# Rating Batters in Test Cricket

Authors: Sohail Akhtar; Muhammad Awais; Ibrar Hussain; Gauhar Ali; Sadique Ahmad; Muhammad Imran Khan; Humera Qureshi; Mohammed ElAffendi
Journal: Mathematical Problems in Engineering
 (2022)

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## Abstract

In test cricket, we rated batters’ performance. We have proposed rating criteria as introduced by Scarf, Akhtar, and Rasool in 2014 with additional explanatory variables on the updated data set. The newly added covariates that we included in our research are the home factor and the ground influence. The same rating system is applied in the previous study. Using multinomial logistic regression, sessions from all days of a test match are modeled to determine match outcome probabilities at the end of each session. These models are based on all of the factors that can influence the outcome of a match. It is discovered that the predictors of home factor and pitch quality have a significant impact on the outcome of the test match. We used multinomial logistic regression to model data and estimate the parameters in the models. We forecasted match outcomes using these models at the end of each session and measured batters’ performances by using these probabilities. This process is repeated in a test match at the end of a session, and batters’ contributions to their team score are accumulated. Both teams’ batters are then ranked based on their rating points. The batsmen are rated based on their performance in the match by adding new factors (pitch effect and home advantage) in the models. The proposed ranking is compared with the ICC’s traditional ranking of batters in the test cricket series.


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## Body

## 1. Introduction

Test cricket is a game of patience [1, 2], and it is littered with renowned batsmen who have set extremely high standards [3]. A batsman has nearly limitless time to set and play each ball individually. It is a ball-and-bat duel that is not defined by the number of deliveries [4]. Despite this, batsmen have struggled to stay at the crease, as conditions and lapses in focus result in the loss of their wicket, particularly in the modern game. In general, traditional measures such as batting average are used to evaluate a batsman in test cricket [5, 6]. Players were awarded points based on the number of runs they score during the game. This time-honored method has several drawbacks [5]. The context of the contest in which the runs are scored is not revealed by the runs scored in the match or the average runs in the series. For instance, scoring 100 runs in a low-scoring contest is not the same as scoring 100 runs in a high-scoring match. Scoring 100 runs in the first innings is not the same as scoring 100 runs in the fourth innings. This is due to the match’s circumstances. Due to deterioration in the pitch, the pitch of the first inning is radically different from the pitch of the fourth inning. Traditional measures such as batting average, on the other hand, overlook such instances. In the same way, playing in Melbourne is not the same as playing in Qaddafi Stadium. The impact of performing in one’s own country or overseas, as well as other factors such as bowling first or second and losing or not losing the toss, are all said to have an impact on cricket results [7]. In any sport, there are various approaches for determining who the top player or team is [8, 9]. You can give them points based on which team performs best. There are both technical and nontechnical approaches for evaluating players or teams. Differentiating points are used to determine the winner in several sports [10]. It is possible to model point difference, but we will not. We are attempting to develop a new statistical measure that will allow us to assess batsman performance in the context of the contest in which runs are scored. We are concentrating on the outcomes of Test Cricket matches. We explored the extent to which a variety of characteristics, such as playing at home or away, batting or fielding first, and pitch condition, influence match outcomes. Initially, we will forecast Test match outcomes using a multinomial logistic regression model. These forecasts will subsequently be used to evaluate the batter’s performance.A large number of studies have attempted to focus on Test Cricket players in various ways around distinct theoretical frameworks [5, 11–17]. Recent research studies on cricket have highlighted the need of examining and comprehending prematch indicators such as toss, ground effects, home ground, and rating of both participating teams, among others [18–22]. Kimber and Hansford studied cricket batting strategy at various levels [23]. They showed how scoring rate, opposition bowling strength, and pitch condition can be accurately integrated with runs scored to create an overall picture of batsmen’s relative attributes. The Test match results were studied by Allsopp and Clarke [24]. They concluded that a team’s first-inning bowling and batting strength, first-inning batting order lead, and home advantage are all good indicators of a winning test match outcome. Barooah and Mangan looked into some of the problems in evaluating batsmen for test matches [25]. They discovered that batters in cricket are mostly valued according to their average score: in test matches, an average of 50 or more provides a rule-of-thumb for distinguishing inordinate players from the purely good. Singh et al. assessed cricket players’ batting performance and calculated the impact of their performance on the ICC ranking system [26]. Male test cricket batters and female test cricket batters were ranked by Rohde [12]. He proposed a straightforward approach for ranking batters based on their performance. Mukherjee used a diffusion-based PageRank algorithm on the networks to figure out how important it is to rate teams and captains [27]. In Test Cricket, Akhtar and Scarf predicted match results session by session [28]. They looked at how to match result probability (win, draw, and loss), and consequences differed from one session to the next. Daud and Muhammad collected a collection of Test matches [29]. They proposed a new ranking system for Test Cricket teams based on the number of runs scored and wickets taken. They suggested that a standard accuracy index be developed to determine the relevance of the discrepancy between the researcher’s proposed rating system and the ICC rating system. Akhtar et al. developed a new rating system for players [5]. They determined the criteria for the best player in test cricket. Shah and Patel applied principal component analysis and weighted average method to rate the captain of captains among all 29 captains included in the study. Brewer and Stevenson suggested a survival analysis to forecast batting abilities in Test Cricket matches [30]. They developed a model in two stages, the first for individual players to assess their initial and balanced batting talents, as well as the rate of change in both. They matched and identified the cricketers who open the batting, which has a positive impact on the batting order. Hussain et al. utilized the International Cricket Council’s ad-hoc point system to assess cricket teams, and it is exclusively based on the number of wins and losses in cricket matches [31]. They compared their findings to those of the ICC. Boys and Philipson used an addictive log-linear model to model run scores [13]. They looked at how an individual batsman’s innings-by-innings variation in runs becomes a source of doubt in their ranking position. Stevenson and Brewer developed a Bayesian parametric model to calculate and estimate how intercontinental cricketers’ batting ability alters across innings using a Gaussian process [32]. They identified which batsmen are struggling or improving their batting skills, which has a real-world influence on sportsman evaluation, aptitude recognition, and team selection strategy. Researchers have long hypothesized that the batter’s performance influences the outcome of test matches [11]. In cricket, the concept of a player’s rating appears to have always piqued the interest of sports analysts. The research on batsmen’s performance also shows the importance of home ground, which can have a substantial impact on the outcome of a match.


## 2. Forecasting Test Matches’ Results

All test cricket matches played between January 1, 2017, and December 31, 2019, will be considered. The cricket website ESPNcricinfo (https://www.stats.cricinfo.com/ci/content/records/307847.html/) is used to get session-by-session data. Rain-affected contests and those with poor lighting will be disqualified. A Test Cricket match lasts five days, with each day consisting of three sessions (lunch, tea, and end of the match). The study only included nine (out of ten) recent ICC (International Cricket Council) sanctioned Test Cricket playing countries. Afghanistan has been removed due to its current status as a Test-playing nation, and, as a result, its participation in a disproportionately small number of ICC-sanctioned matches. Outcomes are measured over three years since it is assumed that for the most part, the core playing group has stayed consistent throughout this time frame. At the end of each session, a series of multinomial nominal logistic regressions is fitted to forecast Test match outcome probabilities. Here, we will look at a model with a multinomial response (win, draw, and loss). Y depicts the match result by assigning values (1, 0, and −1), with each value equating to a victory, a tie, or a defeat. The reference category is draw (0). We employed the Akaike information criteria (AIC) (Sakamoto, Ishiguro, and Kitigawa [33]), which is formulated as AIC= 2∗(number of estimated parameters involved in the model) − 2∗(log-likelihood) and Nagelkarke’s R square to examine the model fit (Nagelkerke, [34]), which is given as R2=1−exp−2L1−L0/n/1−exp2L0/n. In each session of each day, we modeled match outcome session-by-session in Table 1 and forecasted the test match outcome probabilities. In this section, we used those probabilities to assess each batter’s contribution to both teams. To compare our suggested rating system to the existing batting average approach, three distinct Test match series (7 matches) were included. We display the rating points for covariates such as ground effect, no ground effect, home advantage, and no home advantage. We use comparisons to see how these prematch factors affect batters’ ratings.Table 1
Session by session modeling.
DaySessionSet of covariatesKAICR_square (%)Correct prediction (%)MatchesStart of the matchg + h6211.05816.2064.70119Day_1Lunchg + h + l + w_110211.99622.1068.90119Day_1Teag + h + l + w_110202.10632.1068.10119Day_1Endg + h + l + w_1 + w_212192.9739.2073.10119Day_2Lunchg + h + l + w_1 + w_212197.56436.1070.60119Day_2Teag + h + l + w_1 + w_212190.17441.1074.80119Day_2Endg + h + l + w_1 + w_212176.29647.3072.40117Day_3Lunchg + h + l + w_1 + w_212162.24857.0081.20117Day_3Teag + h + l + w_1 + w_212155.3656.7081.40113Day_3Endg + h + l + w_1 + w_212142.55657.3077.70103Day_4Lunchg + h + l + w_1 + w_212125.77461.7077.4094Day_4Teag + h + l + w_1 + w_212119.88460.8079.3087Day_4Endg + h + l + w_1 + w_21293.53266.3078.6070Day_5Lunchg + h + l + w_1 + w_21278.16664.6080.0045Day_5Teag + h + l + w_1 + w_21247.01285.1083.3030


## 3. Measuring Batters’ Contribution

To determine the batter’s contribution, you must first obtain the odds of the test match’s outcome. Nominal multinomial logistic regression is used to calculate the match outcome probability (Sohail and Scarf, 2012). These actual probabilities are written as follows:(1)pAY=ptY=y|H=h,G=g,L=lt,W1=w1t,W2=w2t,where P(Y) denotes the probability (win = 1, draw = 0, or loss = −1) at the end of each session t (t = 1st, 2nd, 3rd,..., 15th), l denotes the lead until session t, w_1 denotes the first team’s wickets, w_2 denotes the second team’s wickets, g denotes the ground effect, and h denotes home advantage. The model assumes Y has a multinomial distribution, that is, Y follows MN pwin,pdraw,ploss with,(2)pwin=pY=1covariates=expαwin+βwinTX1+expαwin+βTwinX+expαloss+βlossTX,pdraw=pY=0covariates=11+expαwin+βwinTX+expαloss+βlossTX,ploss=pY=−1covariates=expαloss+βlossTX1+expαwin+βwinTX+expαloss+βlossTX.We forecast match outcomes based on the above-mentioned explanatory variables for each session of the test match. The potential position for both the reference team and the opponent squad has also been well-defined. At the end of each session, the hypothetical position of the batsmen is defined as follows:(3)pHY=ptY=y|H=h,G=g,L=lt,W1=w1t−1,W2=w2t−1.We assess their contributions after computing their points to determine the best batsman in the Test Cricket matches.


### 3.1. Example 1

Consider an Australia-New Zealand test match at the Perth Cricket Stadium in Australia. When we fit a model at the commencement of a test match, the likelihood of the reference team (Australia) winning, drawing, and losing is 0.67, 0.03, and 0.30, respectively. Table2 contains session-level data. Australia wins the match by 296 runs.Table 2
Scorecard from the 2019 Test Match between Australia (reference team) and New Zealand (opposite team) at Perth (ID 2374).
Day_1Day_2Day_3Day_4LunchTeaEndLunchTeaEndLunchTeaEndLunchTeaEndLead76160248337416307250325417436369296W122461010101116191919W2000005101010121520We depict the Trans-Tasman series, which is played in Australia between New Zealand and Australia. Australia has won this series (3-0). In the series, the Australian cricket team had the benefit of playing at home. The batters’ rating points throughout the series are shown in Table3. Table 4 shows the results of our proposed methodology when both ground effect and home advantage are taken out of the equation. Table 5 shows the batters’ rankings, which are based on traditional batter averages. Labuschagne of Australia received the highest average of 91.50 points. Second, our criteria assign a score to batters based on the probability of each session’s test match result. Instead of the contribution shown in the typical position, a batter who performs well in a critical scenario receives additional rating points. As it stands, batters who perform well against highly rated teams earn more points than batters who do well against average teams. M Labuschagne received the best batsman of the series award in the Trans-Tasman series, as per traditional ratings; he scored the most runs with the highest average. The outcome would be different if the batsman of the series award was awarded using our proposed criteria. At last, we found correlation between our proposed rating system and ICC rating system with r = 0.636 and p-value = 0.000.Table 3
Proposed rating of batters in test series played between Australia and New Zealand in 2019–2020.
BattersBattersMatchesRatingRanking(Australia)(New Zealand)SPD Smith30.2041M Labuschagne30.1522TM Head30.083GD Philipson10.0534T A Blundell20.0455DA Warner30.0386MS Wade30.0387MA Starc30.0368C de30.0359BJ Watling30.03510MJ Santner20.0231TA Astle10.02212JR Pattinson20.01813TD Paine30.00914PJ Cummins30.00915HM Nicholls0.00716JA Burns20.00617TG Southee30.00418LRPL Taylor20.00319NM Lyon30.00220N Wagner30.00221MJ Henry30.00222T A Boult10.00123TWM Latham1024JA Raval3025KS Williamson2026Hazlewood2027WER Somerville1028LH Ferguson1029Grandhomme130Table 4
Rating of batters in Test series played between Australia and New Zealand in 2019–2020 (the covariates home advantage and ground excluded from analysis).
BattersBattersMatchesRatingRanking(Australia)(New Zealand)T A Blundell20.2981M Labuschagne30.2462DA Warner30.1653SPD Smith30.1014TM Head30.075GD Philipson10.0686TD Paine30.0527MS Wade30.058JA Burns30.0469LRPL Taylor30.04510TWM Latham30.04411J A Raval20.03112TA Astle10.02913KS Wlliamson20.02814C de Grandhomme30.02115BJ Watling30.01316MA Starc30.01217MJ Santner20.0118JR Pattinson20.0119PJ Cummins30.00720HM Nicholls20.00721TG Southee20.00522NM Lyon30.00323N Wagner30.00324MJ Henry10.00225T A Boult10.00226WER Somerville1027LH Ferguson1028Table 5
ICC ranking of batters in a Test series played between Australia and New Zealand in 2019–2020.
BattersMatchesInningsRunsAverageRankingM Labuschagne3654991.51DA Warner3629749.52TA Blundell24172433TM Head3521342.64TD Paine3415338.255SPD Smith3621435.676G D Philips1252267JA Burns3615525.838LRPL Taylor3615225.339C de Grandhomme3614824.6710MS Wade3511923.811TWM Latham361262112T D Astle12422113MA Starc34761914BJ Watling3610517.515HM Nicholls246115.2516KS Wlliamson245714.2517JA Raval244511.2518PJ Cummins344110.2519JL Pattinson2216820MJ Santner2432821TG Southee2424622N Wagner36325.3323TA Boult128424NM Lyon34153.7525W E R Somerville1273.526MJ Henry1231.527LH Ferguson1210.528Hazlewood110029


### 3.2. Example 2

Consider the 2019 Test match between Pakistan (batting first) and Australia (batting second) at Brisbane, Australia. We used the coefficients of several covariates to fit a model using sessional data. Pakistan’s chances of winning, drawing, and losing at the start of the match are 0.53, 0.13, and 0.34, respectively. Table6 contains session by session data. Australia wins this match.Table 6
Scorecard from the 2019 Test match between Pakistan (reference team) and Australia (opponent team) in Brisbane, Australia.
Day_1Day_2Day_3Day_4LunchTeaEndLunchTeaEndLunchTeaEndLunchTeaEndLead5712524014045−72−155−292−276−196−72−5W10510101010101013151620W20000013510101010Another example is a Test Cricket match series between Australia and Pakistan that took place in Australia in 2019. The series was won 2-0 by Australia. The Test Cricket series is depicted in Table7. Table 7 shows the results of the analysis when all predictors are considered, whereas Table 8 shows the results when home advantage and ground effect are not considered. All batters who have at least one chance to bat for their team in a test series are rated in Table 7. In Tables 7, 8, and 9, DA Warner, an Australian batter, was ranked best among batters from both teams. In Tables 7 and 8, he had different scores. When the ground impact and home factor are removed from the model, he loses some ranking points in Table 7. According to Table 9, DA Warner remained the greatest batter with the highest batting average based on the ICC’s basic average criteria. In the series, DA Warner was named batsman of the series. It is concluded that there exists a correlation between our proposed criteria and ICC criteria with r = 0.835 and p-value = 0.001.Table 7
Proposed rating of batters in Test series played between Pakistan and Australia in 2019.
BattersBattersMatchesRatingRanking(Australia)(Pakistan)DA Warner20.1671Asad Shafique20.0832M Labuschagne20.0783JA Burns20.0674Mohammad Rizwan20.0625Shan Masood20.0516Yasir Shah20.057Azhar Ali20.0458Babar Azam20.0369Naseem Shah10.01610Imran Khan10.01511MS Wade20.00912NM Lyon10.00913TM Head10.00714Haris Sohail10.00615Iftikhar Ahmed20.00616PJ Cummins10.00517Muhammad Abbas10.00418SPD Smith20.00419TD Paine10.00420Shaheen Shah Afridi20.00321MA Starc10.00322JR Hazlewood10.00323Muhammad Musa10.00224Imam-ul-Hauque10.00125Table 8
Batters’ rating in Test series played between Pakistan and Australia in 2019. The effect of ground and home advantage excluded from analysis.
BattersBattersMatchesRatingRanking(Australia)(Pakistan)DA Warner20.2411M Labuschagne20.132MS Wade20.0783Asad Shafique20.0644JA Burns20.0595Shan Masood20.0576Azhar Ali20.0567Muhammad Rizwan20.0528Yasir Shah20.0399Babar Azam20.03310Naseem Shah10.01111Imran Khan10.01112SPD Smith20.01113NM Lyon10.00914Iftikhar Ahmed20.00715TM Head10.00516PJ Cummins10.00517Haris Sohail10.00518Muhammad Abbas10.00419TD Paine10.00320MA Starc10.00321Shaheen Shah Afridi20.00322Muhammad Musa10.00223Imam-ul-Haq10.00124JR Hazlewood1025Table 9
ICC ranking of batters in a Test series played between Australia and Pakistan, 2019.
BattersMatchesInningsRunsAverageRankingDA Warner22489244.51M Labuschagne22347173.52Babar Azam2421052.53JA Burns2210150.54MS Wade2298495Yasir Shah2419448.56Mohammad Rizwan2417744.257Shan Masood24156398Asad Shafique2414235.59TM Head21242410SPD Smith22402011Azhar Ali246215.512Muhammad Abbas12301513TD Paine21131314NM Lyon21131315Iftikhar Ahmed24441116Muhammad Musa1216817PJ Cummins217718Imran Khan1210519MA Starc215520JR Hazlewood215521Haris Sohail1294.522Naseem Shah1273.523Shaheen Shah Afridi24112.7524Imam ul Haque122125


### 3.3. Example 3

Take, for example, a test match played at Chattogram in 2018 between Bangladesh (reference team) and Sri Lanka. We used coefficients for different explanatory variables to fit the model on session-by-session data. For the reference team (Bangladesh), the chances of winning, drawing, and losing are 0.73, 0.12, and 0.15, respectively. The match has been called a draw. Table10 contains session-by-session lead data.Table 10
Scorecard from the 2018 Test match between Bangladesh (reference team) and Sri Lanka (opponent team) in Bangladesh (ID 2295).
Day_1Day_2Day_3Day_4Day_5LunchTeaEndLunchTeaEndLunchTeaEndLunchTeaEndLunchTeaEndLead120250374467463326218979−99−192−119−1381107W122471010101010101013131515W20000111334710101010Consider another two Test Cricket match series in Bangladesh in 2018 between Sri Lanka and Bangladesh to further investigate the proposed criteria. The series was won by Sri Lanka with a score of 2-1. Players’ batting performance in the series is described in Table11 . When all predictors are included and techniques are used, Table 11 is produced. According to the results, Sri Lankan batter BKG Mendis received the most points (0.173) and was ranked first among all batters. When the covariate home advantage was not taken into account, BKG Mendis came in second with 0.201 points in Table 12.Table 11
Proposed rating of batters in Test series played between Sri Lanka and Bangladesh in 2018.
BattersBattersMatchesRatingRanking(Sri Lanka)(Bangladesh)BKG Mendis20.1731DM de Silva20.1412Mominul Haque20.1003Tamim Iqbal20.0854ARS Silva20.0805Imrul Kayes20.0646Mahidy Hassan Miraz20.0417MD Gunathilaka10.0408Mahmudullah20.0409Mushfiqur Rahim20.02110LD Chandimal20.01911A Dananjaya10.01712FDM Karunaratne20.01613MDK Perera20.01614Liton Das20.01215RAS Lakmal20.00916Sunzamul Islam10.00817N Dickwella20.00518Mosaddek Hossain10.00319Abdul Razzaqk10.00220Tijul Islam20.00221CBRLS Kumara10.00122HMRKB Herath20.00123Sabbir Rahman10.00024Mustafizur Rahman20.00025Sandakan10.00026Table 12
Rating of batters in Test series played between Sri Lanka and Bangladesh in 2018 (the effect of home factor and ground excluded from analysis).
BattersBattersMatchesRatingRanking(Bangladesh)(Sri Lanka)Mominul Haque20.2221BKG Mendis20.2012DM de Silva20.1723ARS Silva20.1274Tamim Iqbal20.1165Imrul Kayes20.0926Mehidy Hassan Mirza20.0687Mushfiqur Rahim20.0678MD Gunathilaka10.0639LD Chandimal20.05310Liton Das20.04511Mahmudullah20.03312MDK Perera20.03313FDM Karunaratne20.0314Sunzamul Islam10.02715N Dickwella20.02516RAS LAkmal20.02517A Dananjaya10.02318HMRKB Herath20.00819Mosaddek Hossain10.00420Abdul Razzaqk10.00421CBRLS Kumara10.00322Tijul Islam20.00323Mustafizur Rahman20.00124Sabbir Rahman10.00025Sandakan10.00026When the covariates home factor and ground factor are removed from the collection of predictors, Table12 is generated. In Tables 11 and 13, the same batter takes the first place. Table 13 is created to rate the players’ batting performances in the Test series using traditional averages. According to Table 13, Sri Lankan batsman BKG Mendis scored the most runs (271) and had the highest batting average in the series. Different criteria are used to grade batters in a conventional rating, and each table has a different top hitter, and our criteria rate batters by summing their hitting performance.Table 13
ICC ranking of batters in a Test series played between Sri Lanka and Bangladesh in 2018.
BattersMatchesInningsRunsAverageRankingBKG Mendis2327190.331Mominul Haque2431478.52ARS Silva2323578.333DM de Silva2322073.334LD Chandimal23117395Mahmudullah2413433.56Liton Das2413132.757Mushfiqur Rahim24120308Tamim Iqbal249924.759N Dickwella237324.3310Sunzamul Islam11242411Imrul Kayes249523.7512MDK Perera237023.3313Mehidy Hassan Mirza236521.6714MD Gunathilaka12301515FDM Karunaratne233511.6716RAS Lakmal233411.3317A Dananjaya12201018HMRKB Herath23268.6719Mosaddek Hossain1216820Mustafizur Rahman23134.3321Tijul Islam2382.6722CBRLS Kumara112223Abdul Razzak1231.524Sabbir Rahman1210.525Sandakan126


## 3.1. Example 1

Consider an Australia-New Zealand test match at the Perth Cricket Stadium in Australia. When we fit a model at the commencement of a test match, the likelihood of the reference team (Australia) winning, drawing, and losing is 0.67, 0.03, and 0.30, respectively. Table2 contains session-level data. Australia wins the match by 296 runs.Table 2
Scorecard from the 2019 Test Match between Australia (reference team) and New Zealand (opposite team) at Perth (ID 2374).
Day_1Day_2Day_3Day_4LunchTeaEndLunchTeaEndLunchTeaEndLunchTeaEndLead76160248337416307250325417436369296W122461010101116191919W2000005101010121520We depict the Trans-Tasman series, which is played in Australia between New Zealand and Australia. Australia has won this series (3-0). In the series, the Australian cricket team had the benefit of playing at home. The batters’ rating points throughout the series are shown in Table3. Table 4 shows the results of our proposed methodology when both ground effect and home advantage are taken out of the equation. Table 5 shows the batters’ rankings, which are based on traditional batter averages. Labuschagne of Australia received the highest average of 91.50 points. Second, our criteria assign a score to batters based on the probability of each session’s test match result. Instead of the contribution shown in the typical position, a batter who performs well in a critical scenario receives additional rating points. As it stands, batters who perform well against highly rated teams earn more points than batters who do well against average teams. M Labuschagne received the best batsman of the series award in the Trans-Tasman series, as per traditional ratings; he scored the most runs with the highest average. The outcome would be different if the batsman of the series award was awarded using our proposed criteria. At last, we found correlation between our proposed rating system and ICC rating system with r = 0.636 and p-value = 0.000.Table 3
Proposed rating of batters in test series played between Australia and New Zealand in 2019–2020.
BattersBattersMatchesRatingRanking(Australia)(New Zealand)SPD Smith30.2041M Labuschagne30.1522TM Head30.083GD Philipson10.0534T A Blundell20.0455DA Warner30.0386MS Wade30.0387MA Starc30.0368C de30.0359BJ Watling30.03510MJ Santner20.0231TA Astle10.02212JR Pattinson20.01813TD Paine30.00914PJ Cummins30.00915HM Nicholls0.00716JA Burns20.00617TG Southee30.00418LRPL Taylor20.00319NM Lyon30.00220N Wagner30.00221MJ Henry30.00222T A Boult10.00123TWM Latham1024JA Raval3025KS Williamson2026Hazlewood2027WER Somerville1028LH Ferguson1029Grandhomme130Table 4
Rating of batters in Test series played between Australia and New Zealand in 2019–2020 (the covariates home advantage and ground excluded from analysis).
BattersBattersMatchesRatingRanking(Australia)(New Zealand)T A Blundell20.2981M Labuschagne30.2462DA Warner30.1653SPD Smith30.1014TM Head30.075GD Philipson10.0686TD Paine30.0527MS Wade30.058JA Burns30.0469LRPL Taylor30.04510TWM Latham30.04411J A Raval20.03112TA Astle10.02913KS Wlliamson20.02814C de Grandhomme30.02115BJ Watling30.01316MA Starc30.01217MJ Santner20.0118JR Pattinson20.0119PJ Cummins30.00720HM Nicholls20.00721TG Southee20.00522NM Lyon30.00323N Wagner30.00324MJ Henry10.00225T A Boult10.00226WER Somerville1027LH Ferguson1028Table 5
ICC ranking of batters in a Test series played between Australia and New Zealand in 2019–2020.
BattersMatchesInningsRunsAverageRankingM Labuschagne3654991.51DA Warner3629749.52TA Blundell24172433TM Head3521342.64TD Paine3415338.255SPD Smith3621435.676G D Philips1252267JA Burns3615525.838LRPL Taylor3615225.339C de Grandhomme3614824.6710MS Wade3511923.811TWM Latham361262112T D Astle12422113MA Starc34761914BJ Watling3610517.515HM Nicholls246115.2516KS Wlliamson245714.2517JA Raval244511.2518PJ Cummins344110.2519JL Pattinson2216820MJ Santner2432821TG Southee2424622N Wagner36325.3323TA Boult128424NM Lyon34153.7525W E R Somerville1273.526MJ Henry1231.527LH Ferguson1210.528Hazlewood110029


## 3.2. Example 2

Consider the 2019 Test match between Pakistan (batting first) and Australia (batting second) at Brisbane, Australia. We used the coefficients of several covariates to fit a model using sessional data. Pakistan’s chances of winning, drawing, and losing at the start of the match are 0.53, 0.13, and 0.34, respectively. Table6 contains session by session data. Australia wins this match.Table 6
Scorecard from the 2019 Test match between Pakistan (reference team) and Australia (opponent team) in Brisbane, Australia.
Day_1Day_2Day_3Day_4LunchTeaEndLunchTeaEndLunchTeaEndLunchTeaEndLead5712524014045−72−155−292−276−196−72−5W10510101010101013151620W20000013510101010Another example is a Test Cricket match series between Australia and Pakistan that took place in Australia in 2019. The series was won 2-0 by Australia. The Test Cricket series is depicted in Table7. Table 7 shows the results of the analysis when all predictors are considered, whereas Table 8 shows the results when home advantage and ground effect are not considered. All batters who have at least one chance to bat for their team in a test series are rated in Table 7. In Tables 7, 8, and 9, DA Warner, an Australian batter, was ranked best among batters from both teams. In Tables 7 and 8, he had different scores. When the ground impact and home factor are removed from the model, he loses some ranking points in Table 7. According to Table 9, DA Warner remained the greatest batter with the highest batting average based on the ICC’s basic average criteria. In the series, DA Warner was named batsman of the series. It is concluded that there exists a correlation between our proposed criteria and ICC criteria with r = 0.835 and p-value = 0.001.Table 7
Proposed rating of batters in Test series played between Pakistan and Australia in 2019.
BattersBattersMatchesRatingRanking(Australia)(Pakistan)DA Warner20.1671Asad Shafique20.0832M Labuschagne20.0783JA Burns20.0674Mohammad Rizwan20.0625Shan Masood20.0516Yasir Shah20.057Azhar Ali20.0458Babar Azam20.0369Naseem Shah10.01610Imran Khan10.01511MS Wade20.00912NM Lyon10.00913TM Head10.00714Haris Sohail10.00615Iftikhar Ahmed20.00616PJ Cummins10.00517Muhammad Abbas10.00418SPD Smith20.00419TD Paine10.00420Shaheen Shah Afridi20.00321MA Starc10.00322JR Hazlewood10.00323Muhammad Musa10.00224Imam-ul-Hauque10.00125Table 8
Batters’ rating in Test series played between Pakistan and Australia in 2019. The effect of ground and home advantage excluded from analysis.
BattersBattersMatchesRatingRanking(Australia)(Pakistan)DA Warner20.2411M Labuschagne20.132MS Wade20.0783Asad Shafique20.0644JA Burns20.0595Shan Masood20.0576Azhar Ali20.0567Muhammad Rizwan20.0528Yasir Shah20.0399Babar Azam20.03310Naseem Shah10.01111Imran Khan10.01112SPD Smith20.01113NM Lyon10.00914Iftikhar Ahmed20.00715TM Head10.00516PJ Cummins10.00517Haris Sohail10.00518Muhammad Abbas10.00419TD Paine10.00320MA Starc10.00321Shaheen Shah Afridi20.00322Muhammad Musa10.00223Imam-ul-Haq10.00124JR Hazlewood1025Table 9
ICC ranking of batters in a Test series played between Australia and Pakistan, 2019.
BattersMatchesInningsRunsAverageRankingDA Warner22489244.51M Labuschagne22347173.52Babar Azam2421052.53JA Burns2210150.54MS Wade2298495Yasir Shah2419448.56Mohammad Rizwan2417744.257Shan Masood24156398Asad Shafique2414235.59TM Head21242410SPD Smith22402011Azhar Ali246215.512Muhammad Abbas12301513TD Paine21131314NM Lyon21131315Iftikhar Ahmed24441116Muhammad Musa1216817PJ Cummins217718Imran Khan1210519MA Starc215520JR Hazlewood215521Haris Sohail1294.522Naseem Shah1273.523Shaheen Shah Afridi24112.7524Imam ul Haque122125


## 3.3. Example 3

Take, for example, a test match played at Chattogram in 2018 between Bangladesh (reference team) and Sri Lanka. We used coefficients for different explanatory variables to fit the model on session-by-session data. For the reference team (Bangladesh), the chances of winning, drawing, and losing are 0.73, 0.12, and 0.15, respectively. The match has been called a draw. Table10 contains session-by-session lead data.Table 10
Scorecard from the 2018 Test match between Bangladesh (reference team) and Sri Lanka (opponent team) in Bangladesh (ID 2295).
Day_1Day_2Day_3Day_4Day_5LunchTeaEndLunchTeaEndLunchTeaEndLunchTeaEndLunchTeaEndLead120250374467463326218979−99−192−119−1381107W122471010101010101013131515W20000111334710101010Consider another two Test Cricket match series in Bangladesh in 2018 between Sri Lanka and Bangladesh to further investigate the proposed criteria. The series was won by Sri Lanka with a score of 2-1. Players’ batting performance in the series is described in Table11 . When all predictors are included and techniques are used, Table 11 is produced. According to the results, Sri Lankan batter BKG Mendis received the most points (0.173) and was ranked first among all batters. When the covariate home advantage was not taken into account, BKG Mendis came in second with 0.201 points in Table 12.Table 11
Proposed rating of batters in Test series played between Sri Lanka and Bangladesh in 2018.
BattersBattersMatchesRatingRanking(Sri Lanka)(Bangladesh)BKG Mendis20.1731DM de Silva20.1412Mominul Haque20.1003Tamim Iqbal20.0854ARS Silva20.0805Imrul Kayes20.0646Mahidy Hassan Miraz20.0417MD Gunathilaka10.0408Mahmudullah20.0409Mushfiqur Rahim20.02110LD Chandimal20.01911A Dananjaya10.01712FDM Karunaratne20.01613MDK Perera20.01614Liton Das20.01215RAS Lakmal20.00916Sunzamul Islam10.00817N Dickwella20.00518Mosaddek Hossain10.00319Abdul Razzaqk10.00220Tijul Islam20.00221CBRLS Kumara10.00122HMRKB Herath20.00123Sabbir Rahman10.00024Mustafizur Rahman20.00025Sandakan10.00026Table 12
Rating of batters in Test series played between Sri Lanka and Bangladesh in 2018 (the effect of home factor and ground excluded from analysis).
BattersBattersMatchesRatingRanking(Bangladesh)(Sri Lanka)Mominul Haque20.2221BKG Mendis20.2012DM de Silva20.1723ARS Silva20.1274Tamim Iqbal20.1165Imrul Kayes20.0926Mehidy Hassan Mirza20.0687Mushfiqur Rahim20.0678MD Gunathilaka10.0639LD Chandimal20.05310Liton Das20.04511Mahmudullah20.03312MDK Perera20.03313FDM Karunaratne20.0314Sunzamul Islam10.02715N Dickwella20.02516RAS LAkmal20.02517A Dananjaya10.02318HMRKB Herath20.00819Mosaddek Hossain10.00420Abdul Razzaqk10.00421CBRLS Kumara10.00322Tijul Islam20.00323Mustafizur Rahman20.00124Sabbir Rahman10.00025Sandakan10.00026When the covariates home factor and ground factor are removed from the collection of predictors, Table12 is generated. In Tables 11 and 13, the same batter takes the first place. Table 13 is created to rate the players’ batting performances in the Test series using traditional averages. According to Table 13, Sri Lankan batsman BKG Mendis scored the most runs (271) and had the highest batting average in the series. Different criteria are used to grade batters in a conventional rating, and each table has a different top hitter, and our criteria rate batters by summing their hitting performance.Table 13
ICC ranking of batters in a Test series played between Sri Lanka and Bangladesh in 2018.
BattersMatchesInningsRunsAverageRankingBKG Mendis2327190.331Mominul Haque2431478.52ARS Silva2323578.333DM de Silva2322073.334LD Chandimal23117395Mahmudullah2413433.56Liton Das2413132.757Mushfiqur Rahim24120308Tamim Iqbal249924.759N Dickwella237324.3310Sunzamul Islam11242411Imrul Kayes249523.7512MDK Perera237023.3313Mehidy Hassan Mirza236521.6714MD Gunathilaka12301515FDM Karunaratne233511.6716RAS Lakmal233411.3317A Dananjaya12201018HMRKB Herath23268.6719Mosaddek Hossain1216820Mustafizur Rahman23134.3321Tijul Islam2382.6722CBRLS Kumara112223Abdul Razzak1231.524Sabbir Rahman1210.525Sandakan126


## 4. Discussion

The results of the analysis revealed that each outcome had a varied impact at various stages of a Test Cricket match. Explanatory variables such as home factor, ground effect, and team strength have an effect on outcomes at the start of a Test match, but this effect fades as the match progresses. Lead has a minor impact at the start of a test match, but it grows in importance as the match develops. During the match, the number of wickets is also significant. A Test Cricket match is made up of five days, each of which has three sessions, for a total of fifteen sessions in a five-day contest. Predictors fluctuate their effect on match results over the course of the five-day match; therefore, we measured all of these sessions one-by-one to anticipate the outcomes at each phase, making it easier for forecasters to forecast on a specific position. Through the statistical analysis, a rating system for Test Cricket matches is presented in this study. Multinomial logistic regression is used to calculate Test match outcome probability. To extend the scope of this study, a larger data set with additional explanatory variables can be used. There is fluctuation in our suggested rating system at the start and end of the Test match. A larger dataset can be used to tackle this problem. In our rating method, batters’ contributions are judged by the difference between the hypothetical probability and the observed probabilities for the first inning and the difference between the supposed probability and the observed probabilities for the second inning. Researchers can utilize a variety of ways to overcome issues relating to the batter’s contributions in a reduced-scoring game. The study methodologies used to rate batters are fairly practical because the proposed rating system is based on session probability, which assesses a batter’s performance in relation to his contribution to the match outcome. We found correlation (0.883) withp-value = 0.001 between proposed criteria and the traditional criteria introduced by ICC.



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*Source: 9215635-2022-08-31.xml*