This question inspired me to look at the etymology of "get a bye". The earliest mentions in a sporting context that I found while searching Google Books were in the Coursing Calendar, the 1872 edition of which contained this baffling sentence:
Bismarck, who was a favourite for the event, had the misfortune to get a bye of terrific length, and this doubtless lost him the stake, as, hard run as he had been, he led his opponent in the concluding course.
Duffer ran a bye, which brought the day's sport to a conclusion at half past three.
On the other hand, we also have from the 1867 Coursing Calendar,
Black Topsy had the good luck to get a bye owing to Blue Bock having injured himself yesterday, so much so that his trainer wisely drew him, with an eye to the future.
The first two instances seem to be using "get a bye" in a completely different sense than the modern one, in which it means to sit out a round in a tournament. The third instance, only five years earlier than the other two, seems to be used in the modern sense. What do "get a bye" and "run a bye" mean here, and is this where the modern phrase, "get a bye," comes from?