I don't think I hunt as much as many of you, but I too cannot ever remember being picked off by a deer in a saddle. I also move around quite a bit, albeit slowly and deliberately, in order to scan 360 for deer and also just to shift my weight, adjust the saddle, and stay warm and comfortable. Even with that I don't think I have ever been picked off. I hunt at 22 feet whenever possible and also try to be near a fork, a branch , or another tree for cover. Every deer except one that I have shot out of a saddle has involved me moving at least 180 degrees around the tree in order to set up for the shot. And still I didn't get seen by the deer.
By contrast, every once in a while I get to hunt at a friend's place out of a 15ft double ladder stand. I have found that I must remain almost entirely motionless to avoid being picked off, and on 2 occasions just the slightest movement trying to get situated for a close range shot has caused the deer to look straight up at me. Additionally, I have missed out on several shot opportunities because the deer was behind me and stayed behind me, and I couldn't get turned around for a shot or the big tree the ladder stand is against blocked a shot opportunity.