I think that if you are working at your local racetrack, you will see a lot of horses sired by your local stallions, and you will get to know the similarities that you see in those horses, and be able to attribute those similarities as coming from that stallion. Whether those attributes ever get the chance to show what they can do in the sport world is the question. And WHO does the work to switch the careers… are they skilled? Or are they idiots?
In the decades past, many of the top riders and trainers characteristically obtained OTTBs directly off the track. I think that in THOSE days, some jumping talent WAS able to be identified. Usually in the local area, local stallions. These days, most of the top riders and trainers are importing expensive horses, and few are buying TBs off the track any more. Thus, those few who do find homes as potential show horses are not getting those top riders and trainers any more. Hard to make judgements when training skills are not top quality.
When I was buying horses off the track to reschool for h/j careers, I had my favourates among local families. But also looked for the “type”, and the movement, and that athleticism that is required. All I know is that when I saw it, I recognized it. And bought it if possible. Worked out well for me. You have to try them to know for sure. Nobody knows in advance of trying them.