Winning one-day international cricket matches: a cross-team perspective

ABSTRACT

The study analyses the predictors of a win for four international cricket teams in the one-day international cricket format. A binary logistic regression is used to determine the relationship between the independent variables, i.e., fours and sixes scored, bowling economy, extras conceded, fielding dismissals, the number of debutants from each side, umpire’s nationality, pitch condition, and season of play vis-à-vis odds of a win. The study found that the number of fielding dismissals and bowler economy significantly influence the odds of winning for all four teams. Further, the nationality of the umpire did not affect any team, while other variables influenced the fortunes of different teams differently. Proposed models in the paper can be used by team management and coaches in devising match strategy and player selection for higher win outcomes based on a combination of historical trend data for specific variables and actual data for the others.

KEYWORDS:

• One-day international cricket
• logistic regression
• sports analytics
• win predictability
• match strategy

1. Introduction

Cricket is a popular team sport today played across more than a hundred countries globally. It has its origins in sixteenth-century England (Kaluarachchi & Aparna, 2010). At present, there are three playing formats accepted officially by the International Cricket Council (ICC), namely, Five Day Test matches, 50-over One Day Internationals (ODI), and the most recently adopted Twenty-Twenty cricket (T20). Sports analytics in general and in an evolving game like cricket in particular, there has been a lot of interest amongst researchers and practitioners in recent times on predictive models using data mining techniques and machine learning models (Jain et al., 2021; Passi & Pandey, 2018; Pathak & Wadhwa, 2016). While research using data analytics has progressed significantly in other sports such as soccer (Duan & Chakravarty, 2021), basketball (Maymin, 2021), and tennis (Angelini et al., 2022), in general, research on cricket is scarce (Jain et al., 2021). In this study, we visit the different dimensions of ODI matches and their interplay in influencing the win-loss outcome modelled at a country level (not assuming one size fits all). We have used a binary logistic regression model to predict match outcomes on a large set of independent variables as the scope of this paper and wish to use machine learning models to predict match outcomes as an area of future research.

The contribution of the paper is threefold. First, it analyses the team-level data for four different national sides with the most extended history of playing One Day International (ODI) cricket to model the winning strategy. We have focussed on a specific team-based strategy rather than considering a generic one size fits all approach as in most studies documented in extant literature (Ahmed et al., 2013; Cannonier et al., 2015; Jain et al., 2021; Premkumar et al., 2020). Second, the predictive models have been tested and validated to devise match strategies for the respective teams, which can be used not just by coaches and team administration, but also sponsors of teams and media companies broadcasting/ streaming the coverage considering the kind of viewership based on predicted match results. Third, to the best of our knowledge, several dimensions are considered together for the first time: number of debutants representing each side, season of play, number of bowlers with specific economy rate, extra runs conceded by each side, and pitch condition. In addition, other dimensions documented in the extant literature, such as the nationality of umpires, fielding dismissals, number of boundaries, to name a few, have also been analysed to arrive at the strategy recommendations. While some of the variables may seem to be intermediate to predict match outcomes, the historical data on the variables may be used as an input. For example, for independent variables like the number of fielding dismissals/ number of bowlers with particular economy rate/ number of sixes and fours scored, etc., the historical means with the specific opponents may be used. This adds to the robustness of the paper’s proposed predictive model, which is a significant gap in extant literature. It is also interesting to note that scoring more sixes and fours directly leads to victory. The results do not reflect the same and vary for different teams (elaborated in the Discussion section). We discuss the interaction effects between the various dimensions to propose a team-specific win strategy.

The paper unfolds with a brief review of relevant literature, followed by the empirical framework and the data set used for analysis. The article explains the different variables and their operationalisation in the data section. The results section, model validation follow it, and a discussion of strategic implications for the four teams studied in the paper. We have concluded the paper with managerial implications, limitations, and future research directions.

2. Review of literature

In the chapter titled “Research Directions in Cricket” published in the book “Handbook of Statistical Methods and Analyses in Sports”, Swartz (2016) has identified significant research trends in cricket analytics. Broadly there are six leading research themes – home team advantage, the influence of umpiring decisions, the effect of batting first, a partnership among batters, change of rules by cricketing bodies, and determining the composition of a team. Other major studies conducted in cricket analytics include player performance, team strength, optimal line-ups, and tactics. Norman and Clarke (2010), focusing on batting, have optimised batting order across all game formats using dynamic programming. Analytical studies on cricket have also been conducted from the perspective of sponsorship (Currie, 2000; Donlan, 2014; Goldman & Johns, 2009), motivation to follow matches (Bennett et al., 2007; Kashif et al., 2019), and public relations (Hopwood, 2005a, 2005b). For more details on the different dimensions of cricket and strategy covered in the extant literature, Appendix A may be referred to.

Our review of the literature indicated that some critical determinants of match outcomes have remained unexplored. More importantly, while generic strategic recommendations were covered (Cannonier et al., 2015), different teams have different playing styles, characteristics, and beliefs. Hence, it is fair to hypothesise that other explanatory variables will influence match outcomes differently. For example, the role of debutants (where the urge to perform is paramount to ensure a place in the side) could affect favourable results for a team, while this may not be true for others. While home side advantage has been studied in the past, the season of play (i.e., winter, summer, autumn, or spring) has been included for analysis in the study. For a team with a strong battery of seam bowlers (i.e., Pakistan, Australia), the season may have a crucial role to play. Other critical determinants considered for the first time are the count of bowlers with a specific economy rate, extra runs conceded by each side, and pitch condition measured as a trinomial categorical variable. We find that studies have dealt extra runs as a part of runs conceded per over, which is at an aggregated level and does not break it down to a tactical level to manage extras, as it has both bowling and fielding implications. Finally, this paper considered three kinds of pitch conditions – home pitches, pitches similar to home, and pitches not similar to home. Overall, we can summarise that the choice of variables for this research has been based on past inclusions, exclusions, and granularity (i.e., extra runs). The paper addresses this gap in extant literature by adopting a team-specific approach to predict win/loss outcomes rather than a generic approach.

3. Empirical framework

Batting, bowling, and fielding have influenced match outcome within the production function approach (Cannonier et al., 2015). The methods adopted in the studies are multiple regression methods to model the relationship between match outcome and independent variables (Akhtar & Scarf, 2012; Asif & McHale, 2016; Bailey & Clarke, 2006; Brooks et al., 2002; Khan et al., 2019). This study added an input categorised as “others” representing dimensions such as the nationality of umpires, number of debutants, pitch condition, and season of play. Hence, the match result is expressed as a function in Equation 1(1) $MatchOutcome=f\left(Batting,Bowling,Fielding,Others\right)$(1) .

(1) $MatchOutcome=f\left(Batting,Bowling,Fielding,Others\right)$(1)

The match outcome is modelled as a logit model. The dependent variable, y*, is the match outcome (i.e., win/ loss) expressed as a binary ordinal variable and measured as a latent variable (Brooks et al., 2002; Dawson et al., 2009). Matches with outcomes other than win or loss (example – tie or abandoned) are not included in the analysis as the focus of the study is on analysing a strategy to win. The structure of the latent variable model is expressed in Equation 2(2) $y_j\ast =x_j\beta +e_j$(2) .

(2) $y_j\ast =x_j\beta +e_j$(2)

x_j represents explanatory variables representing batting, bowling, fielding, and other dimensions. At the same time, β is the matrix of parameters to be estimated. The random error term is represented by e_j. The measured dependent variable is whether the team has won (=1) or lost (=0), where:

y* is the unobserved latent variable and was measured on whether the team won (=1) or lost (=0), where:

$y=1ify\ast >0,andy=0ify\ast \le 0$

Hence the logit model can be denoted as

(3) $P\left(y_j=1|x_j\right)=P\left(y_j\ast >0|x_j\right)=\frac{e^{x_j\beta }}{1+e^{x_j\beta }}=\mathrm{\Lambda }(x_j\beta )$(3)

Where Λ (.) is the cumulative distribution function for a standard logistic distribution. The model is used separately for a cross-country comparison to analyse win/ loss data for four national teams: Australia, England, India, and Pakistan. Explanatory variables were considered for every opposition that played against the countries modelled above for the stated time period under consideration.

3.1. Data

Data was collected for ODI matches played by the men’ “s national teams of Australia, England, India, and Pakistan from the website – https://www.espncricinfo.com/(see, Figure 1). The data ranges from when these countries played their first official ODI matches to the recently concluded ICC World Cup in July 2019. A total of 852 matches were considered for Australia (from January 5^th” 1971 till July 11^th’ 2019), 654 matches for England (from January 5^th’ 1971 till July 11^th’ 2019), 926 matches for India (from July 13^th’ 1974 to July 9^th’ 2019), and 849 matches for Pakistan (from February 11^th’ 1973 till July 5^th’ 2019). Refer to Figure 2 for the breakdown of matches played against different opponents by these nations. It may be noted that all games with a no-win/ loss result have been excluded from the analysis as the focus is to analyse the game-winning strategy. Illustratively, the 2019 ICC World Cup final match between England and New Zealand, which ended in a tie and was decided on the number of boundaries scored, has also been ignored in the analysis.

Figure 1. ODI matches played year wise.

Figure 2. ODI matches played by country¹.

From the first ODI played on January 5^th’ 1971, till July 11^th’ 2019, a total of 8384 official ODI games were held globally, and this analysis includes 40.84% (3424 matches) of it. The reasons for the selection of Australia, England, India, and Pakistan for the research was their duration of play of ODI matches, the share of ODIs played by them, contribution to the sport commercially and viewership, and the geographical representation of the three major cricket playing continents in the world. This also factors the different playing styles and hence the tactics and strategy adopted for winning.

3.2. Variables

In all, there are two batting variables representing batting prowess through the number of fours (FOUR) and sixes (SIX) hit by the respective teams. While the number of boundaries scored by the teams studied in the paper (Australia, England, India, and Pakistan, henceforth known as focal teams) was expected to influence the outcome of wins positively, the relationship was inverse when boundaries scored by opponents were higher. For bowling, two variables were considered. First, the frequency count of the number of bowlers (BOWECON) figuring below a specific economy rate (measured in terms of runs per over, RPO); and second, extra runs (EXTRA) conceded. As the game rules, playing conditions, and strategies evolved significantly between 1971 and 2019, BOWECON was operationalised considering three different time eras. The average runs per over have been steadily increasing since the early days of cricket. The average RPO pre-1986 for all official ODI matches played by all the nations was 4. The same statistic was 4.5 for 1986–1999 and 5 RPO for games post-1999. As our estimation involved only four teams, based on expert inputs, the norms were fixed as 3.5, 4.5, and 5.5 RPO for the pre-1986, 1986–1999, and post-1999 periods, respectively.

For every match involving focal teams, the frequency count of the number of bowlers meeting the criteria was recorded for both the focal team and its opponent. For extra runs conceded, match by match data was scanned, and extras were summed up (i.e., byes, leg byes, wides, no balls, and penalty runs). Frequency count of dismissals (FIELDING) involving fielding skills (i.e., run out, stumping, catch) was done for every match for both the focal team and its opponent to arrive at the single variable in the fielding category. The maximum number of variables figure under “others”, including season of play (SEASON), pitch condition (PITCH), nationality of umpires (UMPIRES), and the number of debutants (DEBUTANT). See, Table 1 for a description of the variables and their expected relationship with the dependant variable – match outcome of a win (WIN). It may be noted that the expected signs signify the direction of influence of the explanatory variable on WIN for the focal team under consideration. Further, each metric variable – FOUR, SIX, BOWECON, EXTRA, FIELDING, and DEBUTANT- has two variables, one representing the focal team and their opponent.

Table 1. Definition of variables.

Variable	Definition	Expected Sign (Focal Team^#)
	Explanatory variables
BOWECON	The number of bowlers from each team which have an economy rate below a certain level. The level has been categorised as pre-1986 era, 1986–1999 era, and 2000 and beyond.	Positive
EXTRA	The number of extra runs offered by either team through wide-balls, no-balls, leg-byes, and byes.	Negative
FIELDING	Number of dismissals by a team through run-out, catch, or stumping.	Positive
FOUR	The total number of fours hit by either team.	Positive
SIX	The total number of sixes hit by either team.	Positive
UMPIRE	Nationality of the umpires. Umpires can be from the home team, opponent team, or neutral.	Ambiguous
PITCH	Familiarity with a team with pitch conditions. Categorised as home ground, pitches similar to home ground, and pitches not similar to home ground.	Ambiguous
DEBUTANT	Total debutants from either side in a match.	Ambiguous
SEASON^^	The season of the year. It is categorised as Summer, Winter, Autumn, and Spring.	Ambiguous
	Dependent Variable
WIN	Match outcome can either be win or loss for the team under consideration.

^#Focal Teams – Australia, England, India, and Pakistan; ^{^}Season has been defined based on the source https://seasonsyear.com/ (accessed on 18/02/2019)

4. Results

From a batting perspective, we observed that the mean value of the number of fours and sixes scored by the Indian side was the highest (see, Table 2). The opponents have the lowest average of four’s against the Pakistani bowling attack, followed by Australians, making them the most formidable side to score boundaries against. Matches involving India also have the highest number of sixes scored per match (5.5 sixes scored per match), making the games more exciting from the viewers’ perspective.

Table 2. Descriptive statistics.

	Australia				England				India				Pakistan
Descriptive statistics (metric variables)
Variable	Mean	SD	Max	Min	Mean	SD	Max	Min	Mean	SD	Max	Min	Mean	SD	Max	Min
BOWECON (FocalTeam)	3.4	1.7	8	0	3.2	1.7	7	0	3.2	1.7	8	0	3.4	1.7	8	0
BOWECON (Opponents)	2.8	1.5	7	0	3.1	1.7	8	0	2.9	1.7	7	0	3.2	1.7	7	0
EXTRA (FocalTeam)	14.6	6.5	40	2	14.1	6.5	42	1	15.2	7.4	52	1	15.0	7.3	44	0
EXTRA (Opponents)	13.7	6.7	38	0	14.6	7.1	43	2	14.7	7.1	39	0	16.4	7.8	59	2
FIELDING (FocalTeam)	5.6	2.1	10	0	5.2	2.3	10	0	5.1	2.2	10	0	4.8	2.1	10	0
FIELDING (Opponents)	4.8	2.2	10	0	4.9	2.2	10	0	4.9	2.4	10	0	5.3	2.4	10	0
FOUR (FocalTeam)	17.9	7.1	43	0	18.6	7.1	44	2	18.9	7.9	48	0	17.1	7.1	41	0
FOUR (Opponents)	17.2	7.2	44	0	18.9	7.0	45	2	17.7	7.3	39	0	16.6	7.3	43	0
SIX (FocalTeam)	2.4	2.8	19	0	2.5	3.1	25	0	2.8	2.7	19	0	2.6	2.5	16	0
SIX (Opponents)	2.2	2.4	21	0	2.5	2.7	23	0	2.7	2.7	20	0	2.1	2.4	16	0
DEBUTANT (FocalTeam)	0.2	0.7	11	0	0.3	0.8	11	0	0.2	0.7	11	0	0.2	0.7	11	0
DEBUTANT (Opponents)	0.2	0.8	11	0	0.3	1.1	12	0	0.3	0.9	11	0	0.3	0.9	11	0
Descriptive statistics (categorical variables)
Variable	Frequency		Percent		Frequency		Percent		Frequency		Percent		Frequency		Percent
SEASON (Summer)	483		53.7		288		40.8		240		25.9		216		24.2
SEASON (Winter)	24		2.7		98		13.9		162		17.5		146		16.3
SEASON (Autumn)	213		23.7		183		25.9		352		38.0		314		35.2
SEASON (Spring)	179		19.9		137		19.4		172		18.6		217		24.3
UMPIRES (Both Focal Team)	389		43.3		244		34.6		247		26.7		225		25.2
UMPIRE (Both Neutral)	170		18.9		162		22.9		372		40.2		377		42.2
Table 2. Contd. UMPIRE (Focal Team and Opponents)	10		1.1		7		1.0		1		0.1		3		0.3
UMPIRE (Focal Team and Neutral)	330		36.7		293		41.5		306		33.0		288		32.3
PITCH (Home Pitch)	426		47.4		302		42.8		326		35.2		179		20.0
PITCH (Similar to Home Pitch)	275		30.6		241		34.1		273		29.5		364		40.8
PITCH (Not Similar to Home Pitch)	198		22.0		163		23.1		327		35.3		350		39.2
LOSS	326		36.3		332		47.0		421		45.5		412		46.1
WINS	573		63.7		374		53.0		505		54.5		481		53.9

For the variable BOWECON, the mean value is highest for the Australian and Pakistan teams, making them the most difficult to score runs off. Regarding conceding extras, India and Pakistan, the sub-continent teams, lack discipline, with England being the most restrictive and the only team conceding fewer extras than its opponents. Australia, England, and India performed better in fielding dismissals with a higher average per match, whereas Pakistan trails its opponents. For Pakistan, the gap is about 0.5 dismissals on average, indicating that fielding is its weakness, while Australia has an advantage at an average of 0.8. Hence, this has implications for team selection, especially if FIELDING is one of the critical variables influencing the outcome. Further, it gains significance when playing season and pitch conditions favour seam bowlers, leading to more opportunities for dismissals.

In “others”, DEBUTANT is the only metric variable, and the rest (i.e., SEASON, PITCH, and UMPIRE) are categorical. It was seen that England and Australia play more than 70% of their matches in home pitches or similar to home pitches. In comparison, Pakistan has the maximum share of games (40.8%), played in similar to home pitches (i.e., in Sharjah, Sri Lanka, Bangladesh, India, and Zimbabwe). Similar to home pitches for Australia and England, include grounds in South Africa, New Zealand, West Indies (in addition to England or Australia as the case may be). At the same time, home pitches for England also include Wales, Scotland, and Ireland. From the umpiring perspective, subcontinent teams have more than 40% of their matches officiated by neutral umpires, with the distribution being least for Australia at 18.9%. As far as the playing season is concerned, winter is the least popular among all four countries, due to seam bowling conditions, fading light in the evenings, and hence shorter playing hours for day matches, to name a few. India (38%) and Pakistan (35.2%) have their most significant share of games played during Autumn, whereas Summer is the preferred season for Australia (53.7%) and England (40.8%). This has a bearing on game strategy, as weather conditions are less likely to assist bowlers during summer and autumn. Hence, batting conditions are likely to be better, and matches could result in high average scores, more boundaries, and more entertainment for the crowd.

Before proceeding with the estimation of the logit model, a test of multicollinearity was carried out, checking the Variance Inflation Factor (VIF). VIF values greater than ten reveal high multicollinearity among predictor variables (Diamantopoulos & Winklhofer, 2001). There was no such concern in our case as VIF values ranged between 1.05 to 8.03. We present the Correlation analysis among the independent variables to check for perfect correlation. As seen in Tables 3, 4, 5 and 6, the maximum correlation between the independent variables is 0.503 (For Australia), 0.482 (For England), 0.554 (For India), and 0.459 (For Pakistan), indicating the absence of perfect correlation among the independent variables.

Table 3. Correlation matrix for team Australia.

	DEBUTANT (Focal Team)	DEBUTANT (Opponents)	EXTRA (Focal Team)	EXTRA (Opponents)	FOUR (Opponents)	SIX (Opponents)	FOUR (Focal Team)	SIX (Focal Team)	BOWECON (Focal Team)	BOWECON (Opponents)	FIELDING (Focal Team)	FIELDING (Opponents)
DEBUTANT (Focal Team)	1
DEBUTANT (Opponents)	0.412	1
EXTRA (Focal Team)	−0.025	0.069	1
EXTRA (Opponents)	−0.069	−0.012	0.155	1
FOUR (Opponents)	0.025	−0.015	0.088	0.115	1
SIX (Opponents)	−0.048	−0.067	−0.009	0.024	0.412	1
FOUR (Focal Team)	−0.018	−0.025	0.073	0.041	0.503	0.410	1
SIX (Focal Team)	−0.029	−0.047	0.024	−0.040	0.367	0.492	0.502	1
BOWECON (Focal Team)	−0.067	−0.026	−0.014	−0.137	−0.472	−0.289	−0.122	−0.091	1
BOWECON (Opponents)	−0.040	−0.019	−0.068	−0.070	−0.192	−0.159	−0.392	−0.329	0.383	1
FIELDING (Focal Team)	0.015	−0.012	−0.006	0.033	−0.147	0.009	0.168	0.123	0.233	−0.052	1
FIELDING (Opponents)	0.002	−0.011	0.076	0.053	0.125	0.130	−0.062	−0.029	−0.134	0.200	−0.071		1

Table 4. Correlation matrix for team England.

	DEBUTANT (Focal Team)	DEBUTANT (Opponents)	EXTRA (Focal Team)	EXTRA (Opponents)	FOUR (Opponents)	SIX (Opponents)	FOUR (Focal Team)	SIX (Focal Team)	BOWECON (Focal Team)	BOWECON (Opponents)	FIELDING (Focal Team)	FIELDING (Opponents)
DEBUTANT (Focal Team)	1
DEBUTANT (Opponents)	0.490	1
EXTRA (Focal Team)	−0.001	−0.010	1
EXTRA (Opponents)	−0.015	−0.006	0.190	1
FOUR (Opponents)	−0.087	−0.042	0.097	0.016	1
SIX (Opponents)	−0.066	−0.053	−0.018	−0.088	0.352	1
FOUR (Focal Team)	−0.063	−0.005	0.099	−0.014	0.482	0.368	1
SIX (Focal Team)	−0.098	−0.075	−0.015	−0.111	0.360	0.482	0.471	1
BOWECON (Focal Team)	−0.017	−0.049	0.047	−0.035	−0.455	−0.338	−0.150	−0.206	1
BOWECON (Opponents)	−0.023	−0.081	0.012	−0.020	−0.203	−0.235	−0.490	−0.416	0.333	1
FIELDING (Focal Team)	0.002	0.019	0.044	0.024	−0.150	0.033	0.137	0.161	0.290	−0.121	1
FIELDING (Opponents)	−0.011	−0.014	−0.011	−0.015	0.173	0.084	−0.120	0.017	−0.208	0.262	−0.145	1

Table 5. Correlation matrix for team India.

	DEBUTANT (Focal Team)	DEBUTANT (Opponents)	EXTRA (Focal Team)	EXTRA (Opponents)	FOUR (Opponents)	SIX (Opponents)	FOUR (Focal Team)	SIX (Focal Team)	BOWECON (Focal Team)	BOWECON (Opponents)	FIELDING (Focal Team)	FIELDING (Opponents)
DEBUTANT (Focal Team)	1
DEBUTANT (Opponents)	0.106	1
EXTRA (Focal Team)	−0.033	0.052	1
EXTRA (Opponents)	−0.035	−0.040	0.215	1
FOUR (Opponents)	−0.009	−0.097	0.044	0.128	1
SIX (Opponents)	−0.009	−0.055	−0.087	0.068	0.404	1
FOUR (Focal Team)	−0.005	−0.033	0.084	0.096	0.554	0.321	1
SIX (Focal Team)	−0.015	−0.029	−0.003	0.041	0.336	0.366	0.410	1
BOWECON (Focal Team)	−0.069	0.029	0.001	−0.076	−0.332	−0.307	−0.062	−0.115	1
BOWECON (Opponents)	−0.085	−0.043	−0.038	−0.014	−0.104	−0.157	−0.399	−0.349	0.360	1
FIELDING (Focal Team)	−0.058	−0.069	−0.036	0.098	0.103	0.122	−0.179	−0.063	−0.174	0.267	1
FIELDING (Opponents)	−0.040	−0.017	0.065	0.019	−0.082	−0.064	0.144	0.085	0.223	−0.066	−0.141	1

Table 6. Correlation matrix for team Pakistan.

	DEBUTANT (Focal Team)	DEBUTANT (Opponents)	EXTRA (Focal Team)	EXTRA (Opponents)	FOUR (Opponents)	SIX (Opponents)	FOUR (Focal Team)	SIX (Focal Team)	BOWECON (Focal Team)	BOWECON (Opponents)	FIELDING (Focal Team)	FIELDING (Opponents)
DEBUTANT (Focal Team)	1
DEBUTANT (Opponents)	0.239	1
EXTRA (Focal Team)	0	−0.039	1
EXTRA (Opponents)	0.007	−0.021	0.156	1
FOUR (Opponents)	−0.08	−0.13	0.053	0.055	1
SIX (Opponents)	−0.024	−0.069	−0.087	0.013	0.365	1
FOUR (Focal Team)	−0.038	−0.036	0.11	−0.018	0.459	0.262	1
SIX (Focal Team)	0.019	−0.05	0.008	−0.023	0.243	0.314	0.348	1
BOWECON (Focal Team)	−0.033	0.059	0.011	−0.109	−0.44	−0.348	−0.076	−0.059	1
BOWECON (Opponents)	−0.07	−0.055	−0.063	−0.006	−0.11	−0.155	−0.421	−0.278	0.371	1
FIELDING (Focal Team)	0.003	0.036	−0.032	0.063	−0.149	−0.015	0.096	0.137	0.199	−0.104	1
FIELDING (Opponents)	−0.017	−0.102	0.068	−0.011	0.168	0.152	−0.132	0.014	−0.126	0.286	−0.084	1

The logit model was solved using hierarchical regression, and the results for the different teams are captured in Table 7 below. Model 1 has only the estimator variables for the individual teams, while Models 2, 3, and 4 include different interaction effects. They are Model 2 – BOWECON*FIELDING, Model 3 – BOWECON*FIELDING, EXTRA*FIELDING; Model 4 – BOWECON*FIELDING, EXTRA*FIELDING, and BOWECON*EXTRA. The model factoring an interaction of all three variables and others did not have a single interaction significant at 5% and hence was not included in the results for discussion. The Hosmer-Lemeshow test results for all four models for each side indicate satisfactory goodness-of-fit with a significance value greater than 0.05. The Nagelkerke R² values for all models are over 0.7 indicating a more than 70% predictability of outcomes. The results are presented in Table 7 below and discussed subsequently.

Table 7. Logit results for Australia, England, India, and Pakistan.

Variable	Model 1				Model 2				Model 3				Model 4
	Aus	Eng	Ind	Pak^	Aus	Eng	Ind	Pak	Aus	Eng	Ind	Pak	Aus	Eng	Ind	Pak
BOWECON (Focal Team)	0.761 (0.11)***	0.681 (0.12)***	1.056 (0.12)***	0.739 (0.11)***	0.361 (0.23)	0.973 (0.28)***	0.999 (0.24)***	1.285 (0.23)***	0.410 (0.23)*	0.969 (0.28)***	0.995 (0.24)***	1.263 (0.23)***	0.508 (0.28)*	0.881 (0.33)***	1.082 (0.28)***	1.028 (0.30)***
BOWECON (Opponents)	−0.778 (0.12)***	−0.690 (0.12)***	−0.890 (0.12)***	−0.621 (0.11)***	−0.479 (0.24)**	−0.630 (0.26)**	−0.654 (0.24)***	−0.995 (0.22)***	−0.438 (0.24)*	−0.607 (0.28)**	−0.674 (0.24)***	−1.017 (0.23)***	−0.269 (0.29)	−0.703 (0.34)**	−0.720 (0.29)**	−0.941 (0.26)***
EXTRA (Focal Team)	−0.072 (0.02)***	−0.072 (0.02)***	−0.023 (0.02)	−0.005 (0.02)	−0.072 (0.02)***	−0.072 (0.02)***	−0.022 (0.02)	−0.005 (0.02)	0.033 (0.05)	−0.019 (0.06)	−0.059 (0.05)	−0.033 (0.05)	0.054 (0.06)	−0.034 (0.07)	−0.045 (0.06)	−0.085 (0.06)
EXTRA (Opponents)	0.039 (0.02)**	0.039 (0.02)*	0.029 (0.02)	0.028 (0.02)*	0.038 (0.02)**	0.040 (0.02)**	0.030 (0.02)*	0.030 (0.02)*	0.102 (0.05)*	−0.066 (0.05)	−0.015 (0.05)	0.110 (0.05)**	0.131 (0.06)**	−0.081 (0.06)	−0.023 (0.06)	0.131 (0.05)**
FIELDING (Focal Team)	0.627 (0.07)***	0.493 (0.08)***	0.557 (0.07)***	0.532 (0.07)***	0.400 (0.13)***	0.663 (0.17)***	0.526 (0.14)***	0.929 (0.17)***	0.728 (0.20)***	0.821 (0.23)***	0.415 (0.19)**	0.846 (0.22)***	0.717 (0.20)***	0.836 (0.23)***	0.402 (0.20)**	0.799 (0.22)***
FIELDING (Opponents)	−0.500 (0.07)***	−0.698 (0.08)***	−0.591 (0.07)***	−0.534 (0.06)***	−0.337 (0.13)**	−0.658 (0.17)***	−0.459 (0.13)***	−0.779 (0.14)***	−0.154 (0.20)	−0.971 (0.23)***	−0.591 (0.20)***	−0.562 (0.18)***	−0.202 (0.20)	−0.978 (0.24)***	−0.586 (0.21)***	−0.577 (0.18)***
FOUR (Focal Team)	0.217 (0.03)***	0.174 (0.03)***	0.186 (0.03)***	0.195 (0.03)***	0.214 (0.03)***	0.175 (0.03)***	0.186 (0.03)***	0.204 (0.03)***	0.214 (0.03)***	0.173 (0.03)***	0.187 (0.03)***	0.204 (0.03)***	0.216 (0.03)***	0.173 (0.03)***	0.187 (0.03)***	0.202 (0.03)***
FOUR (Opponents)	−0.183 (0.03)***	−0.251 (0.03)***	−0.187 (0.03)***	−0.196 (0.03)***	−0.180 (0.03)***	−0.255 (0.03)***	−0.189 (0.03)***	−0.202 (0.03)***	−0.181 (0.03)***	−0.248 (0.03)***	−0.188 (0.03)***	−0.207 (0.03)***	−0.186 (0.03)***	−0.245 (0.03)***	−0.188 (0.03)***	−0.206 (0.03)***
SIX (Focal Team)	0.076 (0.06)	0.161 (0.07)**	0.221 (0.06)***	0.265 (0.06)***	0.086 (0.06)	0.153 (0.07)**	0.224 (0.06)***	0.283 (0.06)***	0.108 (0.06)*	0.150 (0.07)**	0.223 (0.06)***	0.286 (0.06)***	0.110 (0.06)*	0.146 (0.07)**	0.225 (0.06)***	0.292 (0.06)***
SIX (Opponents)	−0.186 (0.07)***	−0.044 (0.07)	−0.200 (0.05)***	−0.203 (0.06)***	−0.191 (0.07)***	−0.042 (0.07)	−0.199 (0.05)***	−0.199 (0.06)***	−0.205 (0.07)***	−0.035 (0.07)	−0.201 (0.05)***	−0.196 (0.06)***	−0.202 (0.07)***	−0.038 (0.07)	−0.202 (0.05)***	−0.197 (0.06)***
UMPIRE (Both Neutral)	0.480 (0.40)	0.572 (0.37)	−0.253 (0.33)	0.227 (0.33)	0.463 (0.40)	0.607 (0.38)	−0.256 (0.33)	0.150 (0.33)	0.470 (0.40)	0.598 (0.38)	−0.265 (0.33)	0.184 (0.33)	0.440 (0.41)	0.600 (0.38)	−0.245 (0.34)	0.202 (0.34)
UMPIRE (Focal Team and Opponents)	−1.528 (1.09)	−0.613 (1.50)	−0.735 (0.38)*	2.357 (1.87)	−1.566 (1.08)	−0.604 (1.46)	−0.719 (0.38)*	2.259 (1.71)	−1.704 (1.08)	−0.759 (1.70)	−0.760 (0.39)**	2.354 (1.63)	−1.615 (1.07)	−0.822 (1.74)	−0.758 (0.39)**	2.375 (1.66)
UMPIRE (Focal Team and Neutral)	−0.184 (0.34)	0.090 (0.38)	0.428 (0.35)	−0.084 (0.37)	−0.173 (0.34)	0.113 (0.38)	0.416 (0.34)	−0.121 (0.37)	−0.168 (0.34)	0.010 (0.39)	0.441 (0.35)	−0.088 (0.38)	−0.179 (0.34)	−0.003 (0.39)	0.431 (0.35)	−0.058 (0.38)
PITCH (Similar to Home Pitch)	−0.466 (0.37)	−0.834 (0.34)**	−0.253 (0.33)	0.145 (0.36)	−0.469 (0.37)	−0.840 (0.34)**	−0.256 (0.33)	0.186 (0.36)	−0.412 (0.38)	−0.821 (0.34)**	−0.265 (0.33)	0.155 (0.36)	−0.460 (0.38)	−0.829 (0.34)**	−0.245 (0.34)	0.148 (0.37)
PITCH (Not Similar to Home Pitch)	−0.626 (0.51)	−0.214 (0.42)	−0.735 (0.38)	−0.129 (0.37)	−0.687 (0.52)	−0.191 (0.42)	−0.719 (0.38)	−0.114 (0.37)	−0.684 (0.53)	−0.194 (0.42)	−0.760 (0.39)	−0.130 (0.37)	−0.644 (0.53)	−0.201 (0.43)	−0.758 (0.39)	−0.114 (0.38)
DEBUTANT (Focal Team)	−0.204 (0.21)	0.003 (0.15)	−0.273 (0.14)*	−0.501 (0.16)***	−0.195 (0.21)	−0.001 (0.15)	−0.263 (0.14)*	−0.569 (0.17)***	−0.157 (0.21)	0.024 (0.16)	−0.269 (0.14)*	−0.590 (0.17)***	−0.158 (0.21)	0.017 (0.16)	−0.274 (0.15)*	−0.580 (0.17)***
DEBUTANT (Opponents)	−0.015 (0.13)	0.421 (0.15)***	0.292 (0.24)	0.202 (0.15)	−0.021 (0.14)	0.441 (0.15)***	0.293 (0.24)	0.261 (0.15)*	−0.029 (0.13)	0.436 (0.15)**	0.307 (0.24)	0.278 (0.15)*	−0.013 (0.13)	0.432 (0.15)***	0.318 (0.24)	0.276 (0.15)*
SEASON (Winter)	0.431 (0.78)	0.129 (0.44)	−0.628 (0.44)	0.784 (0.41)*	0.281 (0.79)	0.120 (0.44)	−0.617 (0.44)	0.754 (0.41)*	0.332 (0.81)	0.139 (0.45)	−0.627 (0.44)	0.798 (0.42)*	0.444 (0.83)	0.153 (0.45)	−0.603 (0.44)	0.813 (0.42)*
SEASON (Autumn)	0.677 (0.43)	−0.038 (0.37)	0.108 (0.37)	0.736 (0.35)**	0.692 (0.43)	−0.055 (0.37)	0.119 (0.37)	0.754 (0.35)**	0.683 (0.44)	0.014 (0.37)	0.103 (0.37)	0.756 (0.36)**	0.730 (0.44)*	0.010 (0.37)	0.104 (0.37)	0.769 (0.36)**
SEASON (Spring)	0.451 (0.40)	−0.372 (0.39)	0.097 (0.43)	0.635 (0.36)*	0.535 (0.40)	−0.389 (0.39)	0.122 (0.44)	0.724 (0.36)**	0.475 (0.41)	−0.335 (0.39)	0.137 (0.44)	0.775 (0.37)**	0.482 (0.41)	−0.325 (0.39)	0.150 (0.44)	0.771 (0.37)**
BOWECON*FIELDING (Focal Team)					0.078 (0.04)**	−0.056 (0.05)	0.010 (0.04)	−0.110 (0.04)***	0.072 (0.04)*	−0.055 (0.05)	0.012 (0.04)	−0.108 (0.04)***	0.075 (0.04)*	−0.055 (0.05)	0.013 (0.04)	−0.101 (0.04)**
BOWECON*FIELDING (Opponents)					−0.058 (0.04)	−0.013 (0.04)	−0.046 (0.04)	0.068 (0.04)*	−0.066 (0.04)	−0.020 (0.05)	−0.044 (0.04)	0.072 (0.04)**	−0.061 (0.04)	−0.017 (0.05)	−0.045 (0.04)	0.075 (0.04)**
EXTRA*FIELDING (Focal Team)									−0.020 (0.01)**	−0.011 (0.01)	0.007 (0.01)	0.006 (0.01)	−0.019 (0.01)**	−0.012 (0.01)	0.008 (0.01)	0.007 (0.01)
EXTRA*FIELDING(Opponents)									−0.011 (0.01)	0.022 (0.01)**	0.009 (0.01)	−0.014 (0.01)*	−0.009 (0.01)	0.022 (0.01)**	0.008 (0.01)	−0.014 (0.01)*
BOWECON*EXTRAS (Focal Team)													−0.007 (0.01)	0.006 (0.01)	−0.006 (0.01)	0.013 (0.01)
BOWECON*EXTRAS (Opponents)													−0.014 (0.01)	0.005 (0.01)	0.003 (0.01)	−0.006 (0.01)
Table 3 Contd .Number of Observations	899	706	926	893	899	706	926	893	899	706	926	893	899	706	926	893
Log-likelihood	492.398	382.966	472.883	509.413	487.161	381.267	471.613	500.791	480.351	375.488	470.160	496.772	478.351	375.016	469.821	494.471
Nagelkerke R^2	0.730	0.759	0.775	0.742	0.734	0.760	0.776	0.747	0.739	0.765	0.777	0.750	0.740	0.765	0.777	0.751
Hosmer-Lemeshow goodness of fit χ^2 (8)	10.459^#	2.563^#	3.971^#	4.691^#	6.219^#	2.667^#	3.783^#	5.254^#	4.115^#	3.885^#	1.537^#	6.505^#	8.582^#	3.678^#	2.958^#	3.774^#

Note: Robust standard errors are in parentheses; *significant at 10%, **significant at 5%, ***significant at 1% (all two-tailed tests). ^#Model significant at 5% (indicated in the last row under Hosmer-Lemeshow goodness of fit χ2). Legend^: Aus – Australia, Eng – England, India – Ind, Pak – Pakistan.

It can be observed that in model 1(not including any interaction effects), the variables BOWECON (Focal Team and Opponents), FIELDING (Focal Team and Opponents), and FOUR (Focal Team and Opponents) are significant at 1% for all four teams. The variable EXTRA (Focal Team) is significant for Australia at 1%, and EXTRA (Opponents) is significant for Pakistan at a 5% significance level. The variables SIX (Focal Team and Opponents) are significant for England, India, and Pakistan at 5% and Australia, India, and Pakistan at 1%, respectively. The variable DEBUTANT (Focal Team) was found to be significant for Pakistan at 1%, while DEBUTANT (Opponents) was found significant for England at the same level. The variable UMPIRE was found to be insignificant for all the teams. The variable PITCH was significant for only England at 5% and SEASON for only Pakistan at the same level.

The results from model 2 (interaction of BOWECON and FIELDING) show that the variables BOWECON (Opponents), FIELDING (Focal Team and Opponents), FOUR (Focal Team and Opponents) are significant at 5% for all the four teams. The variable BOWECON (Focal Team) was significant for England, India, and Pakistan at 1%. EXTRA (Focal Team) was significant for Australia and England at 1%, while the EXTRA (Opponents) variable was also significant for Australia and England at 5%. The variable SIX (Focal Team) was significant for England, India, and Pakistan at 5%, while the variable SIX (Opponents) was significant for Australia, India, and Pakistan at 1%. The variable DEBUTANT (Focal Team) was found to be significant for Pakistan at 1%, while the variable DEBUTANT (Opponents) was found significant for only England at 1%. The variable UMPIRE was found to be insignificant for all the teams (similar to model 1). The variable PITCH was found to be significant for England at 5%. SEASON was significant for Pakistan at 5%, and the interaction effect of BOWECON*FIELDING (Focal Team) was significant only for Australia and Pakistan at 5%.

The results from model 3 (interaction of BOWECON and FIELDING, EXTRA and FIELDING) show that the variables FOUR (Focal Team and Opponents) are significant at 1% for all four countries. BOWECON (Focal Team and Opponents) was significant at 5% for England, India, and Pakistan. EXTRA (Focal Team) was insignificant for all the teams, while the variable EXTRA (Opponents) is significant only for Pakistan at 5%. The variable FIELDING (Focal Team) was significant for all the teams at 5%, while FIELDING (Opponents) was significant for England, India, and Pakistan at 1%. SIX (Focal Team) was significant for England, India, and Pakistan at 5%, while SIX (Opponents) was significant for Australia, India, and Pakistan at 1%. DEBUTANT (Focal Team) was significant for Pakistan at 1% while DEBUTANT (Opponents) was significant for England at 5% level. UMPIRE as a variable was significant only for India at 5%. PITCH was significant only for England at 5% and SEASON only for Pakistan at the same level. The interaction effect, BOWECON*FIELDING (Focal Team), was significant for Pakistan at 1%, while the interaction effect, BOWECON*FIELDING (Opponents), was significant for Pakistan at 5%. The interaction effect, EXTRA*FIELDING (Focal Team), was significant for Australia at 5%, and for “Opponents” was significant for only England at 5%.

The results from model 4 (interaction of BOWECON and FIELDING, EXTRA and FIELDING, BOWECON and EXTRA) show that the variables FIELDING (Focal Team), FOUR (Focal Team), and FOUR (Opponents) were significant for all the teams at 5%. The variables BOWECON (Focal Team), BOWECON (Opponents), and FIELDING (Opponents) were significant for England, India, and Pakistan at 5%. EXTRA (Focal Team) was insignificant for all the teams, while EXTRA (Opponents) was significant for Australia and England at 5%. SIX (Focal Team) was significant for England, India, and Pakistan at 5%, while SIX (Opponents) was significant for Australia, India, and Pakistan at 1%. DEBUTANT (Focal Team) was significant for only Pakistan at 1% while DEBUTANT (Opponents) was significant only for England at the same level. UMPIRE was significant for India at 5%, while PITCH was significant only for England at 5%. SEASON and interaction effect of BOWECON*FIELDING (Focal Team and Opponents) were significant only for Pakistan at 5%. The interaction effect of EXTRA*FIELDING (Focal Team) was significant for only Australia at 5%. In contrast, EXTRA*FIELDING (Opponents) was significant only for England at the same level. The interaction effects, BOWECON*EXTRAS (Focal Team) and BOWECON*EXTRAS (Opponents), were insignificant for all four teams.

To summarise the analysis results, we observe that different teams have different variables (including the interaction effects) significantly influencing the win/loss outcome. Therefore, it is critical to analyse and model the dependent variable for each playing nation separately to predict match results. Coaching staff, cricket administrators, and all other stakeholders who depend on win/loss prediction of match outcomes involving different teams need to separately strategize for each team instead of considering common factors (as discussed in this study). Extant literature on cricket research (refer to Appendix A) includes discussions on specific variables in a generic fashion for different formats of cricket such as ODI or T20 or Test matches or Indian Premier League (IPL). They include Cannonier et al. (2015) on T20 vs. Indian Premier League (IPL) vs. ODI, Ahmed et al. (2013) for player selection attributes in IPL, Premkumar et al. (2020) for player evaluation in ODIs, and Bhaskar (2009) and Dawson et al. (2009) on toss on influencing the outcome of the match. Our study addresses this gap by focusing on specific predictor variables influencing outcomes for four leading cricketing countries.

5. Discussion

This study aimed to determine a team-wise strategy in terms of different explanatory variables and their interactions influencing the log odds of winning. We discuss the winning strategy and implications for the coaching staff and cricket administrators below. For some of the variables considered in the models, historical mean scores may be used to predict match outcomes such as FIELDING, BOWECON, EXTRA, FOUR, and SIX. The other variables will be known in advance, including SEASON, PITCH, and UMPIRE. For the variable DEBUTANT, depending on the nature of the impact of the variable for the specific team, it may be considered in the selection of probable to form the playing eleven. Thus, the independent variables are pre-determined with input values to predict match outcomes. We can see that different variableimpact the match outcome for different teams under consideration. Hence, the winning strategy is not a one size fits all approach as reported in studies in the past.

5.1. Team strategy implications

5.1.1. Australia

The core dimensions of batting, bowling and fielding are significant in influencing the winning outcome for the Australian side. Pitch condition, the season of play, nationality of umpires, and the number of debutants play an insignificant role. In Model 2, it is seen that a higher count of bowlers bowling with a specific economy rate and good fielding display increases the odds of winning by 8%. In comparison, it declines by 7% when the Australian team concedes extra runs, everything else remaining the same. The probability of winning for the side is maximum (at 60%) when fielding dismissals are high, and batters score more fours (at 55%). In Models 3 and 4, the interaction of extra runs conceded by Australian bowlers and fielding dismissals reveals a decline of 2% in the log odds of winning (other things being the same). This indicates the importance of bowling discipline in influencing match outcomes relative to fielding dismissals.

For the Australian team, selectors and coaching staff should pay greater attention to the core dimensions of the game – bowling discipline and fielding prowess. Focus on players with reasonable fitness levels and fielding skills, in addition to bowlers with a disciplined attack and conceding minimum extra runs, should be the key to increasing win probability in the ODI format.

5.1.2. England

More debutants playing on the opposition side increase the log odds of winning for England by more than 50%, as observed in all the models, with other things being unchanged. From a batting perspective, fours scored by the opposition has a higher bearing on match outcome (probability of a win for England at 44% – a gap of 6%) as against the fours and sixes scored by England batsmen (win probability of about 54% – a gap of 4%) with other things remaining unchanged. Once again, it is seen in both Models 3 and 4 that BOWECON and FIELDING have the single most significant impact on the log odds of winning (at 71% and 70%, respectively). In addition to DEBUTANT, it is seen that when England plays in pitches similar to English conditions (i.e., Australia, New Zealand, South Africa, and West Indies), win probability is only 31% compared to home pitches where home conditions favour the team.

To summarise, economical bowling and fielding are vital for England. Batting of the opponents (in terms of fours scored) has a more significant negative influence on the outcome, vis-à-vis the England team scoring boundaries. As to extraneous variables, debutants playing for the opposition and pitches also influence the outcome (DEBUTANT positively impacting a win). Thus, the focus remains on bowling and fielding for the coaching staff and selection committee. Batting plays second fiddle to bowling and fielding.

5.1.3. India

Results for India indicate the power of batting, bowling, and fielding to influence the log odds of a win. At the same time, none of the interactions are significant in any of the models. In Models 3 and 4, it is observed that the log odds of winning for India increase by 21% (55% win probability) and 25% (56% win probability) respectively when the team scores more fours and sixes, other variables remaining unchanged. It has been a clear strategy for the India batsmen to go the aerial route while batting with the highest mean value of sixes amongst all four teams. On the bowling front, Model 4 results indicate that India’s probability of winning is 75% when more bowlers bowl economically and is at 60% when fielding performance through dismissals is high, everything else remaining unchanged. However, winning probability drops to 33% and 36%, respectively, when opposition bowlers are economical and create more fielding dismissals. It is also estimated that the win probability for India is only 32% when the country plays in pitches outside the subcontinent as against in India, namely, Australia, England, New Zealand, South Africa, West Indies, etc.

Hence it can be summarised that economical bowling and on-field dismissals through catches, stumping, and run-outs are vital for a high win probability. This can be seen in the strategy adopted by Indian team management post the 2007 ICC World Cup on player fitness, including minimum sprinting speed criteria for selection, in addition to fielding and bowling coaches.

5.1.4. Pakistan

For Pakistan, in addition to batting prowess through boundaries, winning probability is highest when bowlers are economical (at 73%), and fielding dismissals are high (at 69%), everything else remains the same (see Model 4). However, it is interesting to note that the negative influence of opposition performance is higher for BOWECON, wherein the loss probability for Pakistan is 76%. Scoring boundaries favours a win for Pakistan more than opposition scoring runs through fours and sixes, and it remains a conscious strategy to have more hard hitters in the team. Introducing more debutants turns out to be a dampener, with the win probability at 36%. Compared to Summer, Spring, and Autumn, which are more favourable for wins (at 68%), from a season’s perspective. There are two significant interactions at 5% in Model 4, revealing that the influence is counter-intuitive, though marginal. When more Pakistani bowlers are economical, and fielding dismissals are also high, the win probability is 48%. It increases to 52% when the same interaction effect is considered for the opposition, with everything else remaining the same.

To summarise, Pakistan tends to lose more matches when they introduce debutants, while batters hitting boundaries favour the odds of winning. Economical bowling and fielding dismissals are important, though opposition teams with high BOWECON have a more significant negative influence on match outcome. Spring and Autumn seasons favour the team compared to Summer. The overall summary of team strategy implications is presented in Table 8 below.

Table 8. Summary of team strategy implications.

Team
	Australia	England	India	Pakistan
Strategy Implications	Bowlers were sticking to line and length with minimum extras conceded, and fielders supporting the bowlers by taking catches, run-outs, and stumping is the key to winning.	In addition to fielding dismissals and more bowlers meeting the economic criteria, debutants with opposition side help win while playing in similar pitches, i.e., Australia, New Zealand, etc., does not.	Fielding dismissals and BOWECON are critical for high win probability. When the opponent fields well and is economical, the results are reversed. The Indian team does not fare well in unfamiliar pitch conditions, i.e., Australia, England, etc. Boundaries scored by Indian batsmen help the team to win – a clear strategy to have hard hitters in the side.	Spring and autumn seasons, with runs scored through boundaries, favour win. Debutants do not help the victory cause, while BOWECON and FIELDING are vital.

6. Model validation

The models were validated with an in-sample and out-of-sample estimation exercise independently (refer to Table 9). It was found that the prediction accuracy of match outcome was more than 75% in most models (except in two models for Australia) in the in-sample validation test. A split-case in-sample test was developed with 20% randomly selected matches played by the four sides to arrive at the logit regression coefficients of the estimation variables for each model. Once the equations were formulated with the newly derived logit regression coefficients, the values of independent variables for the remaining sample were used to predict the match outcome.

Table 9. Model validation results.

Model	In-sample^#				Out-of-sample^#
	Australia	England	India	Pakistan	Australia	England	India	Pakistan
Model 1	86.41	76.31	88.88	82.72	84.62	75.00	78.57	75.00
Model 2	81.52	76.97	88.88	84.29	69.23	87.50	78.57	75.00
Model 3	71.73	78.94	87.30	84.29	69.23	62.50	85.71	75.00
Model 4	70.65	78.94	87.30	84.29	61.54	87.50	78.57	75.00

#Prediction accuracy of the models is in percentage terms; In-sample data is taken as 20% of the matches played by the sides for model validation; Total of 39 games considered for out-of-sample validation between July 15 2019and 2nd December’ 2020.

For out-of-sample validation, the model was tested against all matches played by the sides after the conclusion of ICC World Cup 2019. The sample included all the games played by the four countries between July 14th’ 2019 and December 2nd’ 2020. During this period, 39 matches were played by the four teams, with Australia playing 13, England 8, India 14, and Pakistan 4 matches. The prediction accuracy was 75% and above for most models except 12.5% of the cases at about 70% and the remaining 12.5% around 60%. Model validity was ascertained based on the results of both tests and may be applied to devise the game strategy for different teams.

7. Conclusion

Since the first ODI was played between Australia and England on January 5th’ 1971, so far (as of May 22nd’ 2020), 8510 official ODI matches have been played across the globe. The game has evolved significantly over the last five decades with many changes in laws, playing styles, equipment and accessories used, and crowd preferences, in addition to match strategy deployed by the teams. The role of aggressive batting and bowling in winning ODI and T20 matches (Cannonier et al., 2015), home pitch advantage (Davis et al., 2015; De Silva & Swartz, 1997), toss and batting order (Dawson et al., 2009), attendance in test cricket (Sacheti et al., 2016), the role of umpires (Sacheti et al., 2015), and opening partnerships (Valero & Swartz, 2012) were some of the noteworthy studies which covered different aspects of the game influencing outcomes across formats. However, it is critical to acknowledge each national team’s strengths and weaknesses and their approach to a match, which has been a research gap. This study evaluates the same for the four major international teams and recommends the strategy to increase the odds of winning. While journalists and cricket experts discuss and strategize a lot on batting prowess and the role of pinch hitters and hard hitters in ODI cricket, our findings reveal that it is not a common determinant across teams. It has a more significant role to play for the subcontinent teams of India and Pakistan when they score runs through boundaries, but not as much for England and Australia. The two most vital variables influencing win outcome positively for all four teams in the role of fielding dismissals and economical bowling with a higher number of bowlers meeting the economy criteria. It has been a pattern for most teams to appoint specialist fielding and bowling coaches in recent years, and several teams have witnessed the impact of the same as well. Hence, these four teams must continue to invest in the bowling and fielding aspects and thus align team selection strategy on those lines.

In contrast, other teams may consider applying the validated models to devise their respective strategies. Contrary to the past findings, this study does not see the role of the umpire’s nationality influencing outcomes. Similarly, the season of play and home advantage has a differential influence across teams on the match outcome. Debutants are expected to either be match-winner to make a solid claim to the side or fail due to pressure. Our findings show differing results for different teams. Hence, a generalised view of using debutants in pressure matches for a win does not influence the outcome for Australia, England, or India.

8. Managerial implications

This study establishes that different aspects of the game have a differing influence on the winning outcome for different national sides in ODI cricket. The proposed and validated models serve as a solid indicator to devise a match strategy, which could be deployed by the four teams modelled in the paper. Essentially, it entails using historical data applied to the proposed models for the different countries to predict the match results and devise the strategy around batting, bowling fielding, and other criteria. Historical mean scores may be used for variables such as FIELDING, BOWECON, EXTRA, FOUR, and SIX. In contrast, variables like SEASON, PITCH, and UMPIRE shall already be known per the schedule shared by the respective boards and ICC. For those models wherein DEBUTANT is a significant variable, the decision is based on the win/loss outcome impact. Other cricketing nations may develop respective predictive models after testing and validating them as proposed in the study to devise their match strategy.

9. Limitations and future research directions

The study has several limitations. The scope of the study includes four major cricketing nations. Hence, there is a scope to advance the domain to other cricketing countries such as West Indies, Sri Lanka, New Zealand, Zimbabwe, and upcoming performers, namely, Afghanistan, Ireland, Netherlands, etc. Further, the study focuses on data for men’ “s cricket representing national sides, and hence similar comparative study for women” ‘s national side, club, and university level cricket teams remains an interesting and future area of work. Second, the models developed in the study exclude variables such as number of specialist batters, number of specialist bowlers, number of all-rounders, number of spin versus fast bowlers in the team composition. This could be an exciting area of research for the future. Third, the study has been based on historical data of ODI matches. It may also be worthwhile to test and validate the models for T20 cricket and alternately build predictive models for the shorter format. These are future research directions on the domain that will significantly improve the body of literature in the future.

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

The author(s) reported there is no funding associated with the work featured in this article.

Notes

1. Australia – 899 matches from 5^th January’ 1971 to 11^th July’ 2019, England – 706 matches from 5^th January’ 1971 to 11^th July’ 2019, India – 926 matches from 13^th July’ 1974 to 9^th July’ 2019, and Pakistan – 893 matches from 11^th February’ 1973 to 5 July’ 2019.

Appendix A.

Review of literature summary

Table

Attribute	Author (Year)	Methodology	Key Findings
T20 vs. Indian Premier League (IPL) vs. ODI Strategy	Davis et al. (2015)	Conditional (Fixed-Effect) logit model	The paper demonstrated that the best winning strategy in 20 overs and 50 overs is attacking batting and defensive bowling. Data used in the study consisted of Indian Premier League, Twenty 20, and ODI matches played in 2008 and 2009.
Fast Bowling	Feros et al. (2018)	Systematic literature review	The paper found diversity in how fast bowling skills were reported, including bowling speed, accuracy, spell length, delivery sequence, etc. The authors point to a need for standardised fast bowling skill assessment measures.
Wicket Keeping	MacDonald et al. (2013)	Systematic literature review	Findings indicate research papers are scarce about wicket-keeping in cricket. More work around the wicket keeper’s movement needs to be collated with details on their reactive decision-making capabilities for further skill enhancements.
	MacDonald et al. (2018)	Video analysis	Using video footage of the 2011 ODI world cup, the study found movement activities such as lateral step, lateral shuffle, running to the stumps as the essential movement activities. Receiving the ball from the field, underarm throw, receiving the ball following bowler’s delivery was found to be critical skill activities.
Player Evaluation Player Evaluation	Davis et al. (2015)	Simulation	The paper infers on the “Expected run differential”, i.e., how many additional runs a player scores vis-a-vis the same level player.
	Croucher (2000)	Duckworth-Lewis based resource table	The paper proposes a new statistic, “Runs per match”, to measure the performance of batsmen and bowlers in ODIs.
	Lewis (2005, 2008)	Correlation analysis	The paper used the concept of resources consumed as proposed in Duckworth-Lewis’s idea of resources as a means to measure batting and bowling performance.
	Saikia, H., Bhattacharjee, D. & Lemmer, H.H. (2012)	Subjective weights to cricketing parameters.	The paper suggests two measures to determine fielding performance- Preparatory measure and fairer fielding measure. The statistic was demonstrated using data from the final of the 2007 T20 world cup.
	Koulis et al. (2014)	Hidden Markov model	The paper develops a model for assessing individual batting performance in ODIs. It provides details on batsman availability, reliability, failure rate, and mean time to failure.
	Karnik (2010).	Multiple regression	The paper studied player selection criteria in the 2008 IPL and found that the number of runs and wickets taken, all-around performance, lower age, and nationality (preference for players from India and Australia) were desirable player attributes.
	Ahmed et al. (2013)	Multi-objective optimisation	The paper proposes an algorithm for player selection by optimising a team’s batting, bowling, fielding strengths, and other cricketing parameters. The algorithm is validated using data from the fourth edition of IPL.
	Premkumar et al. (2020).	Factor analysis	The paper uses a dynamic approach to generating factor scores for the valuation of players in ODIs.
	Saikia et al. (2013).	The binomial option pricing model	The study developed a measure to quantify player performance and compared it to the valuation of players in IPL.
	Damodaran (2006)	Stochastic dominance rules and Bayesian approach	The paper demonstrates the use of Stochastic dominance rules in determining the performance of Indian batters in ODI matches.
	Prakash et al. (2016)	Machine learning-based approach	The paper developed Deep Performance Index (DPI) to evaluate player performance in IPL matches.
	Singh et al. (2011)	Fuzzy logic	The paper proposes a fuzzy logic-based model to determine the player performance.
Umpiring Umpiring	Sacheti et al. (2015)	Multivariate negative binomial regression	The paper used leg before wicket decisions from 1000 test matches to investigate umpiring decision bias towards the home team. The study used a negative binomial regression and found evidence for home team bias.
	Manage et al. (2010).	Receiver Operating Characteristic (ROC) curves	The paper demonstrated the use of Receiver Operating Characteristic (ROC) curves to assess the quality of umpiring decisions and methods to revise targets for interrupted ODI matches between 1995 to 2009 to compare the accuracy of prediction of umpiring and procedures for procedures setting revised targets for interrupted games.
Toss	De Silva and Swartz (1997)	Bayesian approach	This paper studied the effects of winning the toss and home advantages on the chances of winning. Data from 427 ODI matches during the 1990s was taken for the study. The study suggests no effect of winning the toss on chances of winning, while the home team advantage was found to affect chances of winning.
	Bhaskar (2009)	Chi-Square and Pearson tests	Studied the consistency in choices made by teams in terms of the decision to bat or field first after winning the toss in ODI matches. The study found inconsistency in decision making attributed to information asymmetry and underweighting the opponent’s strength while outweighing its strength (or weakness).
	Dawson et al. (2009)	Logit regression	Paper studied the influence of winning the toss and batting order of the team on increasing the chances of winning in day-night ODIs. The study found that winning the toss and batting first significantly increases winning the toss and bowling first.
Home Advantage	Allsopp and Clarke (2004).	Multiple linear regression	The paper studied the importance of batting order and home team advantage on test matches and ODIs. Data from ODI and test cricket played by major cricketing nations in 1997–2001 was used for the study. The paper concluded that for test matches, a team’s first-innings batting and bowling strength, first-innings lead, batting order, and home advantage are significant influencers of winning. The study found no evidence of winning the toss on chances of winning in ODIs and test matches.
	De Silva and Swartz (1997)	Bayesian approach	Studied ODI cricket and quantified home country advantage in influencing outcome for the team equivalent to 15.6 runs.
	Clarke (1998)	Multiple linear regression	Modelled home advantage and quantified it at 14 runs.
	Davis et al. (2016)	Simulation	Studying T20 matches, they attributed nine runs to home ground advantage
Batting Strategy	McGinn (2013)	Multiple linear regression	The paper studied the effect of batting first in the day and night matches. Data from 616 ODI games played between 1999 to 2011 was used in the study. Using differences in differences estimator, the paper found that batting second provides an advantage by reducing the expected runs per over by 0.2.
	Scarf et al. (2011).	Logistic regression	The paper suggests an optimal batting strategy in test cricket. A negative binomial distribution model was developed between partnership score and innings score. Data consisted of test matches played between 1998 to 2004. The study suggested a batting strategy, especially for the third innings of the game.
	Valero and Swartz (2012)	Non-parametric binomial method	The paper used a non-parametric binomial procedure to investigate partnership synergy between batters in ODIs and tests. Data from test and ODI matches played by ten full member countries of ICC ranging from 2002 to 2012 were used. The study concludes that the synergy of opening partnership is a sporting myth.
	Bracewell, P & Ruggiero, K	Parametric control chart	The authors developed a parametric control chart to monitor batting performance in cricket. They have proposed a mixed distribution named “Ducks’ n’ Runs” using the beta and geometric distribution models.
Match Tactics	Davis et al. (2016).	Simulation	The paper used simulation to develop tactics for T20 matches. The authors assumed that teams must emphasise scoring runs rather than losing wickets while batting and, in the case of bowling, must give more emphasis on not giving runs rather than taking wickets. Thus, the study suggested that an optimal strategy could be achieved by modifying batting and bowling order.
	Perera et al. (2014).	Gibbs sampling	The paper empirically suggests when to declare in a test match. The study suggests parameters such as target score, number of overs left, relative desire to win against draw, and scoring characteristics. Data of test matches played by ten ICC teams between 2001 and 2012 was used for the study.
	Preston and Thomas (2000)	Dynamic programming	The paper developed a representation of optimal batting strategy in limited-overs matches. The article suggests an increasing run rate when setting the target and a decreasing run rate while chasing a set target. Data from English county-level matches from the 1996 season were used to develop the model.
Match Prediction	Akhtar & Scarf (2012)	Multinomial logistic regression	The paper presents a model to forecast test matches in play to enable management to consider an aggressive or defensive strategy. Pre-match team strength, ground effect, and home field were found to be significant predictors of winning.
	Asif and McHale (2016)	Dynamic logistic regression	The paper developed a model to forecast for ODI matches in progress.
	Brooks et al. (2002)	Ordered response (probit) modelling.	Used data of test matches played between 1994 and 1999 to predict test cricket outcomes.
	Santos-Fernandez, E., Wu, P. & Mengersen, K.L. (2019)	Bayesian model	The paper provides a comprehensive review of the use of Bayesian models in predicting match outcome and player performance.
	Bailey and Clarke (2006)	Multiple linear regression	The paper developed a model to predict match outcomes in one-day international matches in progress. The model used home ground advantage, past performances, match experience, performance at the specific venue, performance against the particular opposition, experience at the venue, and current form as the predicting variables.
Managerial Decision making	Sacheti et al. (2015)	Conditional logit regression	The paper finds evidence for social pressure in constraining decision-making in Twenty20 International matches.
	Borooah (2016)	Bayesian updating	The study finds points out the imperfections of the decision review system and suggests investment in umpires rather than in technology.
	Shivakumar (2018)	Logistic regression	The study focused on the quality of decision-making of the umpire as well as the participating teams.