Back in my track days my friends used to fight over who got to exercise or take care of the AP Indys. I mean direct AP Indy offspring. Dated knowledge here.
I don’t know if his temperament is as reliable in second, third, fourth generation – which is where you are most likely to see him now. But he was quintessentially an ammy-friendly stallion, and so was his sire (IMO). His son[s] Flatter and Congrats seem to have inherited the ‘uncomplicated’ characteristic, or at the very least consistently pass it on.
I’ll do a selfish plug for Say Florida Sandy but you won’t be able to find him through sons as far as I’ve been able to tell, which is a real shame because his offspring seem practically broke the moment they’re born.
Big Brown seems to have sensible and uncomplicated horses, just from those I’ve seen find second careers with amateur riders - some who were tackling their first OTTBs.
If you can find a Dixie Brass or Dixie Union horse, they are great jumpers. At this point I think all of his their kids are aged. That is the problem with sourcing jumpers or sport horses from racing - by the time there is a big enough pool of horses from a specific stallion to draw conclusions about the horse’s ability to sire talent, the stallion is usually aged and/or dead.
Lonhro, Ghostzapper and Mizzen Mast are three I correlate with good jumping and kind brains.
On the sport-horse side of TB world there is Innkeeper and Copy Cat Creek, but I’m not sure if either have much in the way of availability anymore. Saketini has already been mentioned. I really like one of his sons (Miso) and if he goes missing from the barn it is not my fault.
And of course… A Fine Romance.
I agree with others its silly to even mention Northern Dancer or Mr P as concerns at this point. The average dirt pedigree is saturated with both, usually 2-5x in the first two pages. You will have a hard time finding a horse without these names. I don’t understand, in particular, the finger pointing at Mr P. He was the least “stampy” stallion to exist and even when he’s linebred six times in a horse you don’t see him come out the way you would see Northern Dancer or Storm Cat come out in similar linebreeding scenarios. He just did not replicate himself.
There are tons of TB stallions that make brilliant jumpers, so the list would be really exhaustive. I’ll add that I think Deputy Minister is a proven source of talent, but I’m not confident he’s always ammy friendly. But that is not a detractor IMO - this is the case for many TB (and WB!) stallions, who are talented as all get out but may need tactful rides. Add in that some TBs retire with a lot of racing baggage that make them sensitive where if they were raised in a sport home, might not need as much tactful riding. It’s hard to quantify until you’ve seen many horses by the same stallion over and over again.