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Research Quarterly for Exercise and Sport
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Prediction of Basketball Skill Using Biomechanical
Variables
a
Jackie L. Hudson
a
Department of Health and Physical Education , Rice University , Houston , TX , 77251 , USA
Published online: 22 Feb 2013.
To cite this article: Jackie L. Hudson (1985) Prediction of Basketball Skill Using Biomechanical Variables, Research Quarterly
for Exercise and Sport, 56:2, 115-121, DOI: 10.1080/02701367.1985.10608445
To link to this article: http://dx.doi.org/10.1080/02701367.1985.10608445
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www.tandfonline.com/page/terms-and-conditionsHUDSON
RESEARCHQUARTERLY
FOREXFRCISE AND SPORT
1985, VOL.56,No. 2, PP. 115-121
Prediction of Basketball Skill Using Biomechanical Variables
JACKIE L. HUDSON
Rice University
This study was designed to examine the use of selected ning ability predicted from physiological and anthro-
biomechanical variables in the prediction of basketball skill. The pometric variables (Pollack, Jackson, & Pate, 1980);
subjects were college women in three mutually exclusive groups of and field hockey performance predicted from a skill
basketball skill: an elite group of six competitors on the United test (Chapman, 1982). The success of prediction in
States team in the World University Games, a good group of these studies ranged from 58-80% when a single cate-
seuen players on a varsity team, and a poor group of nine gory of variable was employed and from 79-93%
members of an instructional class. An accuracy test and digitized
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when two or three categories of variables were used.
film records provided the data for 12 variables related to the
process or product of free throw shooting. Discriminant analysis Although excellent predictive results were obtained
was employed to predict the categorical variable of skill. The most in the previously cited studies, the variables which
discrimination came from variables of accuracy, stability, and were included are indirect or underlying indices of
bight of release rather than from variables of projection. Poor performance. That is to say, it is unlikely that the
shooters were distinguished ly instability; elite shooters were experimental test (e.g., repetitive barbell pressing) will
characterized ly a high point of release and accuracy under occur in the actual sport contest. The predictive value
pressure. Depending on the method of prediction, rates for correct has not been reported for categories of variables
classijication of subjects ranged from 76-100%. Thus, it which are directly involved in the technique of sports
appears that discriminant analysis using bwmechanical variables performance. Therefore, this study was designed to
can be a successful tool in the prediction of basketball skill. examine the use of selected biomechanical variables in
the prediction of basketball skill.
Key words: basketball, biomechanics, discriminant
analysis, elite athletes, performance predic-
tion.
Method
Subjects
At the highest levels of athletic competition, success
can be dependent on the selection of the best perform-
A total of 22 college women in three mutually exclu-
sive groups of basketball skill.gave informed consent
ers. Traditionally, the selection of athletes has been
to participate in this study:Data sets were obtained for
based on objective indices of skill, as well as on subjec-
an elite group of six competitors on the United States
tive measures of performance such as reputation. One
team in the World University Games, a good group of
penalty for greater reliance on subjective rather than
seven players on a varsity team, and a poor group of
objective methods is that performers with high repu-
nine members of an instructional class.
tation and moderate ability may be chosen instead of
players with moderate reputation and high ability.
Selection of Variables
Thus, the identification of objective variables which
predict performance should assist in the selection of The offensive and defensive skills used by a basket-
the best performers. ball player are dictated by the position being played.
Discriminant analysis is a promising technique for The free throw has become the one skill that all play-
the identification of variables with predictive value for ers commonly use. Several characteristics of skilled
classifying performers. This technique has been em- performance in free throw shooting have been dis-
ployed with different categories of variables in a few cussed in the biomechanics literature. In terms of an-
sports to separate good from elite performers. Exam- gle and velocity of projection the recommendations
ples include wrestling skill predicted from psychologi- are to use an angle 2-3" above the minimum angle
cal, physiological, and anthropometric variables (Na- which results in a successful shot (Mortimer, 195 1); an
gle, Morgan, Hellickson, Serfass, & Alexander, 1975; angle 4-8" above the minimum (Hay, 1978);the angle
Silva, Shultz, Haslam, & Murray, 1981); distance run- associated with the minimum velocity of projection
RESEARCH FOREXERCISE
QUARTERLY AND SPORTVOL.56, No. 2
115HUDSON
(Brancazio, 1981); and the angle corresponding to an the collection of extra trials and the loss of informa-
angle of entry of 45" (Mullaney, 1957).For a variety of tion in other trials, complete data sets were available
reasons a high release point is favored by several writ- for 67 free throw trials. For each frame, digitized
ers (Barnes, Fox, Scott, & Loeffler, 1966; Brancazio; coordinates of 17 segmental end points and three
Cooper 8c Siedentop, 1969; Cousy & Power, 1970; points on the periphery of the ball were obtained with
Mortimer; Mullaney; Rush & Mifflin, 1976; a Vanguard Motion Analyzer. The digitized coordi-
Schaafsma, 1971; Stutts, 1969; Tarkanian & Warren, nates and segmental data from Dempster (1955)were
1981; Wooden, 1966; Yates & Holt, 1982). With re- used with a FORTRAN IV program to calculate the
spect to variables of stability, there is agreement that variables of interest.
trunk inclination should remain vertical (Barnes, To determine the projection characteristicsfor each
1980; Hartley & Fulton, 1971; Kaberna, 1968; basketball shot, the location of the ball center was
Schaafsma; Stutts; Wooden) and disagreement about computed by a method of triangulation using the pe-
keeping the center of gravity over the base of support ripheral coordinates. The horizontal and vertical com-
(Barnes, 1980) or moving the center of gravity for- ponents of ball velocity were found by using the dis-
ward during the shot (King & Toney, 1973). placement of the ball center, the elapsed time between
Based on the review of literature, 12 variables were frames, and the equations of motion. The resultant
chosen for analysis. Five variables related to the prod- linear velocity of the ball was calculated from the com-
uct of shooting were included-angle of projection, ponent velocities. The angle of projection (theta) was
velocity of projection, the difference between the an- the angle formed by the resultant velocity and the
gle of projection and the minimum angle of projec- horizontal.
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tion, the difference between the angle of projection The location of the ball at release was used to calcu-
and the Brancazio (1981) angle of projection, and the late the hypothesized optimal projection angles for
difference between the angle of projection and the each shot. The method of Mortimer (1951) was em-
Mullaney (1957) angle of projection. Five variables ployed to find the minimum angle of projection which
related to the process of shooting were analyzed- would result in a clean shot. According to the recom-
height of release ratio, absolute trunk angle, position mendation of Brancazio (198l), the angle of projec-
of the center of gravity, absolute difference between tion associated with the minimum velocity of projec-
the center of gravity and the midpoint of the base of tion was computed. The angle of projection corre-
support, and change in the center of gravity at release. sponding with an angle of entry of 45" was calculated
Also, two variables related to the accuracy of shooting with the Mullaney (1957) method. The real and hy-
were added-percent accuracy in a nonfilmed free pothesized angles of projection were combined to cre-
throw test and percent accuracy in filmed free throws. ate three variables for analysis: the difference between
theta and the minimum angle of projection, the dif-
Testing Protocol ference between theta and the Brancazio angle of pro-
jection, and the difference between theta and the Mul-
For each subject the testing protocol consisted of
laney angle of projection.
(a) a subject-controlled warm-up period, (b) an accu-
The height of release ratio was computed by divid-
racy test of 20 free throw trials, (c) preparation for
ing the height of the ball center at release by the height
filming with the application of colored cloth tape on
of the shooter. The trunk segment was represented by
bony landmarks, (d) additional warm-up time to ad-
a straight line joining the midpoint of the shoulders
just to the filming environment, and (e) three free
and the midpoint of the hips. Trunk inclination was
throw trials which were recorded for analysis. As a
measured in degrees with vertical being zero, back-
precautionary measure, additional trials were record-
ward being negative, and forward being positive. Be-
ed for some subjects.
cause backward lean was considered as detrimental as
forward lean, the absolute trunk angle at release was
Collection and Reduction of Data
selected for the analysis.
The free throw trials were filmed with a Cine-Ko- The anterior-posterior base of support was defined
dak Special camera which was positioned 23 m from as the horizontal distance from the trailing ankle to
the subject on an extension of the free throw line. the leading toe. The location of the center of gravity of
Clear images were obtained by using a camera speed the body with respect to the base of support was con-
of 60.8 k3.6 frames per second, a 90 degree shutter, sidered to be the vertical projection of the center of
an exposure time of 4.12 k0.22 ms, a 50 mm lens, gravity to the base of support. The distance the pro-
4XR reversal film, and 3000 W of additional lighting. jected center of gravity was in advance of the trailing
Camera speed was verified with a sixty cycle clock ankle was divided by the length of the base of support
placed near the subject. to yield the center of gravity ratio. Because the posteri-
All trials for each subject were analyzed. Because of or ankle rather than heel was the point of demarka-
RESEARCH QUARTERLY
FOR EXERCISE VOL. 56, No. 2
AND SPORT
116HUDSON
tion for the base of support, the center of gravity tions.
values are underestimated by about .06. Four classification matrices were examined at each
In addition to the center of gravity ratio, two other step in the analysis in order to assess the number of
center of gravity variables were defined. Information correct classifications. The first matrix was derived
about balance was included by finding the absolute from traditional discriminant procedures. For each of
difference between the center of gravity ratio (adjust- the three skill groups, a classification function was
ed by .06) and the midpoint of the base of support computed with the raw data from all 67 shots serving
(.50). To determine if there were a shift in the center as the basis. After each shot was evaluated by each of
of gravity during shooting, the center of gravity ratio the three functions, the shot was assigned to the skill
immediately prior to release was subtracted from the group corresponding to the highest value on the func-
center of gravity ratio immediately after release. tions. Also, the probability for a given shot to belong to
a given group was known. A shot was considered to be
Treatment of Data classified correctly if the predicted and actual category
Discriminant analysis was employed to predict the were the same.
categorical variable of basketball skill (1 = poor, 2 = The results of the first matrix were used to compile
good, 3 = elite) from 12 biomechanical variables the second matrix. For each subject, the predicted
which were part of the product or process of free classifications of all analyzed shots were combined
throw shooting. Due to the interdependent relation- such that the shooter was assigned to the skill category
ship among many of the variables, each trial was treat- represented by the majority of shots. If a clear major-
ed independently. Thus, the 67 shots taken by 22 ity did not exist, probabilities of group membership
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shooters represented six cases per variable and two were examined to establish the predicted category of
subjects per variable. skill. A shooter was considered to be classified correct-
It is acknowledged that the cases- and subjects-per- ly if the predicted and actual category were in agree-
variable ratios are near the liberal end of acceptability. ment.
However, these ratios were used with the following The third and fourth classification matrices were
justifications: (a) recently published biophysical stud- derived in a manner similar to the first and second
ies have included as many variables as one less than matrices except that jackknifed rather than traditional
the number of subjects (e.g., Silva et al., 1981); (b) in discriminant procedures were followed. In the jack-
the statistical analysis, full rank of the dispersion and knifed procedure each case is classified by applying
correlation matrices is retained unless there are fewer the classification functions computed from all the data
subjects than variables (Cooley & Lohnes, 1971); (c) except the case being classified (Lachenbruch & Mick-
because this study is an introductory, exploratory ey, 1968).
work and the included variables are supported in the The statistical analysis was performed with the P7M
literature, it is impossible to deselect the least signifi- program of BMDP (Dixon et al., 1981) and the DIS-
cant variables without conducting the analysis; and (d) CRIMINANT program of SPSS (Nie, Hull, Jenkins,
a conservative method of retaining variables was used Steinbrenner, & Bent, 1975). The BMDP program
to offset the searching of a liberal number of variables. was used to: (a) calculate means and standard devi-
Because discriminant analysis with 12 variables has ations for each variable, (b) determine if the groups
more than 4,000 possible solutions, it was necessary to were significantly different, (c) generate prediction
develop a strategy for obtaining a single best solution. equations for each group, and (d) classify each shot in
First, forward stepwise selection criteria were em- the group with the highest probability. The SPSS pro-
ployed by adding at each step the variable with the gram was employed to compute standardized dis-
largest F statistic computed from a one-way analysis of criminant weights.
covariance where the covariates were the previously
entered variables. Based on the suggestion of Cos-
Results and Discussion
tanza and Afifi (1979) to use a moderate significance The means and standard deviations for each of the
level (. 10 < p < .25) for including variables, iterations 12 biomechanical variables are given in Table 1. All
were continued until none of the remaining variables three groups were similar in angle of projection and
had an F statistic with significance of p < .lo. velocity of projection. The elite group stood taller and
Next, the set of solutions generated by the stepwise used a greater height of release ratio, which reduced
analysis was examined to select the best solution. After the distance these shots had to travel compared to the
eliminating the solutions which did not have a signifi- shots of the other groups. The average angle of pro-
cant (p < .01) multivariate F ratio for the differences jection for each group was in the 4-8" above minimum
in group centroids, the best solution was deemed to be range recommended by Hay (1978). The poor and
the one which used the minimum number of variables good group means were close to the angle associated
to provide the maximum number of correct classifica- with the minimum velocity of projection which was
RESEARCH QUARTERLY
FOREXERCISE
AND SPORT VOL. 56, NO. 2
117HUDSON
Table 1
Means and Standard Deviations of Biomechanical Variables
Basketball Skill Group
Variables Poor Good Elite
Angle (8) of projection (deg) 52.9 * 5.2 52.5 2 7.3 52.7 f 5.3
-
velocity of projection (m s-')
8 - minimum angle (deg)
7.04 f 0.58
4.9 f 5.7
7.03 f 0.55
5.3 f 7.7
7.10 f 0.50
8.4 f 5.5
8 - Brancazio angle (deg) 1.0 f 5.4 1.1 k 7.5 3.4 f 5.4
8 - Mullaney angle (deg) -3.2 *
5.5 -3.1 f 7.5 -0.9 * 5.3
Trunk angle (deg) 6.7 2 6.7 2.9 2 1.8 2.3 2 1.5
Center of gravity (COG) ratio 0.65 f 0.19 0.51 f 0.07 0.44 f 0.09
COG ratio - midpoint of base 0.21 f 0.19 0.07 2 0.07 0.07 f 0.05
Change in COG ratio at release 0.02 f 0.04 -0.01 f 0.02 0.00 f 0.02
Height of release ratio 1.23 f 0.06 1.25 f 0.05 1.30 f 0.04
Accuracy on 20-shot test ("3'0) 46.9 f 13.3 68.6 f 13.9 74.4 f 7.9
Accuracv on filmed shots I%) 22.9 f 22.0 42.9 f 24.1 64.6 f 13.1
favored by Brancazio (1981). The elite group mean lease ratio, and absolute difference between the center
was close to the angle corresponding to an angle of of gravity ratio and the midpoint of the base of sup-
entry of 45" which was suggested by Mullaney (1957). port. Two significant canonical functions were gener-
However, the variance in each group on the measures ated which accounted for 85.8 and 14.2% of the vari-
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of angle of projection was high. ance explained by the functions, respectively. Thus,
For most of the process variables the mean of the the linear combination of the variables in the first
good group was between the means of the poor and function accounted for 73.6% of the variance in pre-
elite groups, but closer to the elite group. The height dicting group membership. Classification functions
of release ratio increased with the skill of the subjects. for each of the skill groups are given in Table 2. When
The poor group had a moderate angle of trunk incli- traditional classification procedures were employed,
nation while the better groups had minimal trunk 60 of 67 (89.6%) shots were classified correctly. Six of
inclination. After adjusting the mean center of gravity the misclassified shots were the total of trials for one
ratios for the systematic underestimation, the location member of the poor group and one member of the
of the center of gravity was at mid-stance in the elite good group. The remaining mismatched shot repre-
group and progressively forward of mid-stance in the sented one of two trials for a member of the elite
good and poor groups. In examining the absolute group. Thus, 19 of 22 (86.4%)basketball players were
difference between the center of gravity ratio and the matched with the appropriate skill group. The accura-
midpoint of the base of support, it appears that mem- cy of classification was 58 of 67 (86.6%)shots and 19of
bers of the elite and good groups were well balanced 22 (86.4%)shooters when jackknifed procedures were
and members of the poor group were not well bal- used.
anced. Each group exhibited a different style with Because the 20-shot accuracy test could be consid-
respect to the change in the center of gravity ratio at ered a performance variable rather than a biomechan-
release: the elite group showed no change, the good ical technique variable, another discriminant analysis
group moved slightly backward, and the poor group was performed which used the 11 remaining variables
moved slightly forward. to predict skill group. The resulting solution based on
The good group scored between the poor and elite five predictor variables (center of gravity ratio, abso-
groups but closer to the elite group on the 20-shot test lute difference between the center of gravity ratio and
of accuracy. However, when the stress of the biome- the midpoint of the base of support, accuracy on
chanical testing environment was added, the accuracy filmed shots, height of release ratio, and change in the
on filmed shots by members of the poor and good center of gravity ratio at release) was significant at the
groups decreased by about 25%. Members of the elite .0001 level (A = -327, F(10,120) = 9.00). The two
group were influenced to a lesser extent by the testing significant canonical functions accounted for 85.1 and
environment. 14.9%of the variance explained by the functions. Us-
Forward stepwise discriminant analysis was used ing traditional classification procedures, correct classi-
with a set of 12 biomechanical variables to assess the fications were obtained for 54 of 67 (80.6%)shots and
predictability of membership in three basketball skill 19 of 22 (86.4%) shooters. Jackknifed classification
groups. The selected solution was significant at the yielded correct predictions on 5 1 of 67 (76.1%) shots
,0001level (A = .199,F(10,120) = 14.88) and included and 18 of 22 (86.4%) shooters.
five variables: accuracy on the 20-shot test, center of At higher levels of competition, a team selection
gravity ratio, accuracy on filmed shots, height of re- situation would require discrimination between elite
RESEARCH QUARTERLY AND SPORTVOL.56, No. 2
FOREXERCISE
118HUDSON
Table 2
Classification Functions for Poor, Good, and Elite Basketball Groups
Basketball Skill GrouD
Variables” Poor Good Elite
Accuracy on 20-shot test (Yo) 0.195 0.399 0.407
Center of gravity ratio 121.713 128.222 98.817
COG ratio - midpoint of base -95.639 -116.044 -84.855
Height of release ratio 416.293 416.849 439.550
Accuracy on filmed shots (“h) 0.114 0.143 0.191
Constant -291.613 -305.915 -326.275
“Variables are listed in order of stepwise inclusion.
and good, but not poor players. Thus, a discriminant include variables which were significant at the .15 lev-
analysis was performed to predict membership in el.
good and elite skill groups. The original set of 12 When the original set of 12 variables was searched,
variables was used with 38 shots taken by 13 good and the expanded model contained five variables: height
elite players. A parsimonious solution was generated of release ratio, accuracy on the 20-shot test, absolute
which had three predictor variables: accuracy on the trunk angle at release, accuracy on filmed trials, and
20-shot test, accuracy on filmed trials, and height of the change of the center of gravity ratio at release.
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release ratio. The solution was significant at the .0001 This solution was significant at the .0001 level (A =
level (A = .437, F(3,34) = 14.59) and the canonical .356, F(5,32) = 11.56) and had a canonical correlation
correlation was .750. Traditional methods yielded cor- of 302. The classification functions for the good and
rect classifications for 34 of 38 (89.5%)shots and 12 of elite skill groups are given in Table 3. Using the tradi-
13 (92.3%)shooters. Jackknifed classification correct-
ly matched 33 of 38 (86.8%) shots and 11 of 13 Table 3
(84.6%)shooters. A check on the strength of the classi- Classlficatlon Functions for Good and Elite Basketball
Groups
fication functions was made by predicting the skill
category of the 29 shots taken by poor group mem- Basketball Skill GrouD
bers. When both the traditional and jackknifed classi- Variablesa Good Elite
fication methods were employed, 28 of 29 (96.6%)of
poor group shots were labeled as good rather than Height of release ratio 1176.452 1244.212
Accuracy on 20-shot test (“30) 2.936 3.123
elite. Accuracy on filmed trials (%) 0.385 0.453
As with the three-group situation, another two- Trunk angle (deg) -11.660 -12.51 2
group discriminant analysis was conducted with 11 of COG ratio - midpoint of base 507.681 552.253
the 12 original variables (excluding the 20-shot accu- Constant -824.1 19 -925.035
racy test). The resulting parsimonious solution con- Note. Functions are based on the expanded model.
tained two predictor variables (accuracy on filmed tri- ’Variables are listed in order of stepwise inclusion.
als and height of release ratio) and was significant at
the .0001 level (A = .579,F(2,35) = 12.70).The canon- tional classification method, 34 of 38 (89.4%)of shots
ical correlation was .649. Correct categories were pre- and 13 of 13 shooters were correctly identified. Appli-
dicted for 32 of 38 (84.2%)shots and 11 of 13 (84.6%) cation of the jackknifed procedure yielded correct
shooters and 31 of 38 (81.6%) shots and 11 of 13 classifications for 33 of 38 (86.8%) shots and 12 of 13
(84.6%) shooters by the traditional and jackknifed (92.3%) shooters.
classification methods, respectively. The strength of The criterion of permitting the inclusion of varia-
the classification function was verified as 28 of 29 bles which are significant at the .15 level was used in a
(96.6%) poor shots were categorized as good instead discriminant analysis of the two-group situation with
of elite. 11 of 12 variables (excluding accuracy on the 20-shot
In both parsimonious two-group models, the height test). An expanded model was generated which con-
of release ratio was the only non-accuracy variable tained four variables: height of release ratio, accuracy
included. While parsimony may be statistically desir- on filmed trials, center of gravity ratio at release, and
able, in this case it limits the diagnostic utility of the absolute trunk angle at release. This model was signif-
model (ie., a good player striving to be elite might icant at the .0001 level (A = .457, F(4,33) = 9.80) and
profit from having more information in the form of had a canonical correlation of .737. The accuracy of
additional variables which have discriminatory pow- classification was 34 of 38 (89.4%) shots and 12 of 13
er). Thus, both two-group analyses were expanded to (92.3%) shooters with the traditional method and 30
RESEARCH QUARTERLY AND SPORT VOL. 56, NO. 2
FOREXERCISE
119HUDSON
of 38 (78.9%) shots and 11 of 13 (84.6%) shooters with enrolled in the same instructional class and all subjects
the jackknifed procedure. in the good group were players on the same team. As a
The relative importance of the predictor variables is result, there may have been common elements within
indicated by the absolute magnitudes of the standard- these experimental groups which may not be repre-
ized discriminant function coefficients. Table 4 pre- sentative of the populations at the poor and good skill
sents the standardized discriminant function coeffi- levels. For example, six of the seven good subjects had
cients for both of the three-group analyses and the two a small amount of backward inclination of the trunk;
expanded two-group analyses. From these coefficients also, members of this group tended to shift the center
it can be seen that in both the two- and three-group of gravity backward as the ball was released. In actual
analyses, accuracy variables were weighted heavily. In (rather than absolute) trunk angle and change in cen-
the three-group analyses, the center of gravity varia- ter of gravity ratio the mean of the good group was not
bles had high weightings, height of release had a low between the means of the elite and poor groups as
weighting, and trunk angle had no weighting. The would be expected. Thus, for the good group, these
coefficients in the two-group analyses were high for variables may be influenced by sample-specificcharac-
height of release and moderate for center of gravity teristics. However, these variables ranked as the least
and trunk angle. Interestingly, the five variables important in the functions which contained them. If
which did not appear in any function were the varia- there is a sample-specific inhence, it remains to be
bles related to angle and velocity of projection. seen whether these variables would retain their theo-
An examination of the raw data with the discrimi- retical importance as predictor variables or if their
nant functions reveals that the poor shooters were coefficients would change. Replicating this study with
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penalized by a center of gravity which was too far other samples from the populations could provide
forward as well as moving forward, a low release insight into this problem.
height, and inaccuracy. Elite shooters were character- Although one category of variable (ie., biomechani-
ized by having a high release point, little trunk inclina- cal) and one phase of basketball playing ( i e . , free
tion, and accuracy in the stressful testing environ- throw shooting) were used to predict basketball skill
ment. To use this information in a coaching or teach- level, the success of prediction ranged from 76-100%.
ing situation, it appears that poor shooters could try to One explanation for the high success of prediction is
improve stability ( i e . , a center of gravity ratio which that many of the players who have developed skill in
remains in the mid-stance region) and good shooters free throw shooting may have developed skill in other
could concentrate on releasing higher while in an up- aspects of basketball as well. Despite the obvious con-
right posture and practicing under pressure. tradiction exemplified by a few successfulprofessional
Regardless of the number of variables or method of basketball players who are poor free throw shooters,
classification, two subjects were consistently misclassi- discriminant analysis of free throw shooting using bio-
fied. The member of the poor group who was misla- mechanical variables appears to have predictive value
beled held membership in the poor group on the basis as one aspect of the selection of basketball team mem-
of enrollment in a beginning instructional class which bers.
had no upper limit for skill of participants. The elite In addition to using discriminant analysis with bio-
group member who was misdiagnosed may have been mechanical variables to identify skilled players, this
selected to the World University Games team for skills technique appears to have potential in the diagnosis of
other than shooting, or by virtue of reputation. errors which may limit performance. It remains to be
In this study all members of the poor group were seen if a performer can improve skill level by correct-
Table 4
Standardized Discriminant Function Coefficients
Three-Group Analysisa Two-Group Analysisb
with without with without
Variables Test of 20 Test of 20 Test of 20 Test of 20
Accuracy on 20-shot test 0.781 0.826
Accuracy on filmed shots 0.392 0.592 0.520 0.547
Height of release ratio 0.268 0.496 1.213 0.828
Center of gravity ratio -0.61 2 -1.518 -0.505
COG ratio - midpoint of base 0.067 1.248
Change in COG ratio at release -0.141 0.363
Trunk anale -0.548 -0.477
BCoefficients are from Function 1. bCoefficients are from expanded models.
QUARTERLY
RESEARCH FOR EXERCISEA N D SPORTVOL.56, No. 2
120HUDSON
ing errors which this discriminant analysis has identi- Hay, J. G. (1978). The biomechanics of sports techniques (2nd
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Summary Unpublished master’s thesis, South Dakota State Uni-
Based on success rates of 76-loo%, discriminant versity, Brookings, SD.
King, G., & Toney, D. (1973). Basketball. North Palm Beach,
analysis using biomechanical variables appears to be a
FL: The Athletic Institute.
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and, thereby, the selection of basketball team mem- ror rates in discriminant analysis. Technometria, 10, 1-
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For future team selections, population-specific Mortimer, E. M. (195 1). Basketball shooting. Research Quar-
equations could be developed or the functions derived terly, 22, 234-243.
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is required to obtain the necessary data for these func- 38,53-55.
tions, all the predictor variables are based on position Nagle, F. J., Morgan, W. P., Hellickson, R. O., Serfass,
and, therefore, could be acquired without sophisticat- R. C., & Alexander, J. F. (1975). Spotting success traits
ed equipment. in Olympic contenders. Physician and Sports Medicine, 3,
3 1-34.
The coach, teacher, or participant can gain insight
Nie, N. H., Hull, C. H., Jenkins, J. G., Steinbrenner, K., &
about which variables are important in the acquisition Bent, D. H. (1975). Statistical packages for the social sci-
of free throw shooting skill by examining the stan- ewes (2nd ed.). New York: McGraw-Hill.
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dardized discriminant function coefficients. Pollock, M. L., Jackson, A. S., & Pate, R. R. (1980). Discrimi-
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