The aim of this study is to examine the time period and league-ranking effects within different types of goals in the English Premier League. We investigate these effects through the use of six time periods (taken every 15 minutes), eight types of goals and four categories of teams. Based on the Kruskal-Wallis H test followed by the Bonferroni-adjusted Mann-Whitney U test, the key finding of this study is that different types of goals have varying degrees of time period effects and that there is a significant league-ranking effect both within all six time periods and within six types of goals (excluding throw-in and indirect free-kick). The study also reveals that the final 15 minutes of the game is the most prolific time for scoring. Our findings suggest that the top 5 teams have significant advantages in open play goals (elaborate attack and counter attack), while this overwhelming advantage is weakened in the other four types of goals (direct free-kick, corner kick, penalty, and own goal) and even absent in goals from indirect free-kicks and throw-ins. At the same time, there is no significant difference between the lower-middle 5 teams and the bottom 5 teams.

To evaluate collective (macro) performance data in the Chinese Super League, social network analyses and graph theory were implemented in team sports performance analyses. For each team, we constructed a weighted and directed network in which nodes corresponded to players and arrows to passes. A total of 1200 matches during the 2014–2018 seasons were analysed. The results showed significant differences in general network measures among team competitive levels, match locations and match outcomes. Successful teams and home teams had significantly higher link, diameter, density and cluster coefficient values than did the unsuccessful teams or visiting teams; however, the winning teams had significantly lower density and cluster coefficient 2 values than did the losing teams. This study suggested that successful teams or teams with advantages (home, winner) have a high level of total passes and eigenvalues. This is the first report in which eigenvalues (the degree of a team’s distribution of the ball during the match) were able to capture changes in dynamics between different teams. There were positive correlations between all the network variables and the total shots and no correlations between all the network variables and goals.

To explore and compare competitive balance on multiple levels and its evolution within professional football leagues, this study utilized a sample of the results of games in the big five European leagues over 40 seasons (from 1975/1976 to 2014/2015) and then established and applied competitive balance Shannon entropy (CBSE). The results showed that (1) CBSE can independently assess the competitive balance within soccer leagues with regard to multiple aspects. (2) The overall competitive balance in the French Ligue 1 is relatively high, while that in the Spanish La Liga, the German Bundesliga and the Italy Serie A is relatively low. The overall competitive balance within the English Premier League has declined significantly in the last 20 seasons, while that within the other four leagues has not exhibited an obvious change; however, the balance of home games and away games has improved significantly. (3) In the past 20 seasons, the CBSE of the top teams, middle teams and weak teams in the English Premier League has declined significantly; the competitive balance of top teams within the Spanish La Liga and the German Bundesliga has also decreased, while for the top teams, middle teams and weak teams in other leagues, the competitive balance has changed little. (4) In each league, the competitive balance of middle teams is the highest, while that for the weak teams and the top teams is the lowest.