## Materials and Methods  
The study examined 37 soccer players aged 19 to 30 years. They were players playing in the Polish Ekstraklasa league. The study included only the players who had actively participated in training and league matches since the beginning of the season and had not been injured. They were previously qualified for the examinations by a sports physician. Their mean training experience was 14 years (8 to 20 years). The mean body mass (\(\pm\)SD) of the subjects was \(76.8\pm 7.2\) kg, and the body height was \(1.82\pm 0.06\) m. The tests were conducted in the morning, before the training sessions. On the day before the tests, the players did not play any league matches. The study was carried out in the Biomechanical Analysis Laboratory and Scientific Research Laboratory of the Faculty of Sport (both with PN-EN ISO 9001:2009 certification) at the University School of Physical Education in Wroclaw, Poland. All subjects gave their informed consent for inclusion before they participated in the study. The study was conducted in accordance with the Declaration of Helsinki, and the protocol was approved by the Senate's Research Bioethics Commission of the University School of Physical Education in Wroclaw, Poland. Measurements were performed according to International Standards for Anthropometric Assessment (ISAK) [32]. The following anthropometric variables were measured: sitting height (B-vs), lower extremity length (B-tro), shank length (B-ti), biacromial diameter (a-a), biliicoristal diameter (ic-ic), humerus breadth (cl-cm), femur breath (epl-epm), chest girth, waist girth, hip girth, relaxed and flexed biceps girth, thigh girth, and calf girth. Skinfeld thickness was measured at the subscapular, abdominal, suprailiac, triceps, and calf locations to assess body fat. Body height, lengths, and breadths were measured to the nearest 0.1 cm with the use of the GPM Anthropological Instruments (Siber Hegner Machinery Ltd., Zurich, Switzerland). Skinfeld thickness was measured with a Tanner/Whitehouse skinfeld calliper (Holtain LTD, Crosswell, Crymych, Pembs, UK) with a 0.2 mm graduation. Body mass was measured with an electronic weighing scale with an accuracy of 0.1 kg. Body mass index (BMI) was also calculated. The peak muscle torque under isometric conditions was measured to assess the strength of the lower limbs. Peak muscle torque for extensors and flexors of the knee joint was measured at 75\({}^{\circ}\) and 30\({}^{\circ}\), respectively; 0\({}^{\circ}\) at the knee joint was considered to be a full extension. The measurements were performed separately for the right and left lower limbs. The results of measurements of the dominant limb were used for analyses. Biodex System 4 Pro (Biodex Medical Systems, Inc., Shirley, NY, USA) was used for the torque measurements. The conventional hamstring-to-quadriceps ratio (H/Q ratio) was calculated using the following equation:  
\[\text{H/Q ratio}=(T_{f}/T_{e})\cdot 100\%, \tag{1}\]  
where \(T_{f}\) denotes the concentric peak torque value of knee joint flexors of the dominant lower limb and \(T_{e}\) is the concentric peak torque value of extensors of the same joint and limb. The conventional H/Q ratio is possible to calculate during the measurement of peak torque only under isometric conditions [33]. Furthermore, the muscle torques of extensors and flexors were added together, and the muscle torque for the knee joint relative to body mass was calculated:  
\[(T_{e}+T_{f})/\text{BM}. \tag{2}\]  
To supplement the information about the general strength abilities of the soccer players studied, back and handgrip strengths were measured using TAKEI dynamometers (Takei Scientific Instruments Co., Ltd., Niigata City, Japan). Cluster analysis (\(k\)-means) was used in the statistical analysis to distinguish two groups significantly differing in the magnitude of muscle torque. The intergroup differentiation of anthropometric variables in these clusters was evaluated by means of Student's \(t\)-test for independent samples.