A Novel Basketball Result Prediction Model Using a Concurrent Neuro-Fuzzy System

Figures & data

Table 1. Studies in the literature on basketball result prediction.

Dataset	Method	Accuracy	Software	Researcher
NBA League, 2007–2008 season	Feed Forward Neural Network (FFNN)	74.33%	MATLAB	(Loeffelholz, Bednar, and Bauer Kenneth 2009)
Two consecutive seasons of the National Basketball Association (NBA) League Basketball	Logistic regression model	72.8%	WEKA	(Zdravevski and Kulakov 2010)
Asociacion de Clubes de Baloncesto (ACB) Basketball League statistics from 2008 to 2009 season	Linear Least Mean Squares (LMS) estimate	66.7%	KEEL	(Trawinsk 2010)
NBA League ,2009–2010 season	Naive Bayes method	67.0%	RapidMiner	(Miljković et al. 2010)
Basketball League of Serbia B, 2005–2006 season until 2009–2010 season	Neural Network	80.9% (*all dataset)	-	(Ivanković et al. 2010)
NBA League, 2005–2006 season until 2010–2011 season	Simple Logistics Classifier	69.67%	Rapidminer, WEKA	(Cao 2012)
NBA League, 2009–2010 season	Adversarial synergy graph model	69.9%	-	(Liemhetcharat and Luo 2015)
NBA League, 2015–2016 season	Support Vector Machine(SVM), Fuzzy-SVM model	88.26%	-	(Kaur and Jain 2017)
NBA League, 2008–2010	Support Vector Machine (SVM) and Decision Tree	85.25%	WEKA	(Pai, ChangLiao, and Lin 2017)
Basketball tournament of the 2004–2016 Olympic Games	Logistic Regression Model	93.2%	The R Project for Statistical Computing	(Leicht, Gómez, and Woods 2017)

Figure 1. The stages of data mining in records of basketball games.

Figure 2. An ANN architecture.

Figure 3. A basic artificial neuron.

Table 2. Prediction parameters used in predicting basketball results.

Parameter type	Criterion	Prediction parameters	Ranges	Symbols
Input	Teams	Code of the home team	1–16	I1
		Code of the away team	1–16	I2
	Team performances in recent weeks	The average points of the home team in the last four games.	1–2	I3
		The average points of the away team in the last four games	1–2	I4
	Positions in the league	The average points of the home team in the league.	1–2	I5
		The average points of the away team in the league.	1–2	I6
	Quality of the competitors	The average points of the competitors of home team in the last four games.	1–2	I7
		The average points of the competitors of away team in the last four games.	1–2	I8
	Week	Week of the league	1–30	I9
Output	Result	Game result	0,1	O1

Table 3. ANN Parameters.

Hidden layer number	1
Activation function, hidden layer	Tansig
Activation function, output layer	Softmax
Learning rate	0.01
Minimum performance gradient	1e-5
Performance goal	1e-3
Maximum number of epochs to train	5000

Figure 4. The structure of the Fuzzy Inference system.

Table 4. Example of fuzzy rules.

Number of rule		Ranking		Won		Average		Favorite
1	If	VP	and	VN	and	VN	then	P
2	If	VP	and	VN	and	N	then	P
3	If	VP	and	VN	and	Z	then	P
4	If	VP	and	VN	and	P	then	VP
….
48	If	Z	and	N	and	Z	then	N
49	If	Z	and	N	and	P	then	N
50	If	Z	and	N	and	VP	then	ZN
51	If	Z	and	P	and	VN	then	ZN
….
97	If	VN	and	VP	and	N	then	VN
98	If	VN	and	VP	and	Z	then	N
99	If	VN	and	VP	and	P	then	N
100	If	VN	and	VP	and	VP	then	N

Figure 5. Membership functions of input and output parameters: (a) ranking, (b) won, (c) average and (d) favorite team.

Figure 6. Schematic structure of developed Concurrent Neuro Fuzzy System.

Table 5. Confusion matrix for binary classification.

Data Class	Classified as pos	Classified as neg
pos	True positive (tp)	False negative(fn)
neg	False positive (fp)	True negative (tn)

Table 6. Measures for classification using the notation of Table 5.

Measure	Formula	Evaluation focus
Accuracy	$\frac{\mathrm{t}\mathrm{p}+\mathrm{t}\mathrm{n}}{\mathrm{t}\mathrm{p}+\mathrm{f}\mathrm{p}+\mathrm{f}\mathrm{n}+\mathrm{t}\mathrm{n}}$	General effectiveness of the classifier
Sensitivity	$\frac{\mathrm{t}\mathrm{p}}{\mathrm{t}\mathrm{p}+\mathrm{f}\mathrm{n}}$	Effectiveness of the classifier in deciding the positive tag
Specificity	$\frac{\mathrm{t}\mathrm{n}}{\mathrm{f}\mathrm{p}+\mathrm{t}\mathrm{n}}$	Effectiveness of the classifier in deciding the negative tag

Table 7. Confusion Matrix obtained for the ANN model.

		Actual results		Classification overall
		Away win	Home win
Predicting results	Away win	6	2	8
	Home win	5	11	13
Actual overall		11	13	Accuracy: 70.8%

Table 8. Confusion Matrix obtained for the CFNS model.

		Actual Results		Classification overall
		Away win	Home win
Predicting Results	Away Win	8	2	10
	Home Win	3	11	14
Actual overall		11	13	Accuracy:79.2%

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