I have a great friend who worked at Isleworth for nine years. He said when Tiger was there all day practicing, he would spend double the time on his short game as he did on the driving range.
I used to play golf with a guy named Randy Leen, who was an all-American at Indiana, semi-finalist at the US Amateur, low am at the US Open, etc. He was trying to make the Nationwide Tour (or whatever it was called back then) and couldn't. When I asked him why he wasn't out there, he said, "Putting, and confidence."
I once spent 4 days at Bandon Dunes, and had the same caddie, a guy named Hoops, the entire time. I drove the ball very well that week, but my low round was like 73 or 74. Hoops used to caddie for a guy on the tour named Willie Wood. He once told me if Willie drove the ball as well as I did, he would have won quite a bit. Probably blowing smoke up my rear, but it stuck with me.
I once caddied for a buddy in the US Open sectional in Columbus, OH. He was paired with a guy named Brad Elder, who played at Texas, and spent time on both the Buy.com tour and, I believe, the PGA tour. For 36 holes he missed either 4 or 5 greens...I've never seen a guy hit it so good tee-to-green. He did not qualify, because he couldn't make a putt. No lie...on about the 7th hole at Brookside CC in Columbus, he started putting one-handed. Didn't work.
I think amateurs need to practice their short games way more than their long games in order to get better. Same goes for the pros. The very elite pros need to be great at both.