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A New Cricket Statistics American Journal of Sports Science 2014; 2(3): 53-55 Published online April 30, 2014 (http://www.sciencepublishinggroup.com/j/ajss) doi: 10.11648/j.ajss.20140203.11 Form - A new cricket statistics Parag Shah 1, Mitesh Shah 2 1Dept. of Statistics, H. L. College of Commerce, Gujarat, India 2Dept. of Statistics, S.V. College, Gujarat, India Email address: [email protected] (P. Shah), [email protected] (M. Shah) To cite this article: Parag Shah, Mitesh Shah. Form - A New Cricket Statistics. American Journal of Sports Science. Vol. 2, No. 3, 2014, pp. 53-55. doi: 10.11648/j.ajss.20140203.11 Abstract: Traditionally, evaluation of individual player performances in one-day cricket and T -20 has been based on measures such as batting and bowling averages, and strike and economy rates. Whenever a player's performance statistics are quoted, there is nearly always some verbal qualification that is necessary in order to place the statistics into context. We have found a new statistical measure –FORM, which measures the form of a player. We have used what is known as an exponentially decaying average (EDMA) . In this statistic, every score is considered in the calculation, but as you go back in time, each score is discounted by a certain percentage. This means recent score is given highest importance and past scores are given less weightage. Simple logic of short term EDMA and long term EDMA is used for calculating FORM. FORM of individual players is vital as the success of the team depends on the number of players who are in form. It can be used to estimate the total team score. Keywords: Moving Average, Weighted Moving Average, Exponentially Decaying Averages measures have severe limitations in assessing the true 1. Introduction performances and abilities of players. Traditionally, evaluation of individual player Lewis A.C. (2006) has tried to develop a fairer measure performances in one-day cricket and T -20 has been based of player’s performance in one-day cricket. This measure on measures such as batting and bowling averages, and still does not evaluate the consistency of the batsman. strike and economy rates. Use of Statistics in sports is not Lemmer H. H. (2004) in his paper has shown the new and cricket is a sport in which statistics features importance of batsman’s consistency. He has discussed the heavily. Cricket has recently experienced a highly- consistency coefficient and also illustrated its importance successful intervention from the field of Operational by showing that a batsman with a high consistency Research in the form of the ‘Duckworth-Lewis’ method of coefficient has a better chance to get a good score than one adjusting target scores in one day matches (Duckworth & with a low consistency coefficient. He has also shown how Lewis, 1998) which was subsequently adopted by the the consistency curve can be used to assess the present International Cricket Council (Duckworth & Lewis,2004). form of a batsman. He by making use of a data set Player performance remains of significant interest to consisting of the statistics of a large group of one-day cricket team selectors and coaches who are trying to build international players, these three measures will be winning teams from a fixed pool of players or within a combined into a single measure that can be used to assess limited budget, and this imperative to win will probably the performance of a batsman and to compare different lead to developments in the use of cricket statistics – at batsmen with each other. A classification scheme with ten least among cricket professionals. Measuring cricketers classes according to which batsmen can be classified will only through their averages is liable to give skewed and be given. The best batsmen are those who fall into class one. unreliable results. The same procedure will be used to find a formula for Barr G.D.I. and Kantor B.S. (2004) has discussed a batting performance and a classification table for Test criterion for comparing and selecting batsman in limited players. Whenever a player's performance statistics are over cricket and Kimber A.C. and Hansford A.R. (1993) quoted, there is nearly always some verbal qualification has given a Statistical Analysis of Batting in Cricket. But it that is necessary in order to place the statistics into context. is recognized, within the game of cricket, that such David Harper (2009) has explained the use of exponentially 54 Parag Shah and Mitesh Shah: Form - A New Cricket Statistics weighted moving average in the finance domain particularly weightage and weights decreases for the past innings. This on stock market data. Chris P. Tsokos (2010) has discussed K- can be done with the use of exponentially decaying average . th Moving, Weighted and Exponential Moving Average for In this statistic, every score is considered in the calculation, Time Series Forecasting Models. but as you go back in time, each value is discounted by a certain percentage. 2. Methodology Exponentially decaying Moving Averages (EDMA) are widely used in financial mathematics to track the recent In current scenario, runs scored in the innings in which average behavior of stocks. EDMA’s are generally used in batsman remains not out are considered in the total runs systems where the first seen value is of little importance scored by the batsman but while calculating the average compared to the last seen value. So we calculate the that innings is not considered in total number of innings. average by assigning different weights to the moving This actually overestimates the batsman’s performance. average scale. But the underlying awesomeness of EDMA And if not out runs are considered as out runs, it is that it decays exponentially. underestimates the batsman’s performance. Simple avg. = Sum of samples / Number of samples. To overcome this drawback of existing average, we have EDMA = (current EDMA.) * k / sample * (1.00 – k) considered a new logic for the average. There are several implementations of EDMA of which this If not out runs > = average then consider not out runs in is one. Here k = decay factor or constant smoothing factor. his total runs and Many times you might have heard commentators saying If not out runs < average then consider average in his this batsman is in form or is not in form. But form of a total runs. batsman was never quantified. For the first time we are This logic will solve the problem of overestimation or developing a statistics which will quantify FORM of a under estimation. batsman. These statistics can be used as other statistics like To illustrate this logic of new batting average let us batting average, strike rate etc i.e. at a particular point of time. consider runs scored by a batsman new to international FORM of individual players is vital as the success of the cricket in ten innings : 25, 15, 55*, 25, 32*, 6, 65, 89, 12, team depends on the number of players who are in form. 21. * represent that the batsman is not out in that innings. FORM can also be used in predicting the performance of the team. In this paper we have considered batsmen FORM Table 1. Calculation of new batting average. only but similar work can be done for bowlers and wicket- Runs to be added Cumulative New batting keepers. For calculating the FORM of a batsman we have Innings Runs in total runs Runs Average considered five (short term) and eleven matches (Long term) 1 25 25 25 25.00 exponentially decaying moving averages of runs scored. 2 15 15 40 20.00 The not-out scores are replaced by the average till that 3 55 55 95 31.67 match or the not-out runs whichever is higher. The FORM of a batsman is given as: 4 40 40 135 33.75 FORM= (Short term EDMA) / (Long term EDMA)*100 5 32* 34 169 33.80 We have considered FORM in terms of percentage. So, 6 6 6 175 29.17 100 will be considered as a Base of comparison. 7 65* 65 240 34.29 8 89 89 329 41.13 3. Results & Discussion 9 12* 41 370 41.11 To illustrate how FORM can be calculated we have taken 10 21 21 391 39.10 the data of runs scored by Sachin in last 50 innings from www .cricinfo.com website. Here we will assume 4 % decay Here in Table 1 you can see that in fifth innings he has rate and 5 matches and 11 matches exponentially decaying scored 32 runs and was not out. Upto four innings his moving average as short term and long term exponentially batting average was 33.75. As his runs (32) < his batting decaying moving averages respectively. average (33.75), runs that will be added in his total runs will be 34 after rounding off to nearest integer. While in Table 2. Calculation of FORM for Sachin. seventh innings he scored 65 runs and was not out and upto 6 innings his batting average was 29.17. As his runs (65) > Runs 5 EDMA 11 EDMA FORM 99 his batting average (29.17), runs that will be added in his 8 total runs will be 65. 55 The batsman is evaluated on the basis of their batting 71 94 average only or at most their strike rates. But in this batting 30 average simple average is used which gives equal 0 weightage to runs scored in all innings. But for calculating 16 Form of a batsman, latest score should be given more 43 American Journal of Sports Science 2014; 2(3): 53-55 55 Runs 5 EDMA 11 EDMA FORM 4.
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