Are today’s Test cricket batsmen better than the greats of yesteryears? A comparative analysis

1Introduction

Cricket is one of the more popular spectator sports in the world with viewership in billions spread across the globe. The sport is governed by the ICC (International Cricket Council, 2020) which states on its website “The ICC is the global governing body for cricket. Representing 105 members, the ICC governs and administrates the game and works with our members to grow the sport. The ICC is also responsible for the staging of all ICC Events. The ICC presides over the ICC Code of Conduct, playing conditions, the Decision Review System and other ICC regulations.”

Today, cricket is played in three formats: Test match (Test), Twenty20 (T20) and One Day International (ODI). Relatively recently introduced, the last two formats provide fans with fast paced sporting entertainment. In the ODI format, team batting first sets a target score for the team batting second, to chase and exceed. Large score targets combined with limited overs result in batsmen taking more scoring risks. This risk taking behavior is magnified in T20 format which is termed by fans as “hit and run” cricket, hence the term “T20 effect.” In Tests, each team bats twice and frequently these matches end in a draw. Obviously, the objective is to score more runs than the opposing side. Time only becomes a factor in closely contested matches with large scores or when match duration is truncated by weather.

Like other sports, cricket produces vast amounts of data which has attracted the attention of researchers. Significant mathematical analysis of game statistics and applications of analytics can be found in the literature. Swartz (2016) presents a survey of cricket analytics. According to the author, major research streams related to cricket include: analysis of scoring targets, simulations of match conditions and match progression, evaluation of player and team performance. Other studies can be classified as those explaining on-field strategies responding live to changing conditions in the match, strategies optimized for specific cricket formats, models of past performance to improve player contributions, effective team roster selections and simulations to determine effective batting order, all with the ultimate goal to improve the probability of winning.

Research on batting performance has devoted adequate energy testing the validity and efficiency of batting performance metrics. For batsmen, batting average is still the most widely quoted statistic as it is easily understood and accepted by the average fan. Though a simple formula, there are serious drawbacks in what it actually measures. It is a flawed and insufficient measure of a batsman’s true batting potential. Additionally, batting average does not capture scoring consistency expected from batsmen. Several studies have underscored these deficiencies and proposed reformulations. These studies attempt to effectively represent players’ true batting strength, which forms the basis of player ratings, widely disseminated to cricket fans as player rankings. These ratings influence how team selectors assemble squads and enable team captains to dynamically change playing strategies in response to proceedings on the field.

The MRF tyres ICC rankings (previous name, Reliance ICC rankings) are the official record of player rankings and are available from the ICC web site. Updated regularly, rankings are produced in three separate categories: batting, bowling, and all-rounder.

Akhtar et al. (2015) proposed a new system for rating players in a Test match. Their rating system accounted for match conditions by calculating player contributions, separately in the 15 sessions in a Test match (morning, lunch and evening sessions; over five playing days). The fifteen measurements capture player contributions in the context of changing match conditions.

Player contributions in batting, bowling and fielding are weighted into a single score which represents the overall contribution of a player towards the final outcome. The proposed metric can be used to rank players for their contributions in the match. In contrast, the traditional approach is to measure performance once, and upon conclusion of the match.

In their thesis titled “Best Players of The Test Cricket in Last Years 2014” Ahmad and Zada (2015) applied Akhtar et al. (2015) rating system to two test series. The first series was played between Australia and South Africa in Feb/Mar, 2013. Based on batting, bowling, and fielding performance over the entire series, MG Johnson, DW Steyn and BJ Haddin captured the top spots with most significant contributions. Similarly, in Dec. 2014 series played between Australia and India the top three contributors were MG Johnson, NM Lyon and SPD Smith.

Borooah and Mangan (2010) adjusted batting averages of the top 50 all-time best Test cricket batsmen (ranked by career batting average) to derive a new measure CAA (consistency adjusted average). The CAA modified the batting average by incorporating batting consistency. Authors then re-ranked the top 50 on CAA and contrasted those CAA rankings with the original. Their results showed significant deviations.

Works cited above rated performances of players relative to teammates, or players on opposing side, or peers at large. In this paper we contrast career batting performance of Test cricket’s top ranked batsmen from yesteryears (TCG) with the performance of top ranked among still active batsmen (TCA). As cricket fans, we often wonder: how does the batting performance of today’s top ranked Test cricketers such as: Kohli, Smith, Root, Matthews, DM Bravo, Azhar Ali, Taylor and De Kock, measure up to the batting performance of Test cricket’s all-time greats like Tendulkar, Ponting, Cook, Sangakara, Lara, Miadad, Vettori and Amla? This study takes a swing at that question.

2Related work

Motivated by recent popularity of the two short forms of cricket, T20 and ODI are capturing the most attention of current research. Traditional metrics of performance are shown to be flawed in definition or fail to incorporate qualitative aspects of the game. Player performance and team performance related research from all three formats is of interest to the present study. Proposed new metrics and methods from literature are relevant to this work.

Several studies, using cricket data from limited overs formats have proposed playing strategies. Clarke (1988) contrasted batting performance in the first and second inning to estimate optimal scoring rates and resulting winning percentages. Preston and Thomas (2000) provide an analysis of batting strategies deployed in the two innings in English County Cricket with the significant conclusion that strategies of the opposing sides differed. Clarke and Norman (1999) studied the “when to run and when to forgo” strategy in an attempt to protect weaker batsman by keeping him on the non-striker end.

Based on derived models of player performance, another research stream proposed optimum batting lineups. Swartz et al. (2006) conducted simulation studies to determine optimal batting order. Traditionally, batting orders are static as most players eventually settle into their perceived position of strength. Taking match conditions into account Norman and Clarke (2010) applied dynamic programming and proposed batting orders that changed with state of the match and report higher expected scores resulting from dynamic strategies they proposed.

Time in a Test match is not a limiting factor, at least initially. Batsmen are afforded the luxury of time to settle into their natural batting rhythm. In early minutes on the crease all batsmen start slow until they find their groove. Brewer (2008) quantified this as “early inning effect” and estimated Hazard function parameters for Test players. The study concluded that during early minutes of their inning batsmen are more vulnerable and perform at a fraction of their potential ability.

Building on Brewer’s work on slow initial start to batting Stevenson and Brewer (2018) applied survival analysis to predict scoring potential of Test cricketers. Authors concluded that superior “initial batting ability” is not a predictor of a player’s career batting average. Factors such as position in the batting order and strike rate may be better predictors of career performance.

Batting average remains to be the most ubiquitous and supreme measure of batting performance. Runs contributed by individual batsmen and accumulated by the team determine winner in a match. Lewis (2005) proposed alternative performance measures for the ODI format. The proposed measures are based on Duckworth/Lewis methodology which adjusts performance for stages in the inning. An alternate batting performance measure was proposed and tested using five years of Test data by Wickramasinghe (2019) who predicted runs scored from a proposed model derived from the physical attributes of batsmen. Usefulness of actionable analytics was discussed by Jain (2015). He argued that analytics generated from historical performance and broadcast live during matches lack granularity and are not actionable for on-field decisions. He proposed using alternative term “Insights” to describe such static analytics. Pai (2020) applied programming tools to generate analytics which could be metrics useful in shaping the on-field decisions during contests for different sports, including cricket.

Using 2019 IPL (Indian Premier League) data, Joshi (2020) performed network analysis to determine more effective partnerships as measured by runs contributed (by the partnerships) to the total team score. This analysis can be used to plan a more productive batting order. Using historical performance data, Mukherjee (2013) concluded that performance of some teams was significantly influenced by the performance of a handful of players while in other cases it was a genuine team effort. Additionally, teams could achieve superior results by placing key players in selected positions, as influencers.

An author writing under alias NSS (NSS, 2016) compared today’s four superstars: Virat Kohli, Joe Root, Steve Smith, and Kane Williamson. Using the metrics: Consistency, Dominance, Patience / Hitting Strength, and Winning Contribution (using three or all four, depending on the format) the author provided a framework for contrasting their recent performances in all three formats. In the final analysis, Virat Kohli rules in T20 and ODI while the Test format honors go to Steve Smith. Despite the study lacking in sophisticated analytics tools it proposed a useful framework.

3ICC membership

ICC member countries may be eligible to play cricket in all three formats. Both teams must be sanctioned to play the match format. Today, most cricket professionals play in more than one format. The focus of this paper is on the application of analytics to the Test format, specifically, batting performance in the Test format. Therefore, all further references made are limited to batting performance in the Test format.

The very first Test match was played between England and Australia in March of 1877. Currently, twelve countries hold Test status granted by the ICC. These countries are designated as Full Status members of the ICC. Member countries are listed in Table 1, which also shows the year they played their first Test along with the to-date win/loss record. As shown in Table 1, Ireland and Afghanistan achieved Test status in 2018 and have since played in less than ten Tests each. Based on their limited histories, we eliminated Ireland and Afghanistan from further considerations. Previous to that, two countries admitted to this exclusive club were Bangladesh and Zimbabwe with each having played in about 100 Tests. Among the remaining eight countries, last country granted Test status was Sri Lanka (in 1982) with close to 300 Tests played.

The present study is based on player Test batting data from Australia (AU), Bangladesh (BD), England (EN), India (IN), New Zealand (NZ), Pakistan (PK), South Africa (SA), Sri Lanka (SL), West Indies (WI), and Zimbabwe (ZW). The web site, ESPNcricinfo.com offers one of the more complete statistical records of cricket. The records available go as far back as the first Test match and are current as of the last Test match. Expectedly, older data is of poor quality.

4k-Means cluster analysis and applications in sports

In data mining, k-Means cluster analysis is a simple and powerful technique used to partition data into clusters. Clustering is an unsupervised classification technique as it is ideally suited for applications with no definable target variable to predict. The algorithm uses available features describing objects and uses some measurement of similarity to generate groupings. The goal is to create groupings in which each group member is more similar to its own cluster siblings than siblings in all other clusters.

Inputs to the algorithm are features describing each object. No additional information is available on the partitions. The analysis begins with k initial clusters selected from input patterns. Each starting cluster has a known centroid. Subsequent observations are assigned to the nearest cluster based on some evaluation metric. Cluster centroids are updated with every change in cluster membership. The algorithm iterates cluster assignments until convergence is reached or some pre-defined stopping criteria are met.

Kaufman and Rousseeuw (1990) provide mathematical formulation of the k-Means algorithm and Praveen et al. (2017) show a simplified presentation supplemented by an illustrative step-by-step example. Cluster analysis has found its way in many domains: banking, music, medicine, customer segmentation, document clustering, recommendation engines, and image segmentation, to name a few.

Kalman and Bosch (2012) provide a robust example of k-Means clustering application in the NBA (National Basketball association). Traditionally, five players on the basketball court each have one of the following five defined roles: point guard, shooting guard, small forward, power forward and center. As the sport is changing with time those “positions” have become inaccurate descriptors of the skills today’s players are demonstrating. The authors applied k-Means clustering to 10 seasons of NBA data captured by twenty-three variables. Player records were clustered into nine groupings which authors tagged as the new “positions” they proposed. To test effectiveness of these proposed positions they assembled teams to maximize performance. Their results show that the new positions can be used to assemble game line-ups that deliver superior performance.

We applied k–Means clustering to create a Learning Model, which was then applied to obtain Prediction Model. Both of these Models, and the data these were generate from are detailed in the Methodology section.

5Data collection & pre-processing

6Methodology

We performed k-Means cluster analysis in two phases. In the first phase, the Training/Learning phase, we classified eighty TCG using their performance records and generated a Learning Model. In second, the Prediction phase, we applied Learning Model results and classified thirty two TCA into the same number of clusters. The ultimate goal was to statistically test for similarities/dis-similarities in performance. The following k-Means Learning model was defined and TCG data were used to generate cluster associations/memberships. In Prediction phase, the Learning Model centroids were used to predict cluster membership for the thirty two TCA.

k-Means Model

i = 1, 2, 3 ...  ,80 representing TCG players in the Learning Model

j = 1, 2, 3 ...  ,32 representing TCA players in the Prediction Model

k = number of clusters.

Learning Model

C = Cluster Centroids, a vector with cluster means of performance on ten features.

C_A ={AVEe_26A, BF_A, SR_A, ZERO_A, HUN_A, FIF_A, POS_A, BOW_A, CAU_A, LBW_A}

C_B ={AVEe_26B, BF_B, SR_B, ZERO_B, HUN_B, FIF_B, POS_B, BOW_B, CAU_B, LBW_B}

C_C ={AVEe_26c, BF_C, SR_C, ZERO_C, HUN_C, FIF_C, POS_C, BOW_C, CAU_C, LBW_C}

Where

DA_i = Euclidean distance of player i from C_A

DB_i = Euclidean distance of player i from C_B

DC_i = Euclidean distance of player i from C_C

Players are assigned to a cluster using:

Prediction Model

Active players’ classification was generated from distances from Learning Model Centroids.

EA_j = Euclidean distance of player j from C_A

EB_j = Euclidean distance of player j from C_B

EC_j = Euclidean distance of player j from C_C

Players are assigned to a cluster using:

7Analysis and results

We used SPSS for all statistical analyses: DA, ANOVA, independent sample t-tests, and k-Means cluster analysis and related test. We used Excel for data preparation and calculations for the Prediction phase.

Table 2 shows descriptive stats for TCG and TCA. Note the scale differences among variables. Before applying the k-Means clustering algorithm in SPSS, we normalized all variables to the standard (0, 1) distribution.

8Conclusions

There are significant similarities and significant differences in the on-field performance of the TCA and the TCG. Our analysis showed that, with the exception of two anomalies, performance patterns evaluated by the clustering algorithm resulted in groupings which are consistent with impressions of Test cricket fans.

Previously, we have listed “playing role” of members of Elite-A, for both, the TCG and the TCA. To underscore that presentation, we retrieved career bowling records of these players. The six players in Elite A–TCA (3 bowlers, 3 all-rounders), on average bowled 13,726 balls in their careers. For reference, the Elite B-TCA and Elite C-TCA averaged 1,863 and 611 balls respectively. Similar figures for the TCG are: Elite A (11,999), Elite B (1,929) and Elite C (1,770). The bowlers obviously, and the all-rounders are making significant contributions with the ball. These bowlers have achieved sufficient success with the bat also, which earns them a spot in the table TB. The all-rounders, while contributing from both sides of the ball, bat lower in the batting order and contribute fewer runs, as compared to higher order batsmen.

That leaves the five batsmen in Elite A-TCG. These batsmen have attribute patterns which deviate significantly from those of Elite B-TCG and Elite C-TCG. As discussed earlier, the cluster classifications are a net effect of the push and pull between favorable and unfavorable deviations from the centroids. In other words, attribute patterns of these batsmen deviate sufficiently from those of Elite B-TCG and Elite C-TCG. As cricket fans, we are comfortable with the classification assigned to them by the k-Means algorithm.

Among the batting specialists, there were two distinct groupings. These two groupings were similar in performance patterns for the TCA, as well as the TCG. Before concluding that batsmen in one “batting specialists” cluster are superior performers than batsmen in the other, we obtained independent confirmation by performing analysis on official player rankings published by the ICC.

We retrieved current “MRF Tyres ICC Player Ratings” for the Test format (ICC test Match Player Rankings). Previously, and from 2008 to 2016, these rankings were known to cricket fans as “Reliance Player Rankings” named for its sponsor (reliance ICC Player Rankings). For all active players, these ratings are updated regularly and show their current rating along and the career highest rating achieved to-date. For TCG, the rating shown is the highest rating achieved over the entire playing career. For similarity in comparison, we compared the to-date highest career ratings of the TCA with highest career ratings of the TCG.

For each of the three clusters, we calculated average of Reliance/MRF highest ratings. For Elite A-TCG, the average rating was 645.77, and 458.17 for Elite A-TCA. The Elite B-TCG averaged 794.20 as compared to 755.05 for Elite B-TCA while Elite C-TCG came in at 854.30 vs 844.78 for Elite C-TCA. Rather than using these figures for their absolute magnitude, we used them for their relative orders. Conclusions drawn from these averages support our analysis. Elite A, with bowling specialists as members, achieved the lowest average of highest career ratings. Among the established batsmen, Elite C achieved higher averaged career ratings peaks as compared to Elite B.

Comparing Elite C-TCG with Elite B-TCG, players in the Elite C faced more balls which demonstrates patience on the crease. Since time is a less important factor in the Test format, players do not have the urgency to score on every ball. Batsmen can be patient in their shot selection. This patience may have some role in achieving lower number of ZERO outs. Elite C also scored more fifties but did not score significantly more centuries. Elite C were caught out less frequently and were out LBW more often. We will not venture a guess on the impact of DRS (umpire Decision Review System) on this metric. A similar contrast is observed between Elite C-TCA and Elite B-TCA, with one exception that Elite C scored significantly more hundreds.

Arguably (and reluctantly) we conclude that Elite C are better batsmen than Elite B. After all, these are the best of the best batsmen in Test cricket. This conclusions holds for both, the TCG and the TCA.

One potential drawback of the present study is that we compared completed career records of TCG with partially completed career records of the TCA. On average, the TCG played in 179 innings over their entire careers as compared to 117 for the TCA. Even though TCA players have opportunities to improve their performance, it is always an uphill task. It is a mathematical reality that with every additional superior performance, improvements diminish in magnitude. To improve career averages, a player has to achieve superior results (than the past) and the resulting improvements have to carry the weight of entire history. We provide anecdotal evidence, in support.

Selecting one highest ranked TCG player from each of the eight countries, and based on career number of innings played, we calculated their averages at three specific points in their respective careers: at the one third point, the two-thirds point and during the last one-third of the innings played. In presenting these results, we understand this analysis lacks rigor and leave conclusions for the reader to draw. Eight player averages at the one third and two-thirds point are: AVEe₂₆ (47.46 vs 51.32), BF (85.47, 90.77), SR (48.27, 48.29), FIF (0.2207, 0.2156), HUN (0.1106, 0.1315), POS (3.62, 3.53), BOW (0.1254, 0.1491), CAU (0.6832, 0.6715), and LBW (0.1914, 0.1794). Eight player averages during the last one third of career innings are: AVEe₂₆ (51.68), BF (89.90), SR (47.77), FIF (0.1836), HUN (0.1499), POS (3.44), BOW (0.1668), CAU (0.6645), and LBW (0.1687). Comparing performance at the two-thirds point with performance during the last one third of career innings, deviations are small and most likely statistically insignificant. Some players improved performance in some metrics while a similar number saw declines. Singling out one player, Babar Azam, based on the fact that he is early in his Test career and has already earned a spot in Elite B-TCA, we project that if he continues on this performance trajectory, he will go on to earn a spot in Elite C-TCA. All other Elite B-TCA players are further along in their careers and coupled with the fact that any delta from future superior performance will have to lift the entire history, makes the task that much difficult.

The Elite C-TCA players have already achieved performance levels at par with the sports’ greatest. Performance gaps between Elite C and Elite B are relatively small for TCG. With superior future performance and despite it being an uphill task, players in upper echelons of Elite B-TCA can move up and earn a spot in Elite C-TCG. Conversely, poor future performance of players in the lower echelons of Elite B–TCA poses smaller risk of slipping into Elite A-TCG as those performance gaps are much wider.