To add something regarding the contracts of pro athletes as opposed to teacher contracts....

The number of people in the world who can play a sport at that high a level is minuscule. Therefore, if a team wants the best players, they are paying very top dollar as there are so few of them out there.

As for teachers, there are literally millions upon millions of people who can become outstanding teachers worldwide. With a pool that deep, you can pay less because there will be plenty of other outstanding teachers available if a few don't accept the contract you are offering.