Throwing motion analysis
The MER angle during throwing, and shoulder angles of ER, extension and abduction at SFC in the early cocking phase were measured. Prior to the experiment, reflective markers (diameter, 1.5 cm) were placed at the following bony landmarks of the upper body: dorsal side of the distal end of the humerus; distal end of the throwing forearm (wrist); acromion process; and spinous processes of the 7^th cervical (C7) and 8^th thoracic (Th8) vertebrae.

The experimental setting for the data collection was designed to simulate a real baseball practice or game as closely as possible. Specifically, the data collection was performed at an outdoor baseball field, and each subject wore a pair of baseball uniform pants, spiked shoes and a non-sleeved shirt with a hole on the back for the marker placement. The throwing distance was 27.43 m, and the throwing target was a baseball glove held in front of the catcher's chest. Each subject was also asked to wear a glove on their non-throwing hand.

After a regular warm-up, each subject executed five throwing trials toward the target at his maximum effort. The throwing motion was filmed with two high-speed cameras (HSV-400; NAC Image Technology Inc., Tokyo, Japan) and electronically synchronized at 200 frames per second. The positions of the cameras were determined so that the markers were in the field of both cameras during the cocking phase (Sakurai et al., 1993). Therefore, the cameras were located to the right and left rear of the subject. The trial when the thrown ball was most accurately controlled to the target was chosen for further analysis, and then the motion data was transferred to a personal computer (VAIO PCV-LX53/BP; Sony, Tokyo, Japan). The video images were superimposed on the computer display, and the markers were automatically tracked by a 2D-3D motion analyzer (Frame-DIAS II; DKH Inc., Tokyo, Japan). The 3D coordinates of the digitized points in time were obtained using direct linear transformation procedures (Abdel-Aziz et al., 1971).

The definitions of the kinematic models for each shoulder angle calculation are illustrated in Figures 1, 2 and 3. Two corresponding triangles were established between the markers to define the upper body segments for each angle calculation. The corresponding triangles for shoulder ER calculations were formed by the markers on the acromion process, elbow joint and Th8 and those on the wrist, elbow joint and acromion process (Figure 1). The corresponding triangles for shoulder extension angle calculation were formed by the markers on the acromion process, C7 and elbow joint and those on the acromion process, C7 and Th8 (Figure 2). Cosine angles of the inner products calculated with normal unit vectors projected from each corresponding triangle were defined as the shoulder angles (Figures 1, 2). The shoulder abduction angle was defined as the angle between the trunk and the arm lines in the frontal plane (Figure 3). The shoulder angle where the planes (lines in the case of the shoulder abduction calculation) intersected at an angle of 90º was defined as 0°. The ER, flexion and abduction directions were expressed as positive values in this study.

Passive ROM measurement
The passive ROMs of shoulder ER and internal rotation (IR) were also measured by the 2D-3D motion analyzer. Each subject was placed in the sitting position with the shoulder abduction and elbow flexion angles at 90º. The shoulder was moved passively until the angle reached its maximum position. The passive force applied to the distal end of the forearm during the measurement was maintained at approximately 20 N and confirmed by a handheld dynamometer (Micro FETII; Hoggan Health Industries Inc., Draper, UT, USA). A compensatory lumbar extension movement was not observed during the measurement. After the maximum position was determined by one experienced physical therapist, the shoulder position was captured by a digital video camera. The captured data were then transferred to a personal computer for angle calculation.

Muscle strength measurement
Isolated maximum muscle strengths of the shoulder ER and IR were measured by manual muscle testing with the handheld dynamometer. The isometric strengths were tested in the sitting position with shoulder angles of 90° abduction, 90° elbow flexion and 90° ER. The examiner stabilized the distal humerus of the subject, and placed the handheld dynamometer on the distal forearm. The examiner used the break test maneuver for strength measurements (Hislop and Montgomery, 1995). The obtained force was converted to a joint moment by multiplying it by the length of the lever arm (distance between the lateral epicondyle of the humerus and the styloid process of the ulna). Finally, the joint moment was normalized by the body weight.

Statistical analysis
The correlations of the MER with the other three kinematic variables at SFC and the passive ROMs were calculated by the Pearson's rank correlation coefficient. Statistical significance was considered to be indicated at the 5% critical level (p < 0.05).

• It has been reported that the amount of stress imposed on shoulder and elbow joints is correlated with the degree of maximum shoulder external rotation angle (MER) during throwing. Therefore, controlling MER within a normal range plays a key role in the prevention for throwing-related injuries in baseball players.
• Physical and biomechanical factors related to the degree of MER must be addressed to advance the current prevention and rehabilitation strategies for the shoulder and elbow injuries.
• The current finding demonstrated that there was a significant moderate leaner correlation between shoulder internal rotation angle at the initial foot contact in the early cocking phase and MER.