"Overseeding is usually carried out at the end of a particular sporting season"
There are several ways to carry this out. You can broadcast the seed with a pedestrian spreader ideal for cricket squares and bowls greens. Another way for much larger areas is to use a tractor mounted disc seeder. With this option you have much greater control over where the seed is sown and at what depth. Minimal surface disturbance occurs and the big plus on this system is the seed is placed in the soil which helps speed up the germination process as well as keeping it out of reach of those hungry birds.