On Competitive Balance of Chinese Professional League Football Matches

ON COMPETITIVE BALANCE OF CHINESE

 PROFESSIONAL LEAGUE FOOTBALL MATCHES

LI Cai-ping Huang Gang-qiang Wang Dong-jie

(Department of Physical Education, Southwest University of Science and Technology, Mianyang City, Sichuan Province, China, 621010)

Abstract：This paper reviews the elementary theories of competitive balance in overseas professional leagues, and studies competitive balance in Chinese football professional league matches by measuring competitive balance with methods like C5CIB, the Herfindahl index, and Top 3 ranking. It indicates that In the seasons before 2005, the competitive balance of the league is relatively stable, but in the season 2005 and 2006, the competitive balances were broken. Top clubs competitiveness tends to be more balanced, while the competitive imbalance between top clubs and other clubs is further aggravated. Competitive balance affects the vitality of league tournament and relates directly to its development. Comparing with the development of league tournament, competitive balance affects its vitality.

Key words：professional league football matches  competitive balance

1 Introduction

Since the professionalization reform of Chinese football in 1994, the football league has made great achievements. Since the beginning of the Chinese Professional League Football Matches, 13 years have passed, and now, it goes to full professionalization. Documents show that Chinese scholars' studies on competitive balance--- the important factor which influences the development of the league---are still insufficient. Almost all the sports economists abroad have reached an agreement that the competitive balance is vital in professional sports league because it can ensure the uncertainty of the match results. This uncertainty is the source of vitality for all the sports games, and is also one of the best selling points. To ensure the healthy development of Chinese Professional League Football Matches, it is essential to dealt with competitive balance seriously and correctly. This paper will make an in-depth study on the factors that affecting the competitive balance and the current situation of Chinese Professional League Football Matches based on the theories of competitive balance of professional league abroad, and the testing means.

2 Theory of Competitive Balance of Professional League and Testing Means abroad

2.1 Concept of competitive balance

Competitive balance means the state of competitive balance of all teams in professional league. The more evenly the competitiveness of all teams distributes the more uncertainty the result of each game will have; at the same time, the suspense and psychological impact on spectators are greater, and entertaining and recreational effects will be bigger. In an absolute competitive balanced professional league, every team is thought to have the equal opportunity to win a game and champion. Competitive balance should include three main elements: the result uncertainty of each game, that of the result of the season (the uncertainty of one single season), and that of the result of the league matches (the diversity of the result in several years) [1].

2.2 Testing means of competitive balance of professional league abroad

Market concentration is one of the determining factors of market structure. Generally speaking, the higher the concentration is, the more market power a certain firm has, and the less competition it faces. Usually, the indexes, measuring market concentration, are used to measure market structure (mainly the power of market monopoly). The way of absolute concentration, to measure market concentration, mainly includes the concentration ratio (CRn) and the Herfindahl index (HHI).The concentration ratio is the most commonly used and simplest measuring index of absolute concentration, and is a term used to describe the share of certain value x (it can be output value, output, sales amount, sales volume, number of employees, total assets and so on) of several leading firms in the whole industry or market. The number and scale of firms, the two important factors determining the market structure, are reflected by the sum of concentration ratio.

[pic 1]

where CRn is the percentage of market share held by the n largest firms in the industry X; Xi is the certain value of the ith firm in the industry X; N is the total number of firms in the industry X. The most common concentration ratios are the CR4 and the CR8, which means the 4 and the 8 largest firms. When market concentration is used to test the competitive balance of professional sports league, the market concentration ratio of the top 5 clubs will be used; Xi is the total scores of the ith club in the league; N is the total number of clubs of the league. CR5 reflects the competitive imbalance between the top 5 clubs and the rest ones. The increase of the index means the growth of dominance of the top 5 clubs, and the competitive balance of the league is sliding. In professional sports league, the index CR5 ranges from 0 to 1; 0 is absolute competition, and 1 means absolute monopoly of the top 5 clubs.

Due to various reasons, the scale of the league is not unchanged, which makes the competitive balance indexes, of different seasons measured by CR5, cannot be compared directly. In order to make up for the defect, researchers abroad have made further adjustments and improvements; the C5 Index of Competitive Balance (C5CIB) has been put forward, which betters the measurement. The computing formula of C5CIB goes as follow:

[pic 2]

where N is the number of clubs of the league; in a absolute competitive balanced league, the index of competitive balance is always 100 despite its scales; the increase of this index means the decline of competitive balance[3][4][5].

Herfindahl-Hirschman Index is an aggregative index measuring market concentration. It is defined as the sum of squares of the market shares of all the firms. This index comprehensively reflects the distribution of the scales of all the firms. The computational formula is:

[pic 3]

where x is the overall scale of the industry such as total sales, total assets and so on; Xi is the scale of the ith firm. HHI ranges from 0 to 1; HHI close to 1 means higher market monopoly; when HHI=1, only one firm exists in the industry, and the market is in a state of absolute monopoly; HHI close to 0 means higher market competition, and when HHI=0, the market is in a state of absolute competition. Applying to professional league, x is the total score of all the clubs; xi is the score of the ith club. The rise of H index means the decline of the competitive balance. Similar to market concentration ratio, H index is also sensitive to the change of the number of clubs of the league. Adjustments are also used by scholars abroad to make the index more exactly reflex the competitive balance of the league. The formula is: