Change has a curious effect on the brain -- it challenges established habits and makes the golfer re-address fundamentals. the same thing happens when a right-hander tries to putt left handed. It's a staple trick of the "Top Ten Ways to Grow A Bigger Brain" sorts of books -- change your usual pattern and expose yourself to novelty to spur the brain into a higher rpm / gear.
Changing putters to spark a resurgence on the greens is also a steady theme throughout golf history. The articles are very regular and repetitious about this in the books and magazines. here is a sample section from my Research Database:
1.04.07. .-- -- CHANGING PUTTERS / -- SWITCHING PUTTERS
1.04.07. .-- -- CHANGING PUTTERS / -- SWITCHING PUTTERS
1.04.07. Golf Digest All About Putting (New York: Coward, McCann & Geoghegan; London: Kaye & Wind, 1973) 190-191: two theories: the "fresh outlook" theory and the "old faithful" theory; the "fresh-outlook" says you regain touch and feel by changing putters: "The trend among the pros nowadays is toward fairly frequent changes. Many players feel that a change in putters will give them a fresh outlook on the whole putting problem." 190; "Against the fresh-outlook theory, you can set the perhaps more logical line of reasoning that the longer you keep a putter, and the  more familiart you become with its feel and hitting characteristics, the better it will serve you. Jack Nicklaus subscribes to this theory. "I don't switch putters very often," Nicklaus says. "I recommend that you find a putter that gives you the best feel, then stick with it. If you have trouble on the greens, the odds are 100-to-1 against the putter being at fault. More likely the problem rests with you. That's certainly true in my case."" 191: "The important thing is to select a putter that fits you, rather than altering your best technique to fit a putter. Dave Stockton offers sound advice on this point: "Determine which positioning of your hands -- high or low, forward or back, in close or out and away -- gives you the best results. Then select a putter that "sets" your hands in that position. The best putter is the one that feels and looks right to you.""
1.04.07. Golf Magazine Golf Magazine's Handbook of Putting (New York: Harper & Row, 1973; London: Pelham, 1975) 28: "A putter is like a woman; treat her right and she will treat you right." [sexist; what about a female reader?] Change for conditions so that your favorite putters isn't require to give a substandard performance on a green it's not suited for; don't use up your best putter on bad experiences due to green conditions. [goofy]; "Putting, we've always felt, is mental; it's all in the head."; Gene Sarazen had no loyalty to putters that won for him, since he knew [?] he would never hole another putt with them; Ted Ray used to take 4 or 5 putters  with him to every tournament and try them out on the greens and pick the one that worked best for that course. Chick Evans was a poor putter and later wished he had not changed putters so frequently, thinking that if he had stuck with one he would have putted better [probably not]; Changing putters did Vardon no good; "And Leo Diegel also was never satisfied with his putter. Leo had an odd putting style; he stuck both elbows out, but he had even stranger taste in putters. They just couldn't make the putter to suit Leo. He would put weights on them and everything and still he was never happy." 30: "But remember that oftentimes players will find their way out of a real putting slump by a change of putters. For instance, Julius Boros in his 1963 United States Open win had to go  back to an old blade putter that he had given up on several years ago because someone had stolen the one he had been using. The old feel came back and he started to win big."
1.04.07. Palmer, Arnold & Dobereiner, Peter Arnold Palmer's Complete Book of Putting (New York: Atheneum, 1986) 83: "It is surprising how often a change of putter will restore the winning touch, and, once that happens, it is often safe to go back to the regular putter." 84: "The rapport between a golfer and his putter may be a delicate relationship, but the feel of a long-used putter is programmed into your nervous system, and that is valuable asset."
1.04.07. Smith, Horton & Taylor, Dawson The Secret of Holing Putts (New York: Barnes; London: Yoseloff, 1961) 67: "A good deal of the battle is psychological, and if you think that by changing to a new putter you will have more success, do so, but if you can stick with one for years, as so many good putters do, I sincerely believe you will be better off. For usually, the fault lies not in the club but in the man "wielding the stick.""
1.04.07. Stockton, Dave & Barkow, Al Dave Stockton's Putt to Win: Secrets for Mastering the Other Game of Golf (New York: Simon & Schuster, 1996) 125: "[I]t is a good idea to change putters every so often. It should be a radical change, from a mallet to a blade or vice versa. You might also try a different type of shaft, or more or less loft, or more or less weight. The only thing that should remain the same is the lie angle. The main thing is that it looks different. I sometimes switch  from a mallet to a blade putter, just because I dislike blades so much. With a thin blade at the bottom of the shaft, it doesn't look like there is enough club for me to get the ball to the hole, and that makes me stroke the ball more instead of letting the heavier seeming mallet-head do it for me. But more important: When you go back to your regular putter it looks and feels much better. You're glad to have it back in your hands, and you immediately begin putting better. Your spirits are refreshed. In 1993, I won five tournaments on the Senior Tour, three with one putter, two with my "backup." You also may change to suit different conditions. On slow greens, for example, you don't want to change your stroke; just use a slightly heavier putter or put some lead tape on your current putter. "To prepare for all possible circumstances, practice with different putters."
The Research Database is available on the website.
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