International Journal of Research in Science and Technology Volume 1, Issue 1: October - December, 2014

Transcription

1 AN APPLICATION OF MULTILAYER PERCEPTRON NEURAL NETWORK TO PREDICT THE PERFORMANCE OF BATSMEN IN INDIAN PREMIER LEAGUE Hemanta Saikia 1 and Dibyojyoti Bhattacharjee 2 Assistant 1 Professor, The Assam Kaziranga University, Jorhat, Assam Associate 2 Professor, Jawaharlal Nehru School of Management, Assam University, Silchar ABSTRACT The game of cricketgot a new dimension in April 2008, when BCCI initiated the Indian Premier League (IPL). It is a franchisee based Twenty20 cricket tournament where teams are formed by competitive bidding from a pool of Indian and international players. Since valuation of the players are determined through a competitive bidding, performanceof every individual matters. The objective of this study is to predict the performance ofbatsmen who entered the IPL in its fourth season only, based on analyzing the performance of batsmen in the first three seasons of IPL through multi-layer perceptron (MLP) neural network. The actual performances of these batsmen in IPL-IV are calculated, and the external validity of the neural network model is tested. The model was found to be percent accurate.this prediction can help the franchises to decide which batsmen they should target to buy for their team and who should not be considered at all. Keywords: Data Mining, Neural Network, Performance Measurement, Sports, Twenty20 cricket 1. INTRODUCTION Cricket is the only sport that is immensely popular in India. The recent form of Twenty20 cricket got a new dimension in April 2008, when Board of Control for Cricket in India (BCCI) initiated the IPL.It is a Twenty20 cricket tournament being played among eight domestic teams, named after eight Indian well-known cities and owned by different franchises (Mitra, 2010). The franchises form their teams by competitive bidding from a pool of Indian and international players and the best of Indian upcoming talent (Saikia and Bhattacharjee, 2011). Each player has a base price fixed by the IPL authorities. However, there is no upper limit for their bid price. The valuation of players obtained through auction and availability of players performances have allowed researchers to infer on different aspects of this format of the game. Performance measurement is one of the most imperative aspects in any format of the game of cricket as each match generates a huge amount of performance related statistics. Moreover, relative to the other team games, the contribution of individual players to the overall team performance is indispensable in cricket (Damodaran, 2006). Thus, in recent times the application of data mining techniques in the field of sports has evolved, which explores and analyzes the data in order to predict the tournament result, performance modeling, classification, etc.the different data mining techniques that are commonly used in different sports are decision tree, neural network, clustering, genetic algorithms, etc. Among the different data mining tools, neural network is one of such technique that is commonly used in practice. Some of the applications of neural network in different sports are modeling swimming performance by Silvaet al. (2007), Young and Weckman (2008) used neural network to predict the performance of football players by translating players rating values to National Football League (NFL) combined values. In cricket, Bailey and Clarke (2006) used neural network to predict the match outcome in one day international matches while the game is in progress. Also, Choudhuryet al. (2007) have used neural network for predicting the outcome of cricket tournaments. A team has a good chance of winning consistently in any format of cricket provided the performances of individual players are reliable. Though both batting and bowling departments of a team need to perform significantly in determining the outcome of a cricket match, yet the present study is emphasizing on predicting the performance of batsmen in IPL. In traditional measures of batting performances, the individual performance of the players has been measured based on batting average and batting strike rate. Usually batting average is more useful to measure batting performance of the players in test cricket whereas batting strike rate is useful in limited over cricket like One-day and Twenty20. However, it is widely recognized that such statistics only tell a part of the story of a batsman s performance (Lewis, 2005). Moreover, the different traditional performance measures are in different units of measurement so as to assess a players batting performance, it is very difficult to combine them. It would be better if we can use all the statistics to measure the batting performance of a cricketer. For example, the batting average does not reflect the performance well enough to measure the batting ability of a batsman, because it does not take into account any other skills of the batsman. Thus, the paper has used a performance measure called BK developed by Barr and Kantor (2004) to measure the batting 6

2 performance of the players. It was developed by combining three different performance statistics of a batsman viz., batting average, batting strike rate and probability of getting out. Based on the performances of batsmen who had participated in the first three seasons of IPL, this paper tries to predict the performances of batsmen who had participated only in the fourth season of IPL using neural network. The actual performances of these batsmen in IPL-IV are also calculated and the external validity of the neural network model is tested. 2. MULTILAYERPERCEPTRONNEURAL NETWORK Neural network is one of the most preferred tools in data mining applications because of its power, flexibility and ease of use. Let us consider the following relation which describes the functional form of the basic neuron model. where, y = f(x)... (1) f(x) = w 1 x 1 + w 2 x w n x n + b More conveniently, it can be written as y = x i w i + b (2) In the above model, containing a set of n inputs x i, each input signal is multiplied with an associated weight, w i before it is applied to the processing and b is a bias term. Though the above functional form looks linear, it may or may not be true. However, if a linear relationship between dependent and independent variables is appropriate, the result of the neural network should closely approximate a linear regression model. If the nonlinear relationship is more appropriate between the dependent and independent variables, a neural network will automatically approximate the correct model structure (Norusis, 2007). The form of relationship between dependent and independent variables in a neural network is determined during the learning process. Therefore, it would always be better, if we consider that we have some inputs x 1, x 2,,x n and the desired output is represented by response variable y, instead of thinking about the functional form of model structure. A multilayer perceptron (MLP) neural network is an information processing system which consists of many nodes. Let us consider the following diagrammatic representation of MLP neural network. In this information processing system, the x 1, x 2, x 3 elements are called neurons which process the information. The signals between neurons are transmitted by means of connection links (i.e. arrows). The links possess an associated weights w 1, w 2, w 3, which are multiplied along with the incoming signals from inputs of the MLP neural network. The output signal is obtained by applying activations to the net input. In neural network, the dependent variable may be continuous or categorical. Here we have used a categorical dependent variable for predict the performance of the batsmen. This categorical variable has been generated through the Barr and Kantor (2004) batting performance measure (i.e. BK). The different categories are defined by dividing the performance measure BK into some non-overlapping classes by fitting a statistical distribution and using the same probability weight. Now if the predicted value of batting performance measure BK for a particular player falls in any of such class then the performance level of a player can be identified. These intervals are indeed helpful in predicting the performance of the batsmen instead of predicting single values, as intervals are generally robust compared to single values. The details procedure of how the categorical 7

3 dependent variable has been generated from Barr and Kantor (2004) batting performance measure is described comprehensibly in subsequent sections. 3. DATA AND METHODOLOGY Since the level of performance of individuals couldn t be judged fairly from only one or two matches (Bracewell and Ruggiero, 2009),to quantify the performance of players it is necessary that players statistics for a large number of games should be considered. Therefore, the effects of outstanding or poor, single performances are smoothed over the larger number of games (Lewis, 2005). Considering these facts, the players who had satisfied all the following conditions were kept in the training sample. The batsman has played atleast 7 matches in IPL. The batsman has faced atleast 100 balls in IPL. The batsman had atleast 5 completed innings in IPL. There were only 75 players who had satisfied all the above criteria. All these players were considered for the study and information about their performances in IPL,ODIs and Twenty20 internationals have been collected from the website 3.1Selection of Input Variables Like the procedure of regression, one has to choose dependent and independent variables forthe neural network model as well. Several independent/input variables that are supposed to influence the performance of batsmen are considered. These variables are: Age, ODI matches played, Batting average in ODI, Strike rate in ODI, Twenty20 matches played, Batting average in Twenty20, Strike rate in Twenty20, Experience in international cricket, Batting hand and Bidding price in IPL.Here one variable isnominal(e.g. batting hand) while others are continuous (e.g. age, strike rate in Twenty20, etc.) in nature. 3.2Barr and Kantor Batting Performance Measure (BK) According to the proposed measure of Barr and Kantor (2004) a batsman s strike rate along with his batting average should be considered when establishing a batting performance measure. They argued that the batting strike rate is directly proportional to the probability of dismissal of a batsman. Barr and Kantor (2004) defined the probability of a batsman being dismissed as It was observed that Batting strike P( out ) Total number of times dismissed P( out ) (3) Total number of balls faced Total number of runs scored rate Total number of balls faced Total number of times dismissed Total number of balls faced Total number of runs scored Batting average Total number of times dismissed Now in two dimensional space, if strike rate represents the vertical axis and probability of getting out (i.e.p(out)) represents the horizontal axis then any one may plot the characteristics of a batsman in two dimensional space. Let us consider that y represents the strike rate of the batsmen and x be represents the probability of a batsman being dismissed on any given ball then it is very important to note that because of uniqueness Batting average Strike rate P ( out ) y x Therefore, this two dimensional graphical representation simultaneously seizures three very important characteristics of a batsman s performance viz., strike rate, probability of getting out and batting average (Barr and Kantor, 2004). The measure is a weighted product of batting average and strike rate. Let it denoted as BK and was given as 8

4 BK ( Strike rate) ( Batting average) y y x 1 y x 1 1 where 0 α 1 is a parameter of the balance between the strike rate and batting average of batting performance measure BK. Varying α from 0 to 1 reflects the importance of strike rate with the importance of batting average. Therefore, putting α = 0 set no emphasis on batting strike rate and putting α =1 set no emphasis on batting average. Hence, it is better to put α = ½ for weighting both batting average and strike rate equally. 3.3 Classification based on BK The BK values are obtained for all the batsmen who were selected in the training sample. A meaningful classification based on players batting performance would be in terms of suitable intervals from an assumed distribution of BKvalues. Thus, the probability distribution of BK should be examined to facilitate the classification of the batsmen on the basis of their performance. For testing the hypothetical distribution of the BK, the Kolmogorov-Smirnov (K-S) test is used. The Kolmogorov-Smirnov test statistics is given by, D α,n = max S n (x) F(x) (4) Where S n (x) and F(x) are the empirical and theoretical distribution functions of BK respectively. However, for performing the Kolmogorov-Smirnov test, the theoretical distribution needs to be completely specified (i.e. the values of the parameters should be known).the parameters are estimated from the data. The critical value of D n for α level of significance depends on the number of observations and it is denoted by D α,n. The interval [F(x) D α,n, F(x) + D α,n ] provides the 100(1-α)% confidence band for F(x) that can be used to visualize the goodness of fit of F(x). Now after finding the distribution of BK, one can find two real numbers x 1 and x 2 to divide the range [0, ] into three linear intervals namely (0, x 1 ), (x 1, x 2 ) and (x 2, ) with the same probability weight of percent. These intervals are used to categorize the various stages of BKare as: i) Poor if 0 < BK <x 1 ii) Average if x 1 < BK <x 2 iii) Good if x 2 < BK < As of the above classification, the study generated the categorical dependent variable based on Barr and Kantor (2004) batting performance measure to train the MLP neural network. This dependent variable is also used to predict the appropriate class of the batsmen in the fourth season of IPL. The cut of points acquired from BK can be seen in Table DATA ANALYSIS AND RESULTS Since the values of BKare positive (i.e.bk i 0)therefore one probable distribution may be the two parameter gamma distribution which range is also from 0 to. The probability density function of gammadistribution is given as, 1 x 1 x f ( x) e, α>0, λ>0; 0<x< (5) where e x x 1 dx (6) 0 Based on the BK values the estimated value of λ (scale parameter) and α (shape parameter) are obtained using maximum likelihood estimation (MLE) procedure (Johnson and Kotz, 1970) and is given by, 2 ˆ M andˆ M 2 (7) 9

5 2 where M and be the mean and variance of the generated BK values. Now, the estimated values of the parameters are ˆ and ˆ The corresponding value of the Kolmogorov-Smirnov test statistic for goodness of fit test is D α,n = max S n (x) F(x) = (8) The table value of Kolmogorov-Smirnov test statistics with 73 degrees of freedom at5% level of significance is0.1592, providing sufficient evidence that the BK values can be considered to follow the two-parameter gamma distribution. One can also visualize the empirical distribution function (EDF) to the theoretical CDF curve in the following graphical depiction along with the confidence bounds. As the EDF lies within the upper and lower confidence boundsthat also corroborates the fitting of empirical data to the two-parameter gamma distribution. Figure 1: Goodness of fit ofbk to gamma distribution Empirical Distribution Function Plot Probability Bar and Kantor (2004) batting performance measure Table 1: Interval for classification of BK Classification BK Poor Below Average Good & above An important characteristic in building an effective neural network model is the understanding of the issue of training or learning. The process of neural network training refers to finding out the best set of weights for the networks. These weights are also known as parameters of the network model. For instance, in a statistical model, these parameters need to be estimated before the network can be adopted for further use. The weights of the different input variables from input layer to hidden layer and hidden layer to output layer along with overall information of neural network model can be seen in the Appendix. The difficulty arises in an MLP neural network is that the estimated weights are not easily interpretable. It is because a large input to hidden layer weight doesn t necessarily mean that the input has a huge effect on the output and vice-versa. Instead, it may bring around abrupt changes in the output layer. Thus, incorporating both the layers of weights various measures are proposed to measure the importance of input variables. Garson 10

6 (1991) proposed a measure, which is a sum of products of normalized weights. But this measure doesn t take into account the signs of the weights. Milne (1995) modified Garson s formula by taking the absolute values of certain terms. Yet the absolute values are not applied correctly to avoid the cancellation of weights of opposite signs. However, based on the training sample a sensitivity analysis is performed which computes the importance of each predictor in determining performances of the batsmen. The importance of the independent variables for the study can be seen in Figure 2. Figure 2: Bar diagram for importance of independent variables Note:The term T20 refers Twenty20 international matches In the above graphical representation, it can be revealed that the variable strike rate in Twenty20 international cricket (SR_T20) matches has the utmost effect on predicting the performance of the batsmen followed by strike rate in one day international cricket (SR_ODI) matches. Also, it has been seen that the age (Age) of the batsmen has least importance on batting performance. 5. EXTERNAL VALIDATION OF NEURAL NETWORK MODEL To test the external validity of neural network model, a different sample of batsmen is considered. The players considered for the validity exercise are those who had not participated in the first three seasons of IPL but had played in the fourth season only. Six of these players had played at least 5 matches and faced at least 50 balls. To get sufficient information about their batting performance in IPL-IV, eighty two (82) batsmen have been found to satisfy the above mentioned criteria. The information of three important variables viz., batting average, strike rate and probability of getting out, calculating BK for the batsmen was collected from on April 5, The different classes of batsmen s batting performance are identified by same procedure as discussed in section 3.3. The Kolmogorov-Smirnov test statistics value has also confirmed that the BK values for IPL-IV follow gamma distribution. It can also be visualized through the empirical distribution function (EDF) to the theoretical CDF curve in figure 3 along with the confidence bounds. The cut off points obtained from BK to measure the actual batting performance of the batsmen in IPL-IV are given in Table 2. Table 2: Interval for classification of BK in IPL-IV Classification BK Poor Below Average Good & above 11

7 Figure 3: Goodness of fit of BK to gamma distribution in IPL-IV Empirical Distribution Function Plot Probability Bar and Kantor (2004) batting performance measure Finally, the predicted performances of selected batsmen are recorded and their actual batting performances are determined for IPL-IV, to check the validity of the MLP neural network model. The details of which are provided in Table 3. Table 3: Predicted and actual batting performance of six batsmen in IPL-IV Sl. No. Players name Predicted class of the performance in IPL-IV Actual class of the performance in IPL_IV Bid price in IPL-IV 1 J Franklin * Good Good $ J Ryder Poor Average $ RT Doeschate * Good Good $ SA Hasan Good Poor $ W Parnell * Poor Poor $ R Harris * Poor Poor $ *The predicted and actual performances of these players are similar by applying MLP neural network model. In Table 3, it has been seen that the MLP neural network model can predict four of the six cases correctly. Thus, a franchisee depending on the team s requirement can decide which batsman to bid for their team. The fresh auction of IPL-IV was held on 8 th and 9 th January, 2011 with two new teams joining the league. In IPL-IV auctions, we had seen an enormous raise in the players price compared to the auctions of IPL-I. The average bid price of the IPL-IV auction is $495,605 while in the previous auction (before IPL-I) was $448,217. As evident from the above table, it can be concluded that all the franchisee would prefer not to bid for R Harris and W Parnell as both of them fell under poor batting performance category. 6. CONCLUSION The salaries of players in IPL that are decided through auction are a way of quantifying players performance in monetary terms. Thus, it is a matter of decision making on the part of the franchise about which player to be bided for and up to what cost. Therefore, neural network model used in this paper can help a franchisee to take a decision. At the beginning of the fourth season of IPL, new agreements are made through fresh bidding. If the league continues, fresh bidding shall take place after every three years. In such a context, this study may be used to predict the probable category of batsmen on the basis of their previous performances. This prediction 12

8 can help the franchisee to decide which batsman they should target to select for their team and who should not be considered at all. The MLP artificial neural network model when applied for external validity was found to be percent accurate. This has resulted after a training sample used to develop the model was loaded with only 75batsmen. As the age of the league increases, a larger number of batsmen can be considered in the training sample and a much better prediction are expected from the model. However, the form of a batsman when he actually plays in the tournament is a deterministic factor for the actual classification. But the model, once rich in data, is supposed to work well provided the performance of the batsmen is not much variant. REFERENCES Bailey, M. and Clarke, S. R. (2006). Predicting the match outcome in one day international cricket matches, while the game is in progress, Journal of Sports Science and Medicine, 5(4), Barr, G. D. I. and Kantor, B. S. (2004). A criterion for comparing and selecting batsmen in limited overs cricket. Journal of the operational Reasearch Society, Bracewell, P. J. and Ruggiero, K. (2009). A Parametric Control Chart for Monitoring Individual Batting Performances in Cricket, Journal of Quantitative Analysis in Sports, 5(3), Choudhury, D. R., Bhargava, P., Reena, and Kain, S. (2007). Use of artificial neural networks for predicting the outcome of cricket tournaments, International Journal of Sports Science and Engineering, 1(2), Damodaran, U. (2006). Stochastic dominance and analysis of ODI batting performance: The Indian cricket team, Journal of Sports Science and Medicine, 5, Garson, G. D. (1991). Interpreting neural network connection weights, AI Expert, April, Johnson, N. L. and Kotz, S. (1970). Continuous Univariate Distributions, Singapore: John Wiley & Sons Inc. Lewis, A.J. (2005). Towards fairer measures of player performance in one-day cricket. Journal of theoperational Research Society, 56, Mitra, S. (2010). The IPL: India s foray into world sports business, Sport in Society, 13(9), Milne, L.K. (1995). Feature selection with neural networks with contribution measures, Proceedings of the Australian Conference on Artificial Intelligence AI'95, Canberra, available at postscript/525 ps.gz Norusis, M. (2007). The SPSS statistical procedure companion, Prentice Hall: India. Saikia, H. and Bhattacharjee, D. (2011). On Classification of All-rounders of the Indian Premier League (IPL): A Bayesian Approach. Vikalpa, 36(4), Silva, A. J., Costa, A. M., Oliveira, P. M., Reis, V. M., Saavedra, J., Perl, J., Rouboa, A. and Marinho, D. A. (2007). The use of neural network technology to model swimming performance, Journal of Sports Science and Medicine, 6(1), Young, W. A. and Weckman, G. R. (2008). Evaluating the effects of aging for professional football players in combine events using performance-aging curves, International Journal of Sports Science and Engineering, 2(3),

9 APPENDIX Diagrammatic Representation of MLP Neural Network Model Estimation of weights from MLP neural network Predictor Predicted Hidden Layer 1 Output Layer H(1:1) H(1:2) H(1:3) [BK_Class=1] [BK_Class=2] [BK_Class=3] Input Layer (Bias) [Bat_hand=1] [Bat_hand=2] match_odi Bat_avg_ODI SR_ODI match_t20i Bat_avg_T20I SR_T20I

10 Int_crick_exp Age Bid_IPL Hidden Layer 1 (Bias) H(1:1) H(1:2) H(1:3) Overall information about the MLP network model Training Cross Entropy Error Percent Incorrect Predictions 28.8% Stopping Rule Used Max. no. of epochs (100) exceeded Training Time 00:00: Classification information during training Sample Observed Predicted Poor Average Good Percent Correct Training Poor % Average % Good % Overall Percent 43.8% 30.1% 26.0% 71.2% 15