By this logic Ole Bob Bowers would have not been bred to that nothing
mare that produced John Henry.

That "nothing" mare, Once Double, was a winner at 3. She was by Double
Jay, a leading sire of broodmares. The mare had 9 starters, 8 winners,
1 stakes winner, 2 stakes placed. Not too shabby for a "nothing" mare.
Ole Bob Bowers was a stakes winner and equaled the world record for
9 furlongs - but he was ranker than dogshit in the stud and a below average
producer. He brought $900 at public auction when Golden Chance sold out.

Breeding is a game of chance, although you can even the odds somewhat
these days by breeding great mares to the likes of Storm Cat.

As C.V. Whitney has been quoted as saying, ad nauseam, "Breed the best
to the best and hope for the best."

In general there are a lot of horses who have never proven themselves in
any way shape or form due to injury who go on to produce great runners.
This is where the phrase Blood Will Tell came from.

In reality, folks who breed stakes winners to stakes winners are more likely
to produce stakes winners than are folks who breed by any other system -
that's why they have black type in sale catalogs.