I have a mare who, though both her parents are Silver-rated, doesn’t seem to be blessed with a need for speed. 
Her mom, too, was by a Silver-rated stallion, but only made it as high as NW1 races.
My question is, how does personal performance affect lineage? If two awesome horses made a filly that happened to not be a great runner, would she still have a chance of passing on some of her “good” genes? How much or how little would her babies be affected? I’d love to consider checking her in to the broodmare barn once she turns four, but I thought I would ask the veterans first. 
Every breeding has the chance to produce anything from superstar (at least as far as numbers go) to superdud. Those chances are skewed a bit by the quality of the parents (so 2 platinum ranked parents would have a slightly higher chance to produce superstar and slightly lower chance for superdud). The majority (80%+) of breedings are meant to produce “average” foals (though obviously average is a very wide range).
That said, since babies take after their parents (with some randomness thrown in for individuality), if you breed a superstar dirt sprinter to a superstar turf router, you may get lucky and get a very versatile horse, or you may get unlucky and get a so-so horse who hates dirt and turf and can barely run 5 feet.
The breed rankings are based on foal performance. If your horse has a couple of nice foals, she’ll have a high ranking, even if her stats aren’t so great.
Right on. Thanks Shanthi! 