi.org/10.3390/sports5010018

**AMA Style**

Wickington KL, Linthorne NP. Effect of Ball Weight on Speed, Accuracy, and Mechanics in Cricket Fast Bowling. *Sports*. 2017; 5(1):18.
https://doi.org/10.3390/sports5010018

**Chicago/Turabian Style**

Wickington, Katharine L., and Nicholas P. Linthorne. 2017. "Effect of Ball Weight on Speed, Accuracy, and Mechanics in Cricket Fast Bowling" *Sports* 5, no. 1: 18.
https://doi.org/10.3390/sports5010018