What is this (basketball) statistic called?

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.

Example

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.

Question

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.

• So +/- per minute? I don't know if anyone keeps that stat, since a) +/- is already flawed (I play if and only if my teammate LeBron is on the floor, so I have a great +/-) and b) it would likely be dominated by garbage time players with tiny sample sizes. – Michael Myers May 15 '15 at 17:08
• @MichaelMyers (b) is easily fixed by looking only at players with more than (mumble) average minutes per game. – Philip Kendall May 15 '15 at 17:53
• @PhilipKendall: Still, being +10 in 40 minutes seems better than +5 in 12 minutes. But it depends also on the replacement player. This is why there are tons of advanced/adjusted/real/whatever plus/minus systems around. – Michael Myers May 15 '15 at 17:57
• @MichaelMyers, if I were a coach, I would give someone, who gets +5 in 12 minutes time and time again, more playing time to use his skill in a longer period of the game. Probably, his +/- per minute will drop. However, a statistician coach would find an optimum amount of playing time per player. I think that (a) is rarely the case in the long run (although I'm not familiar with basketball so much). – Braamstruik May 18 '15 at 14:54
• If it happens consistently, then the sample size is no longer a problem. – Michael Myers May 18 '15 at 23:23