Personally, I am interested in a player's personal contribution to the game. Therefore, I want to compare the team's performance when he is on the field versus when he is not on the field. I believe that it originates from basketball, but it can obviously be extended to other sports.
Suppose a player plays 12 minutes out of a 48 minutes NBA match. In the time he is on the field, the score is 25-20 for his team. In the other 36 minutes, the score is 70-70. So, his team is performing '5 points better per 12 minutes' when he is on the field. After rescaling to full match time, the statistic would be +20 for this player in this hypothetical match.
Is there a statistic that describes this effect or any one closely related? If not, could you explain why this statistic is not of interest? Personally, I think it says a lot about a player that cannot be counted explicitly, for example defensive positioning.