There is no evidence about the process by which the Germanic sthiz, from s-, "to sow", came to mean keeping better competitors apart in the earlier stages of sporting events, though it is easy to speculate - every gardener knows that seeds should be kept apart for the best results.
The OED's earliest sporting citation for "seed" comes from the magazine American Lawn Tennis in 1898: "Several years ago it was decided to 'seed' the draw in handicap tournaments."
That was in the United States. It was different in this country, and in 1924 the Times reported (presumably about Wimbledon): "This year, for the first time, the draw has been 'seeded'; how little seeding accords with British notions may be gathered from there being no reference in the Oxford Dictionary - at any rate in the smaller one."
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