Equal playing time in soccer

Question

In rec soccer we have 12 players in the team, and each half is 30 minutes long. At any given time there are eight players on the pitch, while the others are on the bench.

The question is how long should each player be benched on average if the coach is trying to give them all equal play time?

I know it has to do with possible combinations of players, and then there is the goalie issue, which possibly can be left out of the problem.

Answer 1

Let's keep the goalie out of the calculations; the same method would work otherwise. The total number of available minutes are $60\times7$ and these should be divided between 11 players (excluding the goalie). So the share of each is $$ \frac{60\times7}{11}=38.18. $$ So each player must be benched $$60-38.18=21.81$$ minutes.

Answer 2

Just add up the total minutes played by all the players and divide by the number of players. That tells you how many minutes each player should be on the field. You don't have to worry (yet) about combinations of players.

Answer 3

Another way to look at it: 2/3 of the players should be on the field at one time, so on average, a player will spend 2/3 of his time on the field.

(This reasoning works with any fraction -- if you exclude the goalie, replace 2/3 with 7/11)