Caste and schooling in professional cricket in India and England

Abstract

This paper’s theme is about opportunities in cricket—offered and denied. It discusses opportunities offered systemically to members of certain groups and denied to those who belong to other groups. In India, this takes the form of a person’s caste to which a person is born; in England, the type of school that one attended is relevant; and in South Africa, skin colour plays an important role in determining one’s chances of playing representative cricket. It is very easy to underestimate the importance of opportunities in sculpting sporting success by, instead, ascribing success to a sportsperson’s talent and natural gifts.

Introduction

An important determinant of social cleavage in India is the caste into which Hindus (80% of India’s population) are born, since this determines forever their position in society and plays an important role in shaping their life prospects (Thorat and Newman 2010). Similarly, in the English context, social position and life prospects are greatly influenced by the school—private or state—attended (Green and Kynaston 2019). In terms of the subject matter of this paper, the relevant question is whether in India certain castes—and in England, products of certain schools—are ‘overrepresented’, while others are ‘underrepresented’, in professional cricket. Following from this, access inequality exists if there is disproportionality between the representation of various groups in the population and their representation in a particular ‘activity’ where, for the purposes of this chapter, ‘activity’ is used to mean presence in a team of professional cricketers.

Against this background, the purpose of this paper was to first detail the role of caste and school in determining the men and women who get to play professional cricket in, respectively, India and England. The second purpose of the paper was to provide estimates of the degree of access inequality in the two countries using a novel index of inequality borrowed from the literature on income disparity.

Caste and Indian cricket

India’s caste system stratifies Hindus into mutually exclusive caste groups, membership of which is determined entirely by birth. Very broadly, one can think of four caste groups: Brahmins, Kshatriyas, Vaisyas, and Sudras.¹Brahmins, who were traditionally priests and teachers, represent the highest caste; lying below them are the Kshatriyas (traditionally, warriors and rulers) and Vaisyas (traditionally, moneylenders and traders); below these three groups are the Sudras (traditionally performing menial jobs) who are commonly referred to by their administrative name—the ‘other backward classes’ (OBC), the term ‘other’ meaning ‘in addition to those who are “outcastes”’ (see below).

Lying at the bottom of the caste hierarchy are those persons (mostly Hindu by religion, but some who have converted to Buddhism or Christianity) whom Hindus belonging to the four caste groups (listed above) regard as being outside the caste system because they are ‘untouchable’ in the sense that physical contact with them—most usually the accepting of food or water—is polluting or unclean. They are referred to as the Ati-Sudras or by their preferred name, Dalits (meaning ‘broken’ or ‘oppressed’).

For the remainder of this paper, Brahmins, Kshatriyas, and Vaisyas are collectively referred to as Forward Caste Hindus (FCH), while the OBC and Dalits, as a collective, are referred to as Backward Caste Hindus (BCH).² It is difficult to get caste data in India except for specific states like Bihar which, in October 2023, released caste data for the state. The Census of India provides data on Dalits (Scheduled Castes) and on Scheduled Tribes but no information on the OBC about which must be inferred from Surveys like the National Sample Survey (NSS). According to the NSS’s 2017–2018 Periodic Labour Force Survey (PLFS-2017/2018) for India,³ 53% of India’s population was BCH (as defined above) of whom 18% were Dalits and 35% were from the OBC; 24% was FCH (as defined above); 14% were Muslim; 7% were from the Scheduled Tribes⁴; and 2% were mainly Christians and Sikhs.⁵

An analysis of the castes of Indian cricketers who were included in the 18-man Test squad for the Australian Tour of 2020–2021 shows that only two (11% of the squad) were BCH even though, as noted above, this group comprises 53% of India’s population; on the other hand, 12 members (67%) were FCH, who comprise 24% of the national population. Moreover, although only about 6% of Indians are Brahmins, four members of the 18-man squad (22%) were of this caste. In total, of the 18-man party, only six (33%) were not FCH: two BCH, two Muslims, and two Sikhs.

A corresponding examination of the castes of Indian cricketers who were included in the 15-woman squad for the T20 World Cup competition played in Australia over February–March 2020 showed that, here too, only two of the 15-woman squad (13%) were BCH.⁶ On the other hand, FCH women (of whom three were Brahmins) claimed 10 of the 15 places (67%).⁷

To guard against the possibility that, by focusing exclusively on inclusion in the national teams, the analysis was providing an excessively narrow picture of access, the caste composition of the cricket squads of the eight Indian Premier League (IPL) men’s teams and its three women’s teams were also studied. Since its inception in 2007, the IPL has become, through its system of buying players in open auction, a major source of income for Indian cricketers and it would be no exaggeration to say that securing a place on one of its squads is today a major aspiration of Indian—and, indeed, overseas—cricketers.⁸

The caste groups of domestic players in the eight men’s and three women’s IPL teams mirror the dominant presence of FCH in the national teams. Of the total of 125 Indian men in the IPL squads, 16 (13%) were BCH, 13 (10%) were Muslim, eight (6%) were Sikhs, and three (2%) were Christians, with the other 84 players (67%) being FCH.⁹ The number of Brahmins in the squads (34) was a little less than the total of non-FCH players (41) and was more than twice the number of BCH players. The women’s IPL tells a similar story. Of the 32 Indian women in the three squads, four were BCH (13%), one was Muslim, four were Sikhs (13%), and two were Christian (6%); the other 21 players (66%) were FCH and, of these 21 FCH players, eight were Brahmin. For women, as for men, the number of Brahmin squad members was twice that of BCH. These figures offer little doubt that both male and female BCH, notwithstanding the fact that they comprise most of the Indian population, are grossly underrepresented in cricket; by contrast, Brahmin men and women, notwithstanding the fact that only 1 in 20 Indians is Brahmin, are greatly overrepresented.

Post-independence India, caste, and cricket

The exclusion of BCH from Indian cricket is largely a post-independence phenomenon. As Majumdar (2006) has pointed out, cricket for Indians in pre-independence India depended greatly on the patronage of native rulers—to name but a few, Natore and Cooch Behar in Bengal; Dhar, Idar, and Gwalior in Central India; Jamnagar in Gujarat; Patiala in Punjab—who recruited without consideration of caste or religion, their sole aim being to show that Indian sides could beat the English at their own game.¹⁰ As Ray (2008) points out in his account of cricket in India, “the 1911 ‘All-India’ side touring India had representatives from all major communities and, almost unbelievably, included an ‘untouchable’, Palwankar Baloo” (p. 1639). Guha (1992) provides a history of cricket in India and recalls the great names and moments of Indian cricket through the selection of ten regional all-time XIs featuring legends such as Ranji, the Nawabs of Pataudi, Merchant, Mankad, Gavaskar, Engineer, Bedi, Viswanath, Abid Ali and Kapil Dev.

Ray (2008) also charts the trajectory of the different sports in the affections of the Indian public. After Indian independence in 1947, football, hockey, and cricket jostled with each other to become the nation’s pre-eminent sport. After some early successes in international tournaments by football and, most markedly hockey—in which India won Olympic gold seven times—both sports went into decline as further success became elusive. By contrast, after a stuttering post-independence start, Indian cricket, after its team won cricket’s World Cup in 1983, went from strength to strength and, four years later, hosted the next World Cup and repeated this feat in 1996, 2011 and 2023. The popularity of cricket in India was greatly enhanced by the Indian Premier League T20 tournament, started in 2007, and acknowledged as the world’s most lucrative and important tournament. Today, cricket is unquestionably, India’s pre-eminent sport followed by people from all parts of India and all sections of society.

In terms of patronage, the fortunes of India’s native leaders declined after independence in 1947 and support of Indian cricket shifted to corporate bodies. The main change here was that companies recruited cricketers as their employees, at decent salaries, to play cricket for the company team but mostly preferred them to be graduates so that, after retiring from cricket, they could be usefully employed in regular company business.¹¹

This change in patronage immediately disadvantaged players from the Backward Castes: the PLFS-2017–2018 showed that 39% of FCH were graduates compared to only 23% of BCH. Consequently, the change from native ruler to corporate patronage saw employment opportunities drying up for Backward Caste cricketers while simultaneously expanding for those from the Forward Castes. Although it would be invidious to regard this contraction/expansion of employment opportunities as direct discrimination, it might be legitimate to see the ‘graduate requirement’ as an instance of indirect discrimination whereby the same requirement—which bore little relevance to the quality of a person’s cricket—imposed on all prospective employees—had a differential impact on persons from different groups.

Barriers to entering professional cricket in India have had two effects. First, they have led BCH sportspersons to drift away from cricket and seek success in other team sports, most notably hockey and football: the 20-member Indian hockey squad for the 2020 International Hockey Federation (FIH) Pro-League hockey tournament included just two Brahmins. Second, the concentration of FCH in cricket has led to a homogenisation of that sport, with both male and female cricketers drawn, by and large, from the same social strata.

Homogenisation can be self-perpetuating because it magnifies the role of family, friends, and acquaintances in securing a favourable outcome about, say, a job, a loan, a home rental, admission into an educational institution or hospital. This is the network concept of allocation under which it is ‘who you know’ that determines the chance of doing well. And who you know (the density of one’s network) depends critically on one’s group identity.¹² Jardina (2019, p.4) makes the argument that identity—‘a psychological, internalised sense of attachment to group’—provides a cognitive structure for individuals to participate in a variety of social, political, and economic activities.

At present, the most usual route to becoming a professional cricketer in India is to seek admission to a cricket training academy¹³ and it is not implausible that networks play a significant role in securing entry. In addition to admission, there is the matter of affordability.¹⁴ The upshot is that cricket in India has become an elite sport, commanding levels of glamour and remuneration that other sports can only dream of. It has been so completely captured by the country’s elites as to make it near impossible for India’s deprived groups to penetrate this bastion. As a non-contact sport, it also provides FCH with the added advantage of finessing any inhibitions they might have about physical contact with the ‘wrong’ sort of person.

Indian cricket can, however, claim credit for the geographical dispersion of the game. Earlier, players were largely drawn from metropolitan conurbations, mostly from Bombay (now Mumbai). Today, however, a significant number of players come from small towns and from a wide range of states. Between 1958 and 59 and 1972–1973, Bombay won the Ranji Trophy—India’s premier first-class competition, played between its states and named after Sir Ranjitsinhji (‘Ranji’ to cricketing aficionados)—15 consecutive times; in the 17 competitions between 2000–2001 and 2018–2019, Mumbai won the championship just seven times. Equally pertinently, teams which had never won the trophy in the twentieth century began winning in the 21st: Railways in 2001–2002 and again in 2004–2005; Uttar Pradesh in 2005–2006; Rajasthan in 2010–2011; Gujarat in 2016–2017; and Vidarbha in 2017–2018 and 2019–2020.

Between 1952 and 1956, there were six occasions on which seven of the men’s Indian Test team were from Bombay and, in the decade 1980–1990, eight cricketers from Bombay made their debut for India. In the decade between 2003 and 2013, however, only three of the 30 male cricketers who debuted for India in Test Matches were from Mumbai with Uttar Pradesh and Tamil Nadu each supplying five, and Delhi providing four debutants.¹⁵ So, the increased geographical spread of cricket in India cannot be in doubt. The fly in the ointment, however, is that geographical diversity has not eroded Indian cricket’s caste concentration and professional cricketers in India continue to be drawn largely from FCH.

It is appropriate to say a few words about the selection process for Indian cricketers because, ultimately, that determines who will play for the country. The selection committee for the Indian men’s and women’s team each comprises five paid members of whom one—currently Ajit Agarkar for the men and Aarti Vaidya for women—is the chief selector. The selectors are chosen without regard to their regional allegiances, and this contrasts with the earlier system of honorary selectors, representing their respective geographical zones and ipso facto pushing for the selection of their zone’s cricketers.

Nonetheless, while the current selection process is a vast improvement on its predecessor, it is handicapped by the allegation that, in assessing talent, selectors base their judgement largely on performance in the Indian Premier League (which, as has been argued, draws players from a narrow section of society) and pay less attention to non-IPL domestic cricket, like the Ranji and Hazare trophies, which might cast the social net more widely.¹⁶ This could also be harmful for the performance of Indian cricket – players who do well in the shortest form of the game (T20, requiring a certain set of skills) are chosen to represent their country in its longest form (Test Matches, requiring an entirely different set of skills).

Overarching selection problems is the fact that, given cricket plays such a prominent role with the Indian public, politicians (or their relatives) have succeeded in occupying prominent positions with the Board of Cricket Control India (BCCI). The politicisation of the BCCI, and the myriad conflicts of interest of those who participated in its affairs led the Supreme Court of India to appoint a committee, headed by retired Chief Justice Lodha, to investigate its affairs. Meyyapan (2022), however, suggests that the Lodha Committee failed to eliminate corruption in the BCCI largely because “favouritism and filial relations replaced outright conflict of interest” (p. 13): most visibly, the Secretary of the BCCI is the son of the Home Minister in the Indian government.

The school system and English cricket

Schooling in England comprises two sectors: an independent (or private) sector which charges fees and a state sector in which education is free.¹⁷ Of the 8.7 million primary and secondary school pupils in England in 2020, 8.1 million (93%) attended state schools—that is, schools which are fully or in part funded by government and under its control—and 577,000 pupils (7%) were educated in independent schools which, to all intents and purposes, are free of government control.¹⁸

It is often argued that the division of schooling in England into an independent and a state sector exacerbates and perpetuates economic and social inequalities. First, as Green and Kynaston (2019) point out, attending an independent (or private) school is the prerogative of the affluent. Given the size of their fees, access to independent schools is available only to the very wealthy and most children attending independent schools are from families with annual incomes of over £120,000 (that is, at the 95th percentile of the income ladder, meaning only 5% of families had a higher income).¹⁹

The benefits of a private education feed into people’s future careers. The Sutton Trust reported that the percentages in the various occupations in 2016 that were privately schooled were as follows: 74% of judges; 71% of barristers; 71% of top military officers; 61% of top doctors; 48% of senior civil servants (Kirby 2016). Of the UK’s 27 Prime Ministers in the twentieth and twenty-first centuries, only seven (Lloyd George, MacDonald, Wilson, Callaghan, Thatcher, Major, and Brown) went to state schools. And all this against the background of the independent sector educating just 1 in 14 pupils in England.

This imbalance is sustained by the fact that the independent sector provides a quality of education, both academic and non-academic, that state schools cannot match (Green and Kynaston 2019). In terms of sports education, a measure of this quality is provided by Smith’s (2012) description of his alma mater, Tonbridge School: ‘we had a 25-m indoor heated pool (now upgraded to a superlative Olympic version with accompanying gym and exercise rooms); we had twelve rugby pitches … two hockey astro-turfs that doubled up as twenty-one tennis courts … an Olympic standard running track … twenty cricket nets, ten artificial and ten grass’ (p. 23).

Against the backdrop of these observations, it is illuminating to examine the school backgrounds of the players in the men’s English Test squad for the India tour of 2021, and the players in the women’s English T20 squad for the World Cup of 2020. Of the 16-man Test squad, seven (44%) went to independent schools, eight went to state schools (50%), and one was educated overseas. So, the proportionate presence of independent schools in the English Test squad was comparable to its presence in the upper echelons of the Civil Service (48%) and more than its presence among Members of Parliament (32%).²⁰ These figures are in stark contrast with those for the English women’s squad for the T20 World Cup. Of the 15 women in this squad, only two (13%) went to independent schools, while the remaining 13 (87%) were the products of state schools.

To guard against the possibility that focusing exclusively on inclusion in the national teams would lead to too narrow an analysis, the school backgrounds of the cricket squads of the eight men’s and women’s squads for The Hundred competition, that had its first season in the summer of 2021, were also studied.²¹ Analysis of the school backgrounds of domestic players in the men’s Hundred teams showed that of a total of 88 franchised players, 43 (49%) attended independent schools, 42 (48%) went to state schools, and three were educated overseas. Correspondingly, of a total of 73 franchised players in the women’s Hundred squads, 18 (25%) attended independent schools, 54 (74%) went to state schools, and one was educated overseas.

Measuring access inequality

The most usual concept of ‘unfair access’ by a group to a particular ‘activity’—the activity here being inclusion in a squad of players—is that there is disproportionality between its representation in the population and its representation in that activity. The important question, however, is how to merge these group disproportionalities into a summary measure of access inequality? Such a measure should satisfy a very important property (known in the inequality literature as the ‘Pigou-Dalton condition’) which, applied to the present study, requires that an increase in the number of deprived persons in the activity, at the expense of an equal reduction in the number of non-deprived persons, should reduce access inequality; conversely, inequality would be increased by a reduction in the number of deprived, with a simultaneous increase in the number of non-deprived, persons in the activity.²²

Suppose that the country’s population in divided into several well-defined subgroups. The first step in measuring access inequality (set out in detail in a technical box) is to compute each group’s representation in the activity (hereafter, the squad) with its representation in the population. With two groups A and B, suppose group A has a 70% representation in the squad (that is, 70% of the squad comprises persons from group A) alongside a 40% representation in the population (that is, 40% of the country’s population are persons from group A), while group B has a 30% representation in the squad alongside a 60% representation in the population. So, the ratio of squad to population representation (SP ratio) is 1.75 = 7/4 for group A and 0.5 = 3/6 for group B. The next step is to aggregate these group disproportionalities, as reflected by the SP ratios, into a single measure of inequality. This is done by computing a weighted average of the SP ratios for groups A and B, the weights being their population shares. One final twist: it is the weighted average of the (natural) logarithm of the SP ratios that is computed, that is, 0.56 = log(1.75) and -0.69 = log(0.5). With this refinement, the inequality index (the single measure of inequality) is:

$$ J = - \left[ {0.4 \times \log (1.75) + 0.6 \times \log (0.5)} \right] = 0.192 $$

When each group’s share in the squad equals its representation in the population, there is no inequality and J = 0: group A’s SP ratio = group B’s SP ratio = 1 and log(1) = 0. The value of J rises with increasing levels of inequality reaching a maximum when the entire squad is composed of persons from (say) group A and there is no one in the squad from group B: the SP ratio of group A = 2.5 = 1/0.4 and the SP ratio of group B is 0 = 0/0.6. However, since log(0) is not defined, the maximum value of J will also be not defined. One can, nonetheless, get as close to the maximum value as one wishes by approximating that (say) 99% of the squad is from group A and 1% is from group B. Then, the SP ratio of group A is 2.48 = 0.99/0.4 and the SP ratio of group B = 0.167 yielding an approximation, J_max = 0.713. From this, one can infer that that the actual level of inequality, J = 0.192, is 26.9% of the maximum level of inequality, J_max = 0.713. The details of the derivation of the inequality index are set out in Appendix to this paper.

Access inequality results

The analysis for India was conducted in terms of four social groups: Brahmins, comprising 6% of the population; non-Brahmin FCH, comprising 18% of the population; BCH, comprising 53% of the population; and ‘Others’, consisting of Muslims, Sikhs, Christians, and the Scheduled Tribes, comprising 23% of the population.²³

Table 1 shows the J values, as defined by Eq. (4) for men and for women: first, for those selected to play for India and then for those selected for the IPL teams. The values of inequality, defined by J in Eq. (4), suggest that the highest inequality was associated with the men’s test squad (59.5) and the lowest inequality was with respect to the women’s T20 squad (52.0). Sandwiched in between these extremes were the men’s and women’s IPL with near identical J-values of 55.1 and 54.5, respectively.

Table 1 Access inequality in Indian cricket: J Values.

The analysis for England was conducted in terms of schooling: independent or state. Table 2 shows the J values, as defined by Eq. (4) for men and for women: first, for those selected to play for England and then for those domestic players, educated in the UK, selected for the Hundred teams. The values of inequality, defined by J in Eq. (4), suggest that, in terms of representing England, the highest inequality was associated with the men’s Test squad (38.4) and the lowest inequality was with respect to the women’s T20 squad (2.0). The men’s Hundred teams (which are city-based franchises) collectively showed a higher level of access inequality than the men’s Test team (47.1 versus 38.4) and the women’s Hundred teams, too, showed higher level of access inequality than the women’s T20 World Cup team (11.1 versus 2.0).

Table 2 Access Inequality in English Cricket: J Values^* Source: Own Calculations

A Comparison of caste-based and school-based access inequality in cricket

To compare caste-based access inequality in cricket in India with school-based inequality in England, the analysis for India was recast in binary terms comprising just two groups: FCH and non-FCH. This meant, firstly, that Brahmins, who are shown separately in Table 1, were now included among the FCH and, secondly, that the non-FCH group now comprised BCH and the ‘other’—Christians, Muslims, and Sikhs—players.

Table 3 shows the J values that result when the analysis of access to cricket in India was based on a binary divide of FCH versus non-FCH. Under this amalgamation, FCH and non-FCH comprised, respectively, 24% and 76% of India’s population.²⁴ Using these proportions, in conjunction with the figures shown in Table 3, in Eq. (4) yielded the J values shown in the last column of Table 3. Comparing the J values from the schools divide in England (Table 2) with the caste divide in India (Table 3) showed that:

• (i) For the men’s Test squads, access inequality based on caste was nearly the same as that based on schooling (J = 38.1 versus J = 38.4)

• (ii) For the women’s T20 squads, access inequality based on caste was 19 times that of access inequality based on schooling (J = 38.1 versus J = 2.0)

• (iii) For the men’s IPL squads compared with the men’s Hundred squads, access inequality based on caste was less (83%) than that based on schooling (J = 39.2 versus J = 47.1)

• (iv) For the women’s IPL squads compared with the women’s Hundred squads, access inequality based on caste was more than three times that of access inequality based on schooling (J = 36.2 versus J = 11.1).

Table 3 Access inequality in Indian cricket between FCH and non-FCH players: J values^* Source: Own Calculations

Taken in their entirety, these results suggest that, for the men’s international squads, access inequality in India based on caste was not different from England’s school-based inequality while, for the men’s franchises, access inequality in the IPL based on caste was less than that of school-based inequality in the Hundred. On the other hand, in respect of women, caste-based inequality in Indian international and IPL cricket was far more pernicious than school-based inequality in English international and Hundred cricket.

How to ameliorate access inequality

The above analysis of access inequality in Indian and English cricket raises the question of what, if anything, those in charge of the game should/could do to ameliorate such inequality. To appreciate the range of possible policies it is important to understand the origins of such inequality by framing the issue in terms of economic analysis.

Suppose that there are two groups, A and B, such that players from groups A and B practise, respectively, H_A and H_B hours per week in conjunction with ancillary facilities (coaches, diet, equipment etc.). These facilities are referred to as the capital stock of groups A and B and are represented by K_A and K_B, respectively, for the two groups. Further, suppose that N_A and N_B players from groups A and B are chosen for the squad.

If the cricketing output (runs, wickets) of the two groups is represented by, respectively, Y_A and Y_B, then the ‘production functions’ of cricketers from the two groups would depend on the total number of person-hours (number of players times hours practised by each player) of the two groups and on their respective capital stocks.

Suppose that players from the two groups are equally dedicated and are willing to practise for the same number of hours ($H_{A} = H_{B} = \overline{H}$) but that group A has better facilities available to it than group B ($K_{A} > K_{B}$). Consequently, for an input of the same number of person-hours by each group, the output of group A will exceed that of group B. However, by the law of diminishing returns, the additional output (referred to as the marginal product) resulting from the addition of another player from either group, falls.

These ideas are illustrated in Fig. 1. The horizontal axis in Fig. 1 represents from left to right the number of players in the squad from group A (N_A), while from right to left it represents the number of players in the squad from group B (N_B) where N_A + N_B = N, N is the fixed number of players in the squad. The vertical axis represents marginal product. The lines RR and SS in Fig. 1 represent, respectively, the marginal products of groups A and B (MP_A and MP_B, respectively). Both lines slope downwards indicating that the marginal product for each group diminishes for additional players from that group. The line RR lies higher than the line SS because group A has better facilities to support its players than group B ($K_{A} > K_{B}$). Output, Y, is maximised at the point X where RR and SS intersect meaning that the marginal product of the two groups is equal: MP_A = MP_B. At X, the squad comprises $N_{A}^{*}$ players from group A and $N_{B}^{*}$ players from group B. For points to the left of X, MP_A > MP_B and output could be increased by including more players from group A and concomitantly fewer from group B; for points to the right of X, MP_A < MP_B and output could be increased by reducing the number of players from group A and increasing the number from group B.

Fig. 1

Optimal Representation in Squads by Members of Groups A and B

In policy terms, there are three ways of regarding the equilibrium at X in which the makeup of the squad of N players is $N_{A}^{*} {\text{ and }}N_{B}^{*} \,$ from, respectively, groups A and B. If policy makers regard the proportion of players from groups A and B in the squad, relative to the proportionate presence of the groups in the general population as, respectively, too high and too low, then a possible solution (adopted in South Africa to redress racial imbalance) would be to impose quotas on the number of players from the two groups with the threat of sanctions imposed on teams which flout these quotas. In terms of Fig. 1, a quota which requires the number of players from group A to not exceed $\overline{N}_{A}$ would be consistent with this model.

Most observers agree that quotas in themselves provide at best a short-term solution to the absence of cricketers of colour in South African cricket.²⁵ Longer-term solutions need to be underpinned by a strategy which focuses on developing the game, among children from minority communities, at the grassroots level in terms of effective coaching, sympathetic player management, taking cognisance of players’ individual circumstances, allied to good facilities and equipment.

The English model involves building capacity among persons from group B by increasing the capital, K_B available to them. In terms of Fig. 1, this shifts the marginal productivity curve for group B from SS to ST. The new equilibrium point is Z and the number of group B players increases from $N_{B}^{*}$ to $\hat{N}_{B}$ with a corresponding reduction in the number of group A players from $N_{A}^{*}$ to $\hat{N}_{A}$.

The Indian model pretends that the problem does not exist. Caste imbalances caused neither concern nor embarrassment to India’s cricketing establishment or to its satellite of cricket commentators.²⁶ Not a single person involved in the running of, or commentating on, Indian cricket was/is prepared to acknowledge that current caste imbalances were derived from historical wrongs emanating from a culture of excluding the lower castes from education, and ipso facto all the benefits that flowed from education, and, instead, herding them into occupations that FCH would regard as dirty and demeaning. It is remarkable that none felt obliged, following the lead set by the Indian Constitution, to express sympathy, much less concern, about past injustices which, by denying opportunities to the backward castes, created these imbalances. Instead, they played caste imbalances with a dead bat: we choose on merit.²⁷ As Sandel (2020, pp. 13, 14) observed:

In an unequal society, those who land on top want to believe their success is morally justified. In a meritocratic society, this means the winners must believe they have earned their success through their own talent and hard work … the more we think of ourselves as self-made and self-sufficient, the harder it is to learn gratitude and humility. And without these sentiments, it is hard to care for the common good.

Conclusions

The narrative of this paper has been one of opportunities offered, missed, and denied. It is very easy to underestimate the importance of opportunities in sculpting sporting success by, instead, ascribing success to a sportsperson’s talent and natural gifts. As Syed (2010) writes: ‘the delusion lies in focusing on individuality without perceiving—or bothering to look for—the powerful opportunities stacked in their favour … practically every man or woman who triumphs against the odds is, on closer inspection, a beneficiary of unusual circumstances’ (p. 11). As a former English table tennis champion, Syed acknowledges the singular childhood and adolescent circumstances which worked in his favour and launched him as a future champion. As he himself modestly acknowledges:

I was the best of a small bunch … what is certain is that if a big enough group of youngsters had been given a [international standard] table tennis table at eight, had a brilliant elder brother to practise with, had been trained by one of the top coaches in the country, had joined the only twenty-four hour club in the country, I would not have been number one in England. I might not even have been number one thousand and one in England. (Syed 2010, p.10)

But how are such opportunities to be created? Prior to answering this question, administrators must admit that a problem exists. The choice facing countries is whether to turn their backs on diversity and maintain the status quo by preserving things as they are or to actively seek change through, perhaps long-term, policies aimed at spreading the jam of success more evenly over the national bread.

These choices echo Berlin’s (1969) distinction between negative and positive liberty. Negative liberty is the absence of interference by other parties in one’s actions. It is this notion of liberty that motivates those who resist change: people who think selection should be colour-blind, or casteless, or pay no heed to the type of school attended. Positive liberty, on the other hand, is the possibility of acting to take control of one’s life and realising one’s potential. Political conservatism supports negative liberty by claiming that the preservation of individual liberty requires strong curbs on the activities of the state;²⁸ proponents of positive liberty, on the other hand, argue that the concept of liberty includes citizens’ self-fulfilment, and this may require a degree of state intervention. In the context of cricket, the choice, as this paper has shown, is between negative liberty for the few or positive liberty for the many.

So, why do so many in the cricketing world resist change through diversity? It cannot be because performance standards will fall: increased geographical diversity in cricket in India has led its team of small-town players, after successive series wins against Australia and England, to the final of the 2021 World Test Championship, in contrast to the regular humiliations suffered by Bombay-centric Test teams at the hands of overseas opponents; quotas notwithstanding, the South African team inflicted an innings defeat on the West Indies in the Gros Islet Test on 12 June 2021; and England’s men’s Test side, an independent-school heavy team, crashed to a 3–1 series loss to India in March 2021 and, following that, to a 1–0 series defeat to New Zealand. In contrast, England’s women cricketers, almost all of whom are state-school products, head the International Cricket Council’s (ICC) World Cup rankings.

The obdurate belief of cricket’s supremos that nothing is wrong, when clearly something is, evokes John le Carré’s description, in his novel The Perfect Spy, of the English establishment: ‘Not bad men by any means. Not dishonest men. Not stupid. But men who see the threat to their class as synonymous with the threat to England’ (le Carré, 1986, p. 374).

Appendix: Mathematical derivation of the inequality index

Suppose that a population of N persons is divided into M mutually exclusive and collectively exhaustive groups with N_m (m = 1…M) persons in each group such that N_m and H_m are the numbers in each group in, respectively, the overall population and in the selected squad. Then, $N = \sum\limits_{m = 1}^{M} {N_{m} } {\text{ and }}H = \sum\limits_{m = 1}^{M} {H_{m} \, }$ are, respectively, the total number of persons in the overall population and in the squad.

One way of measuring inequality in a variable is by the natural logarithm of the ratio of the arithmetic mean of the variable to its geometric mean. As Theil (1967) and Bourguignon (1979) demonstrate, such a measure satisfies inter alia the Pigou–Dalton condition. This idea translates very naturally from its usual application to income inequality, to measuring the degree of inequality associated with selection outcomes in which people belonging to different population groups meet with different degrees of success of being selected for the squad.

The variable of interest is the access rate to the squad of persons from group m—defined as $h_{m} = H_{m} /H$, the proportion of persons from that group who are selected—and it is inequality in the distribution of this rate between the M groups that is sought to be measured. This inequality is referred to as ‘access inequality’.

The success rate (SR) of group m (denoted e_m) is $e_{m} = H_{m} /N_{m} , \, 0 \le e_{m} \le 1$. This is the proportion of persons in that group $(N_{m} )$ who are selected $(H_{m} )$. Then, the arithmetic and geometric means of e_m are, respectively:

$$ \overline{e} = \sum\limits_{m = 1}^{M} {e_{m} n_{m} {\text{ and }}\hat{e} = \prod\limits_{m = 1}^{M} {(e_{m} ){}^{{n_{m} }}} } {\text{ where }}n_{m} = N_{m} /N, \, \sum\limits_{m = 1}^{M} {n_{m} } = 1 $$

(1)

And the measure of access inequality is:

$$ J = \log (\overline{e}/\hat{e}) = \log (\overline{e}) - \sum\limits_{m = 1}^{M} {n_{m} \log (e_{m} )} > 0 $$

(2)

since, by the property of means, the arithmetic mean is greater than or equal to the geometric mean.

Now from the definition of e_m, above:

$$ e_{m} = H_{m} /N_{m} = \left( {H_{m} /N_{m} } \right)\left( {N/H} \right)\left( {H/N} \right) = \, (H_{m} /H)(N/N_{m} )(H/N) = \left( {h_{m} /n_{m} } \right)\overline{e} $$

(3)

${\text{where}}: \, h_{m} = H_{m} /H{\text{ and }}n_{m} = N_{m} /N$ are, respectively, group m's share in the squad and in the population. Substituting Eq. (3) in Eq. (2) yields:

$$ J = \log (\overline{e}/\hat{e}) = \log (\overline{e}) - \sum\limits_{m = 1}^{M} {n_{m} \log (e_{m} )} = \log (\overline{e}) - \sum\limits_{m = 1}^{M} {n_{m} \log \left[ {\frac{{h_{m} }}{{n_{m} }}\overline{e}} \right]} = - \sum\limits_{m = 1}^{M} {n_{m} \log \left[ {\frac{{h_{m} }}{{n_{m} }}} \right]} $$

(4)

From Eq. (4), inequality is minimised when J = 0. This occurs when $n_{m} = h_{m}$, that is, when each group’s share in the ‘population’ (n_m) is equal to its share in the squad (h_m), and higher values of J are associated with greater levels of inequality.

Now from the definition of e_m, above:$e_{m} = H_{m} /N_{m} = \left( {H_{m} /N_{m} } \right)\left( {N/H} \right)\left( {H/N} \right) = \, (H_{m} /H)(N/N_{m} )(H/N) = \left( {h_{m} /n_{m} } \right)\overline{e}$(5)${\text{where}}: \, h_{m} = H_{m} /H{\text{ and }}n_{m} = N_{m} /N$ are, respectively, group m's share in the squad and in the population. Substituting Eq. (3) in Eq. (2) yields:

$$ J = \log (\overline{e}/\hat{e}) = \log (\overline{e}) - \sum\limits_{m = 1}^{M} {n_{m} \log (e_{m} )} = \log (\overline{e}) - \sum\limits_{m = 1}^{M} {n_{m} \log \left[ {\frac{{h_{m} }}{{n_{m} }}\overline{e}} \right]} = - \sum\limits_{m = 1}^{M} {n_{m} \log \left[ {\frac{{h_{m} }}{{n_{m} }}} \right]} $$

(6)

From Eq. (4), inequality is minimised when J = 0. This occurs when $n_{m} = h_{m}$, that is, when each group’s share in the ‘population’ (n_m) is equal to its share in the squad (h_m), and higher values of J are associated with greater levels of inequality.