Research on Referee's Enforcement Stability in Chinese Football Association Super League Based on DEA Method

Football sport is becoming more popular and influential in China than ever. In addition to performance of teams, level of referee's law enforcement also plays an important role in a football match. This paper provided a feasible and objective evaluation method for judging the enforcement level of referee. We suppose referee' enforcement level is relative to his enforcement stability which refers to the stability of maintaining a certain degree of enforcement strength. To test this hypothesis, we collected the data of 720 games played in the Chinese Super League (CSL) in 2011-2013 seasons. 21 Chinese referees who refereed more than 10 games per season were selected and their enforcement stability were studied through the data envelopment analysis (DEA) method. We found that there was a significant linear negative correlation between referee's enforcement frequency and his DEA mean (p = 0.004 <; 0.01, r = - 0.604), the DEA value of the referee who had high enforcement level obeyed the normal distribution approximately (p > 0.05). Moreover, if the variance and the skewness of the DEA value are smaller, the referee's enforcement stability and his enforcement level are higher.