I am doing research on the relationship of income inequality on team performance in soccer. The team performance I measure through share of points, so the number of points a team got in a particular season, divided by total points earned by all teams. However, I have data on multiple years, and in each year, the number of teams in the competition differs, and also at a particular moment, the number of matches played differs. Of course, this has impact on the share of points. When there are more teams in the competition, it is logical that all shares will be lower, than when having fewer teams. How can I account for this? I guess it will affect my model.
If you simply divide the total points earned for one team divided by the total points for all teams, it will be unfair to teams that have good defense and are able to win low-scoring games. So, I think your performance index you created is the performance of only the offense.
Also, a team's goal is not to score as many points as possible and prevent the other team from scoring as much as possible. The goal is to win. Therefore, the most straight forward approach is to calculate the percentage of games won in the regular season in each year (not counting playoffs because only some teams play).
If you really want to take the scores into account, maybe, for every game, subtract points scored by the other team from the points scored, and average across all games in that season.
You may also consider multivariate approaches that take all those as variables as indicators of a latent variable called performance.