Sabermetrics for jockeys

I know almost nothing about horseracing and have never placed a bet, but I did stop by a racetrack the other day to see the horses race, and had the following question.

To what extent is it possible to separate the performance of the horse from the performance of the jockey? And does anyone do this? There are some celebrated jockeys who have very long and successful careers, and I’m wondering to what extent this is based on a dispassionate, numbers-based assessment of how well they can get a given horse to race versus just veteran horse-racing guys watching them ride and assessing that they’re good jockeys.

As it happens, in one of the races I saw, the jockey of the favorite fell off the horse almost out of the gate. The horse kept on running and came in first, though was disqualified for having no jockey (which makes sense in that it wasn’t carrying a load). But apparently horses - like greyhounds - will run around the track even without a jockey, so I fell to wondering how much the jockey actually adds, and how one might determine that. (To me they all seemed to be doing the exact same thing, but then I don’t know much about horse-racing, as above. I suppose there would be strategy elements in terms of how to pace the horse and how to position it and so on.)