In the 3rd round of the Masters this past weekend, Tiger 3-putted four times and 4-putted once. Wow! As he said himself, he had zero feel for the greens that day, so maybe now he knows how most of us amateurs feel on a regular basis.
From about 20 feet, the 90s shooter will 3-putt about 8% of the time and average about 2.2 putts, whereas a pro will only 3-putt about 2% of the time from that distance and average about 1.8 putts. Obviously the skill difference impacts that result, but mindset also plays a role. Given their higher skill, pros embrace a 'make' mentality knowing that they won't be too far from the hole if they miss. Amateurs, on the other hand, would likely be better served going into 'lag' mode from 20 feet or longer. When you are in 'lag' mode, you are really more focused on just distance control above everthing else and there is less pressure to get the line and speed perfectly right. Missing the putt a foot or two on the high or low side still leaves you with a very short putt if you get the distance right. With one thing to focus on, your chances of executing correctly get immensely better.
The skill of lag putting is the absolute key to avoiding 3-putts. The old adage of trying to get all your longer putts inside an imaginary 3 foot circle around the hole is very applicable. The Golfing Analytics app tracks how well you lag putt from various distances ranges so that you can see how close to the hole you lag putt on average. If, from a certain distance, your average is higher than the 3 foot target, then obviously that would be an area which could use some practice and skill improvement. There's lot of drills on the internet to help in this area.
As Tiger showed, everyone 3-putts and the goal is really to just reduce how often you do it. Improving your feel and skill from various distances through practice will help, but so will changing your mentality around when you 'go for it' vs. when you just accept the fact that you'd be better off just trying to get it close. Your stats should guide you where the break even point is for your skill level.