60 Ethnic sorting in football In the previous formula, refers to the proportion of ethnic group m in the total population for M groups. E then equals to the sum of each group’s proportion multiplied by the negative natural logarithm of that proportion. The minimum score of E equals 0. In this case there is no uncertainty because all individuals belong to the same group: 1(− 1) = 0. The maximum score of E is the natural log of the total number of groups and occurs when each respective group comprises the exact same numbers of individuals. For seven groups (six ethnic categories and one rest group), this equals 1.946. The entropy score is an expression of the diversity of a certain population. On its own, however, this score cannot be used to say anything about the degree in which groups evenly or unevenly distribute over lower-level organizational units such as clubs. In order to do that, we must use the entropy score E to calculate the information theory index H. The information theory index can be understood as an expression of the weighted sum of deviates of entropy on the lower organizational level from the entropy on the population level. Its expression takes the following form (Theil, 1972): = 1 −∑ In the above formula, refers to club j’s size, T refers to the total member population size, refers to the entropy score of club j, and E refers to the entropy score of the total member population. When H = 0, each club’s ethnic composition perfectly resembles the total population - i.e. no difference between the levels in entropy - suggesting the absence of any inbreeding. In these cases, the relative proportion of ingroup and outgroup co-membership ties are the same as the relative proportions of these groups in the total member population. Higher values for H indicate that ethnic groups are less evenly distributed over clubs, with H = 1 meaning that clubs are entirely mono-ethnic. In these cases, ingroup co-membership ties are, on average, overrepresented and inbreeding is occurring. The interpretation of H is not entirely straightforward. Reardon and Yun (2003) advise to use the following cut-off points: Extreme (0.4-1), high (0.25-0.4), moderate (0.1-0.25) and low segregation (0-0.1). The calculation of the entropy score and information theory index can be easily adapted to express dichotomous segregation instead of multigroup
RkJQdWJsaXNoZXIy MjY0ODMw