His instincts were right, as Sea and Sage struck him as he was protecting the girl, forcing his hospitalisation with multiple fractures.
Shear had been paddock guard when the horse bolted from the walking ring before the third race.
Shear's son, Mike, said his dad had improved considerably overnight.
"I went and saw him last night in ICU (the intensive care unit) and he didn't look good," he said.
"His voice wasn't good and his face was black and blue. I went back this morning to see him at 10.30 and there was a complete, 180 degree turnaround.
"He was sitting upright, talking, laughing and completely coherent and he's stable.
"He's got multiple fractures. I'm not sure about all of them, but we do know he has one fracture in his pelvic area.
"He was hurt about four years ago in a paddock accident at Hollywood Park and the doctors inserted a rod in that area which may've been dislodged yesterday.
"The doctors think this has caused some internal bleeding in that bone area and he did lose a significant amount of blood yesterday.
"The latest word is that he's not going to have to undergo surgery at this time, which is great news," said Shear.
Shear's act of selfless heroism has created national interest, far beyond the scope of horseracing.
"I'm completely blown away and humbled by the response from fans at the track and from those on all the social media sites. It's amazing how many people that don't even know my dad have expressed their well wishes," said Shear.
"My dad does about 35 pushups a day and he eats well and stays fit. I think that's the biggest reason he's recovering so quickly.
"I'm extremely proud of him. I'm the most proud of him that I've ever been. He's overcome a lot in his life - from where he came from and what's he's been able to accomplish.
"We're not really sure how long he's going to have to stay in the hospital. A lot depends on whether he's going to (eventually) need surgery.
"We'll probably know more later today."
John Shear, a former jockey, has been employed at Santa Anita Park since December 23, 1961.
Video footage of the incident showed that Shear, instead of dropping the perimeter rope he was holding and protecting himself, ran in front of the loose horse and threw himself in front of, and on top of, the young girl in the crowd.