Journal of Digital Life 2022,2,3

ArticleThe relationship among skills/factors and theirstructure and wins/losses in games in basketballclassesKen Nagamine 1*,Osamu Aoyagi 1,Akihito Yaita2,Ikuo Komure 1,Tsuyoshi Kawazura 2,Shinya
Tagata3,Tomohiro Annoura4 ,Yasufumi Ohyama5
1

Faculty of Health and Sports Science, Fukuoka University, 8-19-10 Nanakuma, Jyonan-ku, Fukuoka 814-0180 JAPAN
Faculty of Sports Science, Kyushu Kyoritsu University, 1-8 Jiyugaoka, Yahatanishi-ku, Kitakyushu 807-8585 JAPAN
3
Hitachi High-Tech Cougars, 844 Ichige Hitachinaka Ibaraki 312-0033 JAPAN
4
Japan University of Economics, 3-11-25 Gojo, Dazaifu-shi, Fukuoka 818-0197 JAPAN
5
National Institute of Technology, Sasebo College, 1-1, Okishimmachi, Sasebo Shi, Nagasaki 857-1193 JAPAN2*Correspondence: knaga@fukuoka-u.ac.jp; Tel.: +81-93-871-6631ffiliation

Abstract
This study aimed to extract the structure of plays/fouls of basketball games in university PE classes using
MDS and to investigate the relationship between wins/losses and their structure using logistic regression
analysis in the games. Targeted games were 20 games performed in university PE classes at F-university andthe plays/factors observed were assessed by a 5-point scale. The items observed were 52 items chosen from
“Passing,” “Dribbling,” “Shooting,” “Rebounding,” “Fast break,” “Cooperative plays,” “Violations,” and“Fouls.” After the principal component analysis was applied to the whole data, the items that did not show
significant loadings were removed from the analysis, and a correlation matrix among only the items that hadsignificant principle loadings was computed. Another principal component analysis was performed and theprincipal component scores for each skill/factor were computed. Nonmetric MDS was applied to thecorrelation matrix, a two-dimensional space was extracted, and the rotation of axes by Varimax criterion andclustering by hierarchical cluster analysis were applied to the two-dimensional space. Finally, logistic
regression analysis to predict wins/losses was carried out using skills/factors including gender and evaluators
to remove their influence as independent variables. As a result, the following results were obtained:
1) The two-dimensional space obtained was interpreted as “Individual skills and skills leading tofouls/violations” and “Individual – group skills.” Again, the four clusters obtained were also named “Balladvancing individual skills,” “Under-basket individual skills,” “Cooperative skills,” and “Against-rule andunskilled plays.” 2) Although the likelihood ratio test of logistic regression analysis with all independent
variables was not significant, the test of the model after the independent-variable selection was significant,in which “Shooting,” “Cooperative plays,” “Fouls,” and “Gender” were included. In the univariate analysis
using correlation ratios, “Dribbling,” “Shooting,” and “Cooperative plays” were significant, but “Fouls” were
not. It is thought that “Dribbling” lost its significant relationship with wins/losses when removing theinfluence of “Cooperative plays,” and insignificant “Fouls” in the univariate analysis showed an important
impact on wins/losses because the fouls provided the change of offense and the risk of a losing score increased.
Keywords: Basketball ; University PE ; Individual skills ; group skills.

1. Introduction
Many studies examining factors influencing wins/losses in basketball games where outstanding players played havebeen conducted and a relatively large number of researchers indicated 2-point shooting, 3-point shooting (Oida andShimada, 1969; Tamaki, 2007; Yaita and Nodera, 2007), defensive rebounds (Goto and Iwaki, 2006; Okamoto, 1989),
Received: 14 January 2022, Revised: 27 January 2022, Accepted: 24 February 2022, Published: 4 March 2022
* Correspondence: knaga@fukuoka-u.ac.jp
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The relationship among skills/factors and their structure and wins/losses in games in basketball classes
Ken Nagamine, Osamu Aoyagi, Akihito Yaita, Ikuo Komure, Tsuyoshi Kawazura, Shinya Tagata, Tomohiro Annoura and Yasufumi Ohyamaassist (Maeyama, 1996; Sampio and Sebastina, 2004), and others as decisive plays for game outcomes. However, inthe case of junior players, the common playing characteristics of “little dribbling,” “fast break with only two players,”and “frequently found fouls” that were not found in outstanding players were detected (Koh et al. ,2011; Ortega et al.,2006). This fact enables us to easily deduce that lower level players produce largely different outcomes and suggests
conducting further research. Another common characteristic among researchers was that they used (canonical)
discriminant analysis (Dillon and Goldstein, 1984) which is a multi-variate technique. As the reason that not just ttests, but discriminant analysis is also used is that they aimed to investigate the relationship between independent
variables (a variety of factors assumed to influence game outcomes) and a dependent variable (game outcome) while
statistically holding other independent variables constant. Although significant association is frequently found in playsthat are not independently performed with each other in the sequence of the game, the use of discriminant analysis
has the advantage of taking this relationship into consideration. Also, when investigating comprehensive factors, since
we must handle many variables/factors, it is sometimes hard to put the findings obtained together. For this reason,studies exist that already examine the structure of plays to summarize the relationship of the factors of interest (Ohgaet al., 1990; Sakai et al., 1998). As procedures to extract the structures, they have used factor analysis or
multidimensional scaling (MDS; Takane et al., 1977; Young and Torgeson, 1967). Then, many studies extracted thefactors corresponding to three types of score getting that they have in common, i.e., 2-point shooting, 3-point shooting,and free throw (Kodama et al., 2010; Kodama and Suzuki, 1990; Suzuki and Kodama, 1988).
Incidentally, basketball games are performed in basketball classes in PE classes, of which one of the characteristicsof the training is to make an effort to win games with poor skills. For instance, although skilled players advance theball while using short and frequent passing in which many players are involved, it is sometimes effective and safe forunskilled players to perform dribbling, not passing, with only a few players because conducting frequent passing leads
to making many errors in proportion to the number of plays. Also, skilled players are spread out evenly all over the
court, as reflected in the strategies of “making a space, running into the space, and receiving the ball (Shimada, 1992)”
which are utilized. However, at the level where high-level strategies cannot be use, many players gather around theball regardless of being offensive or defensive players, i.e., being crowded together in what is called “Dango-jyotai”
in Japanese. Many researchers focused on this “Dango-jyotai” as a critical factor in learning to progress from unskilled
to skilled conditions (Hirose et al., 2012; Nakanishi et al., 2003; Sakakibara, 1994). Also, with the structure of skills,
although a sequence of plays with a scoring pattern was found in skilled players, which is brought about by strategic
factors, these strategic play patterns cannot be expected from unskilled players, and only a skill structure based on
individual skills can be expected.
As such, since the factors affecting wins/losses are different depending on skill levels, it can be easily expected thatthe actual conditions of the games in PE classes are different from games involving skilled players because of thepoor skills of the players in the PE classes. For this reason, the extraction of factors influencing wins/losses in PE
class games and examination of their relationship with wins/losses provide us good information about what should betaught to unskilled players in PE classes, and the class curriculum can be studied based on these findings.
Thus, this study aimed to examine the relationship between skills/factors and wins/losses in PE basketball games inwhich unskilled players played, after extracting the structure of plays/skills and fouls using the MDS that traditional
studies have utilized. However, although almost all the traditional studies used discriminant analysis, which has thelimitation of normality and homoscedasticity, this study used a logistic regression model (Hair et al., 2010) which ismost effective in a two-group classification.
2. Methods
2.1 Games observed and observations/assessments
Taping video of 20 games held in basketball PE classes at F-university, the frequencies of the following observation
items were counted/assessed. Two evaluators assessed the plays of the students. One was a coach of a femalebasketball team at a university and a holder of a license A certified by the Japan Basketball Association. The otherwas a male university coach who has an official license B. At the same time, game outcomes were also recorded.
2.2 Observation/assessment items for skills/factors
As the main individual and group skills in basketball games, roughly the six domains of passing, dribbling, shooting,rebound, fast break, and cooperation plays were assumed (Kimura, 1986; Seki, 1974). Furthermore, the two domainsof fouls and violations were also included because useless illegal plays also give the opponents the chance to get ascore, which is one of the characteristics of unskilled players. That is to say, whether the following 52 plays/factors
were found or not was checked: six passing plays, specifically: “Desperate passing,” “Vertical long passing,”“Horizontal passing,” “Passing to change the offensive side,” “Passing to reorganize an offensive line,” and “Passing
attacking opponents’ carelessness;” six dribbling plays, namely “Dribbling while watching the ball,” “Dribbling while
protecting the ball,” “Dribbling while looking around,” “Changing direction while dribbling,” “Breaking throughCopyright: © SANKEI DIGITAL INC.

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The relationship among skills/factors and their structure and wins/losses in games in basketball classes
Ken Nagamine, Osamu Aoyagi, Akihito Yaita, Ikuo Komure, Tsuyoshi Kawazura, Shinya Tagata, Tomohiro Annoura and Yasufumi Ohyama

while dribbling,” and “Going away while dribbling;” five shooting plays, specifically “Dribbling and shooting,” “Layup shooting,” “Long-range shooting,” “Mid-range shooting,” and “Shooting after dodging the opponent;” fiverebounding plays made up of “Rebounding by one player,” “Rebounding by two players,” “Trying to get the inside
position,” “Rebounding by three players,” and “Jumping into a rebound by dodging the opponent,” nine fast-breakplays, namely “A player who was the first to hold the ball and carried it by dribbling,” “A player who is good at ballhandling carried the ball,” “The ball was carried by passing,” “The ball was carried by a straight-line dribble,” “Theball was carried by dribbling,” “The ball was carried with dribbling while shaking the defensive players off,”“Consistently getting the basket when the offensive players were outnumbered,” “Three-line fast break,” and “A
successive/secondary offense from a fast break;” eight cooperative plays consisting of “Outlet passing,” “Pass-andplay,” “A cooperative play with a post man,” “A ball screen play,” “A cooperative play between two specific players,”“A cooperative play by two specific players,” “A cooperative play by three specific players,” and “A ball screen playamong three players;” eight violations comprised of “Traveling when catching the ball,” “Traveling when passing,”“Traveling when moving to receive the ball,” “Travelling when faking,” “Traveling when stopping,” “Linecrossing,” ”Double dribbling,” and “3-second over time;” and five fouls, namely “Body contact when trying to rob
the ball,” “Body contact when trying to steal,” “Body contact when trying to stop the opponent drive,” “Body contact
when competing the position,” and “Fouls or charging against shooting.” Each item was assessed using a 5-point
scale: 5: very good; 4: good; 3: unknown; 2: bad; and 1: very bad. A five-point scale was employed to obtain a moredetailed evaluation.
2.3 Statistical analysis procedures
2.3.1 Compound scores of skills/factors
First of all, in order to make a comprehensive evaluation of each skill/factor, principal component analysis was
conducted, and the first principal component structure loadings were computed. If the loadings were not significant,principal component analysis was computed again after removing the skills/factors because the skills/factors were notreflected in the principal component. Then, principal component scores were computed from skills/factors with only
significant loadings.
2.3.2 Extraction of the structure of skills/factors
In order to investigate the structure of skills/factors, after computing a correlation matrix, dissimilarity was computed
using the following translation into the correlation. Then, nonmetric multidimensional scaling was applied:Dij = (1-rij)1/2,
where Dij stands for dissimilarity and rij for correlation coefficient.
The nonmetric multidimensional scaling was conducted using the function of “sammon” in R. The number ofdimensions was determined by the change of stress. Subsequently, clustering was conducted by using hierarchicalcluster analysis into the configuration obtained. Interpretation of not only clusters but also axes was conducted using
Varimax rotation (Harman, 1976).
2.3.3 Association between wins/losses and skills/factors
In order to investigate the association between eight skills/factors and wins/losses, whether the association existedfrom the significance of correlation ratios or not was first examined. Next, to examine the relationship after holding
other skills/factors constant, logistic regression analysis was conducted using wins/losses as a dependent variable andeight skills/factors as independent variables. However, in order to remove the influence of gender and evaluators, they
were also included as independent variables. Moreover, independent variables were selected to find variables withmore contribution to wins/losses after considering the interaction with each other. Independent variables were
included or removed using the criterion of the probability of the Wald test being 0.2. The correct and incorrect
discrimination rates due to logistic regression analysis after the selection was computed using a cut-off point in which
the ROC curve was close to the upper–right corner, the point of the horizontal axis was 0, and the vertical axis was 1.
3. Results
3.1 Principal component analysis to obtain composite scores of skills/factors
The principal component loadings are shown in Table 1. Principal component analysis by skill/factor showed nosignificant loadings less than 0.3 in “Vertical long passing (-0.158)” for passing; “Dribbling and shooting (-0.046)”
and “Lay-up shooting (-0.225)” for shooting; “Jumping into a rebound by dodging the opponent (0.105)” forrebounding; “The ball was carried with passing (0.022);” “Consistently getting the basket when the offensive players
were outnumbered (0.239);” “Three-line fast break (0.327 for the first time, but 0.258 for the second time);” “A
successive/secondary offense from a fast break (-0.031)” of a fast break; “A cooperative play with a post man

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The relationship among skills/factors and their structure and wins/losses in games in basketball classes
Ken Nagamine, Osamu Aoyagi, Akihito Yaita, Ikuo Komure, Tsuyoshi Kawazura, Shinya Tagata, Tomohiro Annoura and Yasufumi Ohyama(0.204);” “A ball screen play (0.294);” “A cooperative play by three specific players (0.231);” and “A ball screen playamong three players (0.068)” in cooperative plays.
Table 1. Principal component loadings

no.
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52

Skills/factors

passing
plays

Dribbling
plays

Shooting
plays

Rebounding
plays

Fast-break
plays

Cooperative
plays

Violations

Fouls

Analytical items
Desperate passing
Vertical long passing
Horizontal passing
Passing to change the offensive side
Passing to reorganize an offensive line
Passing attacking opponents' carelessness
Dribbling while watching the ball
Dribbling while protecting the ball
Dribbling while looking around
Changing direction while dribbling
Breaking through while dribbling
Going away while dribbling
Dribbling and shooting
Lay-up shooting
Long-range shooting
Mid-range shooting
Shooting after dodging the opponent
Rebounding by one player
Rebounding by two players
Trying to get the inside position
Rebounding by three players
Jumping into a rebound by dodging the opponent
A player who was the first to hold the ball and carried it by dribbling
A player who is good at ball-handling carried the ball
The ball was carried by passing
The ball was carried by a straight-line dribble
The ball was carried by dribbling
The ball was carried with dribbling while shaking the defensive players off
Consistently getting the basket when the offensive players were outnumbered
Three-line fast break
A successive/secondary offense from a fast break
Outlet passing
Pass-and-play
A cooperative play with a post man
A ball screen play
A cooperative play between two specific players
A cooperative play by two specific players
A cooperative play by three specific players
A ball screen play among three players
Traveling when catching the ball
Traveling when passing
Traveling when moving to receive the ball
Travelling when faking
Traveling when stoppingLine crossing
Double dribbling
3-second over time
Body contact when trying to rob the ball
Body contact when trying to steal
Body contact when trying to stop the opponent drive
Body contact when competing the position
Fouls or charging against shooting

The
first
time
-0.668-0.158
0.600
0.869
0.914
0.840
-0.448
0.498
0.782
0.890
0.912
0.797
-0.046-0.225
0.853
0.809
0.604
0.393
0.791
0.878
0.833
0.105
0.665
0.665
0.022
0.747
0.810
0.451
0.239
0.258†-0.031
0.665
0.702
0.204
0.294
0.795
0.755
0.231
0.068
0.871
0.882
0.884
0.846
0.883
0.455
0.399
0.582
0.784
0.864
0.850
0.776
0.814

The
secondtime-0.641
0.617
0.874
0.921
0.842
-0.448
0.498
0.782
0.890
0.912
0.797
0.867
0.824
0.593
0.396
0.794
0.879
0.831
0.722
0.717
0.772
0.808
0.338

0.672
0.693
0.839
0.783
0.871
0.882
0.884
0.846
0.883
0.455
0.399
0.582
0.784
0.864
0.850
0.776
0.814

†) This item was removed because of 0.327 for the first time, but 0.258 for the second time
3.2 Configuration of skills/factors
Since the first principal component scores had the highest correlations with variables used, it can be thought that thefirst principal component scores influenced the characteristics of the skills/factors. Thus, after computing thecorrelation matrix among them, nonmetric multidimensional scaling was applied. Figure 1 shows the change of stressfrom the first to fifth dimensions. As the number of dimensions increased from the first dimension to the third
dimension, stress rapidly decreased, in which the tendency was not found in the third dimension or later. In short, theelbow was found in the third dimension so a two-dimensional solution was adopted. Table 2 is the coordinates ofskills/factors, by which the two-dimensional space for them is drawn as in Figure 2.

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The relationship among skills/factors and their structure and wins/losses in games in basketball classes
Ken Nagamine, Osamu Aoyagi, Akihito Yaita, Ikuo Komure, Tsuyoshi Kawazura, Shinya Tagata, Tomohiro Annoura and Yasufumi Ohyama

Table 2. The coordinates of MDS configuration after Varimax rotation
no.
1
2
3
4
5
6
7
8

Skills/factors
Passing plays
Dribbling plays
Shooting plays
Rebounding plays
Fast-break plays
Cooperative plays
Violations
Fouls
Variance

The 1st-0.57895-0.55315-0.12019
0.03032
0.20592-0.25248
0.678170.59035
1.57110The second-0.32790
0.03956-0.23050-0.71203
0.38846
0.52771
0.41354-0.09885
1.27936

3.3 Interpretation of skills/factors
The results of the hierarchical cluster analysis using the Ward method that was applied to the two-dimensional
configuration are indicated by the dendrogram in Figure 3. At the same time, an interpretation of the two axes was
also conducted. Figure 4 is the rotated configuration onto which the clustering was superimposed.
Hierarchical cluster analysis allowed us to produce four clusters: Cluster 1, in which dribbling and passing skills were
included; Cluster 2, which included shooting and rebounding skills; Cluster 3, in which only cooperative plays werecategorized; and Cluster 4 for fast breaks, violations, and fouls.

Cluster 1 was interpreted as “Ball-advancing individual skills” because both dribbling and passing skills were theskills to advance the ball. The fact that both shooting and rebounding skills are individual skills under the basket
allowed us to interpret Cluster 2 as “Under-basket individual skills.” Cluster 3 should be named “Cooperative skills”
because the cluster was comprised of one skill. In Cluster 4, violations and fouls that violated the rules were included.
It is thought that violations were caused by unskilled plays or that ignorance of rules or fouls was caused throughbody contact with the opponent because the players could not control their bodies well. Again, fast breaks performed
using a vertical long pass without involving hard work and elaborate ball advancing where many teammates
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The relationship among skills/factors and their structure and wins/losses in games in basketball classes
Ken Nagamine, Osamu Aoyagi, Akihito Yaita, Ikuo Komure, Tsuyoshi Kawazura, Shinya Tagata, Tomohiro Annoura and Yasufumi Ohyama

cooperated in the process was not seen. This fact allows us to consider that the reason why these fast breaks, violations,and fouls were categorized into one cluster was that the lack of skills was the common factor. Thus, this cluster wasnamed “Against-rule and unskilled plays.”
Also regarding the axis interpretation, since skillful ball advancing by individuals (Cluster 1) and violations or fouls
by unskilled plays or body control (Cluster 4) were found at both ends of the first dimension, the horizontal axis wasinterpreted as “Individual skills and skills leading to fouls/violations.” The vertical axis was named “Individual –group skills” because there were individual shooting and rebounding skills performed under the basket and cooperative
plays reflecting group skills at both ends of this axis.
3.4 Relationship between wins/losses and skills/factors investigated individually
Table 3 shows the correlation ratios (etas) and the results of significant tests of them with means and standard
deviations of each skill/factor by wins/losses. Significant correlations were found in dribbling (eta = 0.200, p<0.05),
shooting (eta = 0.252, p<0.01), and cooperative plays (eta = 0.243, p<0.01), in which any of the winning teams had
higher skill scores compared to the losing teams.
Table 3. Correlation ratios between wining/losing and skills/factors

Skills/factors
Passing plays
Dribbling plays
Shooting plays
Rebounding plays
Fast-break plays
Cooperative plays
Violations
Fouls

Winning teams
The number
Meanof games
0.231
0.363
0.335
0.008
57
0.056
0.363
-0.197-0.123

SD
1.679
1.798
1.131
1.447
1.640
1.546
2.230
1.824

Losing teams
The number
Meanof games-0.231-0.363-0.335-0.00857-0.056-0.363
0.197
0.123

SD

Correlation
ratio

F-value

1.831
1.788
1.446
1.564
1.465
1.371
2.015
1.843

0.131
0.200
0.252
0.005
0.036
0.243
0.093
0.068

1.967
4.671
7.576
0.003
0.147
7.024
0.984
0.513

Df1

1

Df2

112

P-value
0.164
0.033
0.007
0.955
0.702
0.009
0.323
0.475

*
**

**

Note: *: significant at the 5% level; **: significant at the 1% level
3.4 Relationship between wins/losses and skills/factors holding the influence of other skills/factors constantSubsequently, in order to investigate the relationship between wins/losses and skills/factors that held the influence ofother skills/factors as well as gender and evaluators constant, logistic regression analysis using the eight skills/factors
as independent variables and wins/losses as a dependent variable was conducted. Table 4 shows the results when using
all independent variables. Although the Wald test indicated that cooperative play was significant at the level of 5%,
this model was not significant because the -2 log-likelihood of the model including only constant (Null model) was
158.04 and that of the model including all variables (Full model) was 140.42 and chi-square = 17.62，df= 11, p=0.091.
Table 4. Logisistic regression analysis with all variables

Skills/factors
Passing plays
Dribbling plays
Shooting plays
Rebounding plays
Fast-break plays
Cooperative plays
Violations
Fouls
Gender(Male)
Evaluator1
Evaluator2
Constant

Partialregression
coefficient-0.1741
0.16290.4047-0.1430-0.05020.4466-0.0393-0.1007-0.9423-0.3749-0.60161.0600Standard
error

Odds
ratio

Wald

0.19430.19610.23000.18170.19050.19750.18300.1676
0.58840.89240.89540.77200.8402
1.17691.49880.86680.95111.56300.96140.90420.38970.68740.54792.88650.80290.6897
3.09720.61930.06945.1121
0.04620.36132.56430.17640.4514
1.8853df

Note. Likelihood ratio test: χ2=17.61, df=11, p=0.09
Note: *: significant at the 5% level

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P-value
0.37020.40630.07840.43130.79230.02380.82990.54780.10930.67440.50170.1697*

The relationship among skills/factors and their structure and wins/losses in games in basketball classes
Ken Nagamine, Osamu Aoyagi, Akihito Yaita, Ikuo Komure, Tsuyoshi Kawazura, Shinya Tagata, Tomohiro Annoura and Yasufumi OhyamaThen, to find skills/factors with a higher contribution while considering mutual interaction, the independent variables
were selected, during which inclusion or removal was repeated using the criterion of p=0.2 in the Wald test. The
results are shown in Table 5.
Table 5. Logisistic regression analysis after variable selection

Skills/factors
Shooting plays
Cooperative plays
Fouls
Gender(male)
Constant

Partialregression
coefficient
0.39640.3673-0.1681-0.7686
0.5988

Standard
error

Odds
ratio

Wald

0.17740.15660.11690.5436
0.46571.48651.44380.84530.46371.81994.99545.49882.0674
1.99891.6534df

P-value0.02540.01900.15050.1574
0.19851**Note. Likelihood ratio test: χ2=15.26, df=4, p<0.001
Note: *: significant at the 5% level-2 log-likelihood of the model with only constant (Null model) was 158.04 and that of the model after variableselection (Full model) is 142.77, and the likelihood ratio of them was chi-square =15.26，df= 4, p=0.0042. In short,the model including only variables with high contribution was significant at the 1% level. Selected skills/factors wereshooting, cooperative plays, fouls, and gender. The Wald tests indicated that shooting and cooperative plays among
them were significant at the 5% level. Table 6 shows the odds ratios between partial regression coefficients. Shooting
had 1.03 times higher contribution to wins/losses compared to cooperative plays, 1.76 times to fouls, and 3.21 times
to gender. The contribution to predicting wins/losses of cooperative plays to shooting was 0.97 times higher, that tofouls 1.71 times, and that to gender 3.11. That of fouls was 0.57 times higher than that of shooting, 0.59 times thancooperative plays, and 1.82 times than gender. Gender contributed to the prediction of wins/losses 0.57 times morethan shooting, 0.59 times more than cooperative plays, and 0.55 times more than fouls.
Table 6. Comparison of odds ratios among variables

Shooting plays
Cooperative plays
Fouls
Gender

Shooting plays
1.000
0.971
0.569
0.312

Cooperative plays
1.030
1.000
0.585
0.321

Fouls
1.759
1.708
1.000
0.549

Gender
3.206
3.114
1.823
1.000

Figure 5 is a ROC (Receiver Operating Characteristic) curve with FPF (False Positive Fraction) as a horizontal axis
and with TPF (True Positive Fraction). An oblique line indicates a non-discriminated situation and the further the
ROC goes up, the more discrimination increases. The area under the curve is referred to as the AUC (Area Under theCurve) and is 0.712, which is significant (chi-square = 17.83, df=1, and p<0.001) in the statistical test of whether thearea under the oblique line is significantly greater than 0.5 or not. In short, the prediction of this model was verified
to be effective. When obtaining the probability of the best discriminating cut-off point between wins/losses as thenearest point to the point of the top right-hand corner, it is 0.4837, in which FPF=0.298, TPF=0.754, and distance =0.386. Based on this cut-off point, a cross table between actual and predicted wins/losses is shown in Table 7.
Table 7. Sensitivity and specificity with the cut-off value =0.4837

Estimated results by logistic regression
Winning

LosingWinning42

15

Sensitivity

73.68

Losing17

40

Specificity

70.18

Total

71.93

Actual results

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The relationship among skills/factors and their structure and wins/losses in games in basketball classes
Ken Nagamine, Osamu Aoyagi, Akihito Yaita, Ikuo Komure, Tsuyoshi Kawazura, Shinya Tagata, Tomohiro Annoura and Yasufumi Ohyama

The table shows that sensitivity, which correctly predicted the winning teams, was 73.68% and specificity, whichcorrectly predicted the losing teams, was 70.18%. Again, predictive accuracy was 71.93%.
4. Discussion
4.1 Homogeneity in skills/factors
Although principal component scores were computed in order to obtain highly homogenous skill/factor scores, only
“Vertical long passing” did not show a significant principal loading in passing plays. Goto et al. (2000), who examined
the relationship between passing and pivot skills, described that the more skillful a player is in pivoting, the moreaccurate they are in passing. It is thought that “Vertical long passing” did not show a significant association with otherpassing skills because vertical long passing for one’s own basket did not require the pivot action.
As a characteristic of games involving unskilled players, it is well known that an in-a-pack condition (Dango-jyotaiin Japanese) where all the players are concentrated around the ball occurs (Hirose et al., 2012; Nakanishi et al., 2003;
Sakakibara, 1994), which is often observed in the shooting scene around the basket. At that time, a player who intends
to shoot cannot break through the opponent’s defense because of their underdeveloped dribbling skills and in manycases passes the ball to another teammate in desperation. Since the other player who receives the ball shoots from the
spot where they received the ball, shooting after dribbling and lay-up shooting are rarely seen. For this reason, it isthought that vertical long passing is not associated with other passing plays.
Again, the result that “Jumping into a rebound by dodging the opponent” did not show a significant correlation withother rebounding plays can be explained by the very small frequency at which skills like these are performed because
they are too high level for beginners. Similarly, it is thought that their lack of skill development hindered theimplementation of high-level performance like this is the reason why the skills did not appear prominently in the fast
break and cooperative plays. For instance, since an in-a-pack condition (Dango-jyotai in Japanese) where all players
are concentrated around the ball often occurs in both offensive and defensive situations, individual skills around theball were found. Additionally, only a skilled player advances the ball, and few successive offensive plays with two or
more players were found.
4.2 Structure of skills/factors
The two-dimensional space obtained comprise the two axes of “Individual skills and skills leading to fouls/violations”
and “Individual – group skills,” and the four clusters of “Ball-advancing individual skills;” “Under-basket individual
skills;” “Cooperative skills;” and “Against-rule and unskilled plays.” “Ball-advancing individual skills” are ballhandling skills in which both dribbling and passing skills control the ball and have in common the fact that pivoting
and other skills are required. At an unskilled stage, a rebound is often gained by a shooter using their own sense oftiming. The case where a player other than the shooter gains a rebound is limited to when the ball lands at the spot
where the player is standing. For that reason, it is thought that shooting and rebounding are associated with each other.
The fact that “Cooperative skills” was composed of only one skill can be explained by the reason that the ball isadvanced by a skilled player or around two players to an area under the basket, and elaborate cooperative plays withmany players are rarely seen. Finally, the reason that the relationship between the factors of violations/fouls and fast
breaks are found in “Against-rule and unskilled plays” can be explained by the following reasons: In the early stageof a fast break, the offensive players easily commit violations such as traveling and line-crossing when they start todash toward the basket and defensive players easily commit fouls such as slapping the opponent’s hand and bodycontact in order to prevent the movements of a quick offensive player.

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The relationship among skills/factors and their structure and wins/losses in games in basketball classes
Ken Nagamine, Osamu Aoyagi, Akihito Yaita, Ikuo Komure, Tsuyoshi Kawazura, Shinya Tagata, Tomohiro Annoura and Yasufumi Ohyama

4.3 Influence of plays/factors when considering the relationship of mutual independent variables
The maximum likelihood test chose the model that included “Shooting,” “Cooperative plays,” “Fouls,” and gender.
Statistical tests using a correlation ratio that did not take into consideration the mutual relationship among independent
variables found that “Dribbling“ was significant, as opposed to “Fouls” which was significant in multivariate analysis,in addition to “Shooting” and “Cooperative plays” that were common in both analyses. It is thought that although“Dribbling” apparently seems to be important on its own, “Cooperative plays” that are close to “Dribbling” in a twodimensional space required similar skills and compensated for it. Instead, violations such as traveling and crossing
the line or fouls such as careless body contact that are caused by their lack of skills are thought to be the decisive
factors for wins/losses in games.
4.4 Difference of plays/factors influencing wins/losses involving skilled players
Although it is natural that shooting be considered a decisive factor for wins/losses involving both skilled and unskilledplayers, many studies have commonly reported that (defensive) rebounding and assist passing are influential factors
in game outcomes involving skilled players, no significant relationship was found in this study. It is thought that
rebounding is achieved by the shooter in almost all instances involving beginners, and it is too hard to get a reboundshot by another player while synchronizing it for beginners.
5. Conclusion: Proposal for training of unskilled players
First of all, the concentration of both offensive and defensive players around the ball (Dango-jyotai in Japanese) canbe cited as a characteristic of plays performed in basketball games involving unskilled players, such as in basketball
PE classes. It can be said that this prevents the development of many kinds of basketball skills. Therefore, this issomething that is important for both offensive and defensive players to notice. For instance, to prevent theconcentration of players around the ball, what should be considered is adopting strategies such as zone defense of thezone or man-to-man defense to defend a specific player. By doing so, it is also envisioned that unnecessary bodycontact against the opponent could be reduced. To progress to a more advanced level, training that allows students tolearn advanced skills using the space on the court produced using these strategies is advised.
Author Contributions
Conceptualization, K.N.,O.A; methodology, K.N., O.A.,A.Y.,I.K.,T.K.,S.T.,T.A.,Y.O; validation, K.N.,A.O.; formal
analysis, K.N.,A.O; investigation, K.N, A.O, A.Y; writing—original draft preparation, K.N.; writing—review andediting, A.O.; visualization, A.O.; supervision, K.N., A.O.; project administration, A.O.; funding acquisition, A.O.,
A.Y.;All authorshave read and agreed to the published version of the manuscript.
Funding
This work was supported in part by funding from Fukuoka University (Grant No. 196008)
Scientific Research (Grant No. 20K11381).

Grant-in-Aid for

Data Availability Statement
The data in the study are not publicly available in order to protect privacy of the participants.
Informed Consent Statement
Informed consent was obtained from all participants involved in the study.
Conflicts of Interest
The authors declare no conflict of interest.
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