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Physiological Profile of Lacrosse Athletes of California State University San MarcosMayra ArambulaTyler MunnKrizia PalosKristina SatherBritney TaskerHector TorresExercise Physiology 326Spring 2014 AbstractBackground: As a result of the current emphasis placed on preventive sports medicine, it is essential to analyze the physical and physiological responses of male collegiate lacrosse athletes. ?Assessing body composition, speed, agility, maximal aerobic power, and muscular strength further strengthens the understanding about ?physiological systems of lacrosse athletes. Aim: The purpose of this study is to evaluate Cal State San Marcos Lacrosse players of different positions to determine if there are differences among physical and physiological markers. ?Due to the limited research on lacrosse, the results of the study will help to identify appropriate training options and establish methods in order to track progress and evaluate program success. ?Methods: Sixteen male lacrosse athletes (n=16) performed six physiological ?tests to measure current fitness level (age: 18.94 ±1.28years, weight: 83.17 ±10.34 kg, height: 177.87±7.79 cm). ?Organization of data is based on the sport’s positions of midfielders, defensemen, attackmen, and goalie. ?The subjects performed testing within anthropometric, aerobic power, speed, agility, and strength testing measurements. ?Results: ?Using a one way ANOVA, data showed there is no significant difference observed between positions with the exception of average lean weight (p<0.037), post heart rate (p< 0.001) and 40 yard dash (p<0.001) measurements. ?Conclusion: Our results indicate that CSUSM male collegiate lacrosse athletes reveal average physical fitness based on the analyzed assessments. Our hypothesis was not supported, the attackmen position showed the highest aerobic and anaerobic capacity compared to the other positions. ???IntroductionLacrosse is a growing sport that has been considered “the fastest sport on two legs.” With the quickness and agility of ice hockey, the roughness of American Football, and the understanding of the game of soccer; lacrosse is an anaerobic sport supported by aerobic components (Steinhagen, 1998). There are a limited amount of studies available about lacrosse. Nevertheless, there is an understanding mentioned in Lacrosse: Sport Demands Analysis (2010) by Laurens Hoffer that lacrosse players must gain size (body mass), strength, power, speed, agility, and endurance for optimal performance.Lacrosse player’s physiological profile depends on the position of the player. All players show to have a higher body weight due to the aggressive physical contact allowed during a game (Hoffer, 2010). Midfield and attack players show to have low body fat percentage compared to the other positions, this is due to the need for agility and speed (Hoffer, 2010). Lacrosse is classified as 70% anaerobic energy and 30% aerobic energy; it is estimated that the goalie, defensemen and attackmen get 80% of their energy through the ATP-PC system and 20% from anaerobic glycolysis whereas midfielders are most likely to derive 60% of the energy through the ATP-PC system, 20% from anaerobic glycolysis, and 20% from aerobic glycolysis (Steinhagen et al 1998). Due to the variability of the player’s positions, strength and endurance of the entire team are to be assessed. Defensive and offensive players stay on the field throughout the entire game; in result, these positions show greater aerobic capacity compared to the other positions. Whereas, midfield positions last between 2 to 5 minutes of anaerobic power (Hoffer, 2010). In an assessment of power output with the use of a Wingate test involving 30 seconds of all-out max effort on a cycle ergometer showed high power output across all positions (Steinhagen et al., 1998). Nevertheless, the defensemen position showed the highest max (847.1 W), mean (682.3 W) and total work output (20.5 kJ) compared to the other positions (Steinhagen et al, 1998). From the Steinhagen study, it was found that the absolute power output was higher than those reported for rugby and elite soccer players, but lower than Olympic ice hockey players. For Vo2max, there was no great discrepancy observed between positions (average: 49.6 ml/kg/min) (Steinhagen et al, 1998). Due to the lack of information available on the physiological profiles of male lacrosse players, the purpose of the study is to assess the aerobic and anaerobic capacity of California State University San Marcos lacrosse players to further strengthen the understanding of the sports physiological components. The hypothesis for this study is that ?there will be physiological differences observed between positions, specifically among midfield positions excelling in anaerobic power and defense positions in aerobic capacity. MethodsData was collected for sixteen subjects over a four week on season period during Spring 2014. ?Anthropometric, estimated aerobic capacity/endurance, agility and strength were assessed. Testing was performed in a laboratory and field setting.Participants: Sixteen male collegiate lacrosse players (n=16) participated in the study (age: 18.94 ±1.28 years, weight: 83.17 ±10.34 kg, height: 177.87±7.79 cm). Informed consent outlined expectations and procedures to the participants. ?Subjects filled out a questionnaire listing any pre-existing injuries, health conditions, behaviors that may influence the results, and any physical activity outside of lacrosse. A majority of the subjects did an average of 1 hour of exercise 3-4 days a week outside of practice. ?While only two subjects participated in physical activity everyday, one subject did not participate in any physical activity outside of practice. Lacrosse players were categorized into midfielders(n=8), defensemen (n=4), attackmen (n=3) and goalie (n=1).Experimental ProtocolAnthropometric: Body weight (kg) was measured on a scale and height (cm) was measured with a measuring tape for all participants. Assessment of subcutaneous fat was assessed by three site skinfold using a Lange Skinfold Caliper (Best Technology). Three site skinfold measurement consisted of the chest, abdomen, and thigh on the right side of the body. Measurements were taken three times in chronological order from chest, abdomen, and thigh. A double thickness of skin and underlying adipose tissue was obtained for correct measurement. An average of the three measurements of each skinfold site was obtained. ?Each measurement was recorded in millimeters. Identification of whole body composition as a percentage of body fat (%BF), lean body mass (%LBM), and fat weight (FW) was calculated for each position. Body density was calculated with the use of the Jackson & Pollock (1985) formula:Body density (men)= 1.10938 - 0.0008267 (sum of three skinfolds) + 0.0000016 (sum of three skinfolds)^2- 0.0002574 (age)Body density varies by age, gender, and ethnicity; nevertheless body density of fat tissue equals 0.9 g/cc^3 and density of fat-free tissue is approximately 1.1 g/cc^3 (ACE, 2010). To estimate body fat percentage, the Brozek et al. (1963) formula was used:% Fat= (457/Body density) - 414Determining fat weight in pounds was calculated by multiplying body weight to body-fat percentage and lean body mass was calculated by subtracting fat weight to total weight. All measurements in pounds were converted into kilograms for the results data table. ??Aerobic Power Measurement: All Participants completed the George et al. (1993) single-stage submaximal treadmill test for individuals between the ages 18-29. Gender, weight, speed and heart rate was used to calculate VO2max with the use of the George et al. formula:VO2max = 54.07 + 7.062 * GENDER (0 = female; 1 = male) - 0.1938 * WEIGHT (kg) + 4.47* SPEED (miles.h-1) - 0.1453 * HEART RATE (bpm)Estimate of ?VO2max (ml/kg/min) at a 5 percent grade and at a speed of 4.3-7.5 mph was recorded. The trial lasted an average of 4 minutes. Each subject had a polar heart rate monitor to access their heart rate pre, during, and post. After 30 seconds of a steady state heart rate, the heart rate was recorded and the test ended. Average ± standard deviation of post steady state heart rate was calculated. Strength Testing (BioDex):Subjects participated in peak torque assessment of full extension and flexion of both legs. ?Subjects performed a five minute warm up on the cycle ergometer. ?After warm up, subjects were strapped to an isokinetic dynamometer. Straps were placed over the shoulders and pelvis in a seated position. ?The dominant and nondominant leg were tested at random for each subject. ?The testing leg was strapped at the thigh for stability. ?Practice trial of one repetition of extension and flexion was recorded for full range of motion. ?Subjects performed one set of five repetitions of extension and flexion at a contraction velocity of 30°/s for each leg. ?Verbal encouragement was applied during the testing period for each participant.Speed and Agility Assessments: Speed as well as anaerobic power was assessed with a 40 yard sprint. Measurement was performed on a non turf field and marked with cones at the start and finish. Subjects were asked to perform two trials with a five minute break in-between. ?For each trial, two stop watches recording to the nearest .01 second were used and the average of the two recorded times were obtained for each trial. The trial with the best time was used in the data for our subjects as there could be a learning curve with the activity. The time started when the subject’s dominant hand left the ground and ended when they crossed the cone. Agility was reviewed using a T-Test. The test was conducted on a non turf field with cones used as the markers. Like the test done by Abbas Asadi (2013), cones were set up in a t shape with the starting cone and the first cone 10 meters apart and two cones set to the left and right of the first cone 5 meters apart. Subjects started at an initial cone placed at the start position and were asked to sprint towards the first cone 10 meters away. Upon reaching the first cone, subjects had to side shuffle to the right cone 5 meters and touch it. After side shuffling to the far left cone 10 meters away, subjects had to side shuffle returning to the first cone 5 meters away. The subjects backpedal cross the first initial starting cone concluding the test. Two stopwatches recorded the time to the nearest .01 seconds and the best time of the three trials was recorded.Figure 1. T-test protocolStatistical Analysis: A comprehensive statistical analysis of CSUSM Club lacrosse players during season 2013-2014 was done using a one-way ANOVA to identify variation among positions with statistical program SPSS. The mean and standard deviation of physiological markers were determined using ?Microsoft excel. The data was graphically represented to choose significant difference between positions. Descriptive statistics are expressed as means and standard deviation (SD). According to the data, the normality distribution of the mean was analyzed by variance comparison by means. Linear regression was obtained from the least squares method for each individual. All differences are significant at P < 0.05.RESULTSTable 1 Subject Variables by PositionG (1)M (8)A (3)D (4)N=16Sig.AGE (yr)18± 0.019.38±1.6818.67±.5718.50±.5718.94±1.28.609Height (cm)175.26± 0.0176.68±5.05174.41±12.00183.51±9.36177.87±7.79.429Weight (kg)97.52±0.081.18±10.6576.35±11.8388.67±3.2683.17 ±10.34.201BF (%)32.90±0.016.27±7.8416.93±.6519.20±5.9218.16±7.26.184LBM (kg)60.78±0.067.13±2.7763.40±10.2775.81±6.0368.21±7.01.037FW (kg)29.89±0.013.89±8.9512.95±1.5614.99±6.2214.99±7.85.283Vo2Max (ml/kg/min)41.98±0.047.24±2.6948.97±4.0844.02±2.5346.46±3.38.099Post HR (bpm)134±0.0128.37±5.92124.33±4.04142.5±2.08131.5±8.22.001Left LegKE Torque (FT/lbs)180.90±0.0188.23±34.67219.66±69.98181.55±13.79192.00±38.08.608KF Torque (FT/lbs)105.00±0.0107.75±15.12104.00±34.16106.57±11.50106.58±17.06.992Right LegKE Torque (FT/lbs)184.30±0.0187.66±33.52211.50±83.09196.10±32.21194.03±41.74.882KF Torque(FT/lbs)107.90±0.0114.86±17.40110.86±27.66105.35±13.24111.30±17.19.86440 yard dash(s)5.63±0.04.88±.404.67±.225.16±.275.08±.16.001T-test(s)10.69±0.010.01±.5610.19±.5210.33±.4110.30±.25.654G: Goalie, M: Midfield, A: Attack, D: Defense, BF%: Body Fat Percentage, LBM: Lean Body Mass, FW: Fat Weight, KE Torque: Knee Extension , KF Torque: Knee FlexionAnthropometric: Measurements of the lacrosse team were taken prior to the beginning of testing. Results were taken in measurements for height (ht), weight (wt), and skin fold in three locations Chest (c), Thigh (t) and Abdomen (a) to determine body composition. Each player was measured and grouped according to their position category. The goalie’s measurements were highest for weight with 97.52±0.0 kg and the attackmen least with 76.35±11.83 kg. The tallest position was defenders measuring 183.51±0.57 cm and shortest measuring 174.41±12.0 cm. Skinfold measurements for the chest site read highest in the goalie with 44±0.0 mm and lowest in defensemen with 15.85±5.56 mm. The abdominals measured lowest in attackmen with 20.966±0.65 mm and highest in goalie with 32±0.0 mm. The thigh region of the body measured highest in goalie at 52.6±0.0 mm, and lowest in midfield with 17.475±6.22 mm.Table 2. Differences in skinfold measurements by positions. Skinfold MeasurementsAbs (mm)Chest (mm)Thigh (mm)M (8)25.475±15.0217.125±9.5217.475±6.22A (3)20.966±0.6517.533±3.0122.63±1.74D (4)25±13.0415.85±5.5618.125±10.25G (1)32±0.044±0.052.6±0.0G: Goalie, M: Midfield, A: Attack, D: Defense, Abs: AbdominalsAerobic Power Measurements: V02max data showed no significant difference amongst all positions (p<0.099). Post heart rate assessment displayed a significant difference at (p<0.001). There is a correlation between body mass and VO2max players with higher BMI had a lower VO2. While comparing positions, attackmen have the highest mean estimate of ?VO2max 48.97 ± 4.08 mL/kg/min and a standard deviation of 2.74 from the midfielders (47.24±2.69 mL/kg/min), defense (44.02±2.53 mL/kg/min) and goalie (41.98±0.0 mL/kg/min) positions. Strength testing: Knee flexion (P<0.864) and extension (p<0.882) of the right leg did not show a significant difference between positions. Average right knee extension showed a p< 0.873. The attacker position showed to have the highest peak torque for both right (211.50 ± 83.09 FT/lbs) and left (219.66 ± 69.98 FT/lbs) knee extension. Knee extension of both the right (180.90 FT/lbs) and left (184.30 FT/lbs) was lowest in the goalie position. Nevertheless, the goalie did not show the lowest peak torque for knee flexion of both the right and left knee. Left leg peak torque measurements did not show a significant difference between positions for each test, but did show a difference between knee flexion and extension tests. Knee flexion of the left leg showed a p< 0.608 and knee extension of the left leg showed a p< 0.992. Overall, left and right leg knee extension and flexion test did not show a significant difference between the different positions. ?Table 3. H:Q RatioVelocity (deg/sec)NRight SideLeft SideLacrosse Athletes1630 (deg/sec)56.25 ± 10.757.39 ± 8.9Table 3 shows that the H:Q ratio for all subjects at 30 deg/sec was 56.25 ± 10.7 for the right side and 57.39 ± 8.9 for the left side. ?Speed and Agility Assessment: The 40 yard dash assessment displayed a significant difference (p<0.001) amongst different positions of lacrosse. ?Attackmen presented the fastest average score for the 40 yard dash of 4.67±0.22 seconds opposed to midfielders, defense, and goalie positions. Goalie position obtained the slowest average score for the 40 yard dash of 5.63±0.0 seconds compared to midfielders, defense, and attack. The mean average score of 40 yard dash amongst all positions time was 5.08±.16 seconds. T-test assessment demonstrated no significant difference amongst all positions (p<0.654). The mean average score of all positions was 10.30±0.25 seconds. Midfielders obtained the fastest mean average of 10.01 ±0.56 seconds compared to attack, defense, and goalie positions. Goalie position obtained a slowest mean average of 10.69 ±0.0 seconds. ?Discussion??? The primary aim of the study is to assess the physiological components of lacrosse. Out of the limited research available on lacrosse, there is an understanding that there are both aerobic and anaerobic components to the sport. The primary findings from this study is that there is no significant difference observed between positions with the exception of average lean weight (p<0.037), post heart rate (p< 0.001), and 40 yard dash (p<0.001) measurements. From the differences observed among the three measurements, the data indicates that body composition between positions varies and has an affect on the other two tests. According to the American Heart Association (2014), heart rate is affected by body size and in our data we can observe that a difference in body weight has an effect on post heart rate after a single-stage treadmill test. The 40 yard dash test is a measurement of speed. With larger body compositions, we can observe that the goalie and defensemen positions showed to have the slowest 40 yard dash times due to having the highest body weight measurements. There was no significant difference observed between positions in VO2max, muscle strength, agility, and speed.?Body Composition: Results indicated differences between the positions regarding body fat %, lean body mass, fat weight, height, and weight. However, the differences between the positions except for the goalie is not statistically significant. The goalie has a higher body fat % compared to the other positions possibly due to the lack of movement his position requires compared to the others. A study done by Steinhagen et. al (1998), college club sport lacrosse athletes showed similar results to our study. Similar to the Steinhagen et al. study, the same parameters in body composition were compared, and differences in defensemen were observed to have higher body fat % when compared to other positions. Results revealed a higher body fat % in defensemen when compared to attack and midfielders. However, the goalie position in our study had the highest body fat % mean compared to the study by Steinhagen et. al (1998). This difference could be due to different training regimens of the programs for their goalies. The body fat % of the subjects was closer to the study done on Division 3 male lacrosse collegiate athletes (Collins et. al 2014) as well as the club lacrosse athletes (Steinhagen et. al 1998) than compared to the studies done on basketball players by Ostojic et. al (2006) and K?klü et. al (2011). This difference could be due to demand of the sport as basketball players move up and down the court more often than lacrosse players move up and down the field. Since Lacrosse offensive possessions are a lot longer than those in basketball, the players experience more down time. Another factor is the size of the field compared to the court; Lacrosse players need to cover more ground when there is a change in possession which demands longer sprints and leads to faster fatigue, in which case there would be a line change among the midfielders. The differences aerobically and anaerobically between the two sports could be a cause of the difference in body fat %. In our results we can see how body fat % affects the players aerobically and anaerobically. The goalie who had the highest body fat % of the positions showed a lower VO2 max, 40 yard, and T-test, compared to the other positions. As mentioned in the study done by Collins et al. (2014), body fat % affects performance by lowering the aerobic and repetitive as well as maintained anaerobic capacity of the players. This could be attributed to our results as we can see a correlation between body fat %, VO2 max, 40 yard, and T-test results with all the positions. Aerobic Power Measurements: Lacrosse is a moderate intense sport with short burst of energy it is expected that player’s cardiorespiratory health be fairly higher. The larger Vo2max a player has would represents that they are more capable to get oxygen and burn of fuel to provide the energy needed to do work. Single-stage VO2max treadmill test estimates the players’ capacity to perform sustained paring CSUSM lacrosse player’s true statistic means of Vo2max with other findings was limited. The study by Steinhagen (1998) shows similar means among players even with a larger sample size. The single-stage submaximal treadmill test method by George al el., (1993) has limitations and standards of error including human and mechanical, but it does provide valid means that can be observed in all players that have an average maximal oxygen consumption for their age group, level of fitness, and training (Ebbeling, 1991). Steinhagen (1998) classified lacrosse as 70% anaerobic energy and 30% aerobic energy; each position having a variation in physiological assessment findings. It was expected that goalie, defensemen, and attackmen have a lower Vo2 max because of energy system used for other work done in those position (Steinhagen et al, 1998). Aside from genetic factors, other components that influence Vo2max are age, gender, and possibly altitude (Ebbeling, 1991). Isokinetic Dynamometry: In an assessment of knee extension and flexion using a Biodex-System, 115 professional soccer players were evaluated to examine the effects of professional training age on the composite strength profile of the knee and ankle joint (Fousekis, Tsepis & Vagenas, 2010). On average, 5-7 years of professional training, the right leg’s eccentric knee extension at 60 deg/sec showed to be the highest (310 FT/lbs) measurement. A decrease was observed with an increase in testing speed (ECC 60 to 180: 310 vs 282 FT/lbs). At 11 plus years of professional training experience, at 60 deg/sec of knee extension of the right leg showed to be the highest measurement (318 FT/lbs), decreasing with an increase in testing speed (318 vs 295 FT/lbs). Comparing to our study’s data, the highest average measurement was 194 FT/lbs for knee extension of the right leg at 30 deg/sec. Nevertheless, the highest position measurement observed in our data was for the attacker position (219.66 ± 69.98 FT/lbs). Under the age of 30, isokinetic normative data for knee flexion/extension ratio at 90 deg/sec is high at 53%, average at 48% and low at 44% (Harbo, Brincks & Andersen, 2012). Average knee flexion/extension ratio for the left leg at 30 deg/sec is 55% and 57% for the right leg. Comparing the flexion/extension ratio at 30 deg/sec to the normative data available at 90 deg/sec, it can be observed that the subjects in all positions are above 53% (high ratio). Due to the decrease in speed during our testing, subjects from all positions fall under the high-average category for knee flexion/extension ratio. In a study assessing hamstring:quadriceps ratio in intercollegiate athletes, data represents that for soccer players the H:Q ratio is 57.87 ± 15.68% for the right leg and 59.26 ± 17.37% for the left leg at 60 deg/sec (Rosene, Fogarty & Mahaffey, 2001). Total mean and standard deviation of our study’s subjects is 56.25 ± 10.7% for the right leg and 57.39 ± 8.9% for the left leg at 30 deg/sec. Comparing the H:Q ratio of collegiate soccer players at 60 deg/sec to collegiate lacrosse players at 30 deg/sec shows that CSUSM lacrosse players should be able to exert a higher force due to a decrease in speed. Overall, CSUSM lacrosse player’s average peak torque is not at the level of professional and collegiate soccer players, but is at an average to high flexion/extension ratio according to isokinetic normative data. Speed and Agility Assessment: In a study that examined 40 yard dash performance, collegiate males that were drafted into the NFL were compared to non drafted collegiate males to identify professional level speed (Sierer et al.,2008). Subjects in the study were separated into two categories consisting of skilled players (wide receivers, cornerbacks, running backs, and safeties) and linemen (defensive tackles, offensive tackles, offensive guards, and centers). Drafted players obtained a significantly faster 40 yard dash time compared to non drafted players. The significant difference in skill players (p<0.001) was reported to have a faster 40 yard dash time of 4.490 seconds as opposed to non drafted players. Linemen obtained a significantly slower 40 yard dash time of 5.205 seconds (p<0.003). Skill players typically obtain a lower body mass compared to linemen that obtain a higher body mass. As compared to our data for speed assessment, attackmen obtained the fastest measured 40 yard dash time of 4.67±0.22 seconds. The goalie obtained the slowest measured 40 yard dash time of 5.63 ± 0.0 seconds. Similar to the previous study on football, the goalie acquired a higher body mass affecting 40 yard dash time whereas attackmen acquired a lower body mass, resulting in a faster 40 yard dash time. Previous studies’ data and our studies’ data could imply that positions with lower body mass have an overall faster 40 yard dash time compared to positions with higher body mass. In a similar study that conducted T-test performance, comparisons in Division 1 and Division 2 players were assessed in male basketball players (K?klü et al., 2011). The positions in basketball were split into 3 groups consisting of centers, forwards (small, power forwards) and guards (shooting, point guards). Centers T-test performances were worse than both forwards and guards (p≤0.05). Guards had a significantly faster T-test data of 9.24±0.56 seconds opposed to forwards 9.48±0.46 seconds and centers with the slowest time of 10.04±0.35 seconds. In our results for the T-Test speed assessment, midfielders have the fastest posted time of 10.01±0.56 seconds. The goalie obtained the slowest T-Test time of 10.69±0.0 seconds. Both the previous study on basketball and our study show the center and the goalie had the highest amount of body mass which resulted in the slower T-Test time in comparison to the guards and midfielders with less body mass giving a faster T-Test time. Both of these studies imply that with an increase in body mass, an increase in T-Test time will result.Limitations: Series of limitations were present for our study. ?Our data collection process occurred during the on-season of the sport. As the subjects practiced everyday and majority of them working out individually, some subjects might not have had adequate amount of rest prior to testing. Also a few tests were only able to be administered after practice which could have influenced some of the results. Our position group size ratio is a limitation for our study. Lacrosse demands more midfielders compared to other positions, the smaller group of attack (3), defense (4), and goalie (1) could have affected the results. Even though it was limited with the use of two stopwatches, human error could have affected our results in regards to the 40 yard and the T-test. Another limitation is the submaximal VO2 max treadmill test our subjects had to perform, which was just an estimate and could have an error of calculation and true ranges, as well as it not being specific to athletes. Comparisons between previous data using different testing speeds (deg/sec) compared to our study’s 30deg/sec is a limitation in the analysis.CONCLUSION??? Based on the physiological profiles of male collegiate lacrosse athletes, there was a difference observed between positions in regards to the different tests administered. Our hypothesis indicated that the midfield position would excel anaerobically and defensemen aerobically due to midfield positions’ need for explosive power and defensemen positions’ prolonged activity during a game. Due to our findings, the data rejects the hypothesis. Attackmen displayed the highest aerobic and anaerobic capacity by exceeding in the VO2max and biodex assessments. Due to the lack of research and findings about lacrosse, comparisons in results were limited; however, our study provides a marker for future research. ?REFERENCESACE Personal Trainer Manual (Fourth ed., pp. 175-188). (2010). San Diego, CA: American Council on Excercise.2. AHA, All about heart rate (pulse) (2014). In American Heart Association. Retrieved May 11, 2014, from ?, U. (2012) The Relationship Between Muscle Strength, Anaerobic Performance, Agility, Sprint Ability and Vertical Jump Performance in Professional Basketball Players. Journal of Human Kinetics, 31:149-158Asadi, A. 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