First, it is grip strength. It has never been more apparent to me than in the past year or so. I was having trouble shooting both fast, and accurate. And I was getting more muzzle flip. I could still shoot small groups, but I needed split times in the 0.4 range or more. More than twice what I was a few years ago. That led me down the path of trying to figure it out and when I measured my grip strength, it was around 65 pounds. About 40 pounds less that it was. Well, I had severe spinal stenosis and my spinal column was pinched off by about 40%. The pain came as I was trying to manage my pistol shooting. Well, I had surgery and I am recovering. But I ended up with a lot of dead nerves and some necrosis. Having a high pain threshold is not good.
Anyway, I had always known about grip strength and I have several exercises to improve it. The average male peaks at about 100 ft-lbs in the mid 20s and falls off as age takes its toll. Women are about 30 pounds below a male. We did a survey of top level GMs (lots of things actually) grip strength. All were over 100, most were in the 110 to 120 ft-lbs range. They are gripping their pistols with 80 to 100 ft-lbs. When you grip, max strength, it slows down the speed of the trigger finger, and imparts movement to the rest of the hand (which drives the gun off target). With PT and exercise, I am again improving my grip strength, and the target shows it, as well as the timer.
The trick is to grip the pistol as hard as you can, while still maintaining the flexibility of the trigger finger.
Second, most top GMs are tuned in to their pistols. Their shoulders and elbows are not locked, but they absorb some recoil. Elbows out, so that the gun recoils in only one plane. They also push into the recoil some. This is muscle memory, training, tuning, and comes from 10s of thousands of rounds.
Third, tuned guns and ammo helps. Some powder/bullet combinations feel softer than others, even with the same power factor. You will find most top level competitors are using fast powders with heavy bullets for their competition load. Getting the explosion over with faster helps you recover sooner and give you an advantage from the inertia perspective.
I take a Hand Dynamometer to classes and measure people's grip strength. It helps me know how fast I can push them and it also helps me give them feedback on what they need to focus on, and grip strength improvement. I have a squeeze ball in my vehicle. It gets 10 pumps everytime I get in, both hands. I have a Gyroball for flexibility and the thumbs and a forearm trainer.
And yes, I have spoken about this with Jerry, and yes, Jerry has a mean handshake. Shooting a pistol is just alinging the sights and causing it to fire without messing up the sight picture. Anyone can do that. But to be fast, you have to have the grip strength. This is also why women, even with massive effort and practice, will never be faster than a male given the same amount of effort. They have a natural 30 pound deficit that can not be overcome.