My first year I broke 40 for 9 holes, but I was doing 9 holes about 3 times per week. It is the VERY rare person who is a natural at golf, and I am certainly not one of them. I have a friend who IS such a person and he can come back and golf after not playing for 2 years and shoot par golf.
The most impressive "natural" golfer I ever heard of was Jim Brown (former pro football player and one of the greatest running backs EVER). The first time he ever picked up a club he did it at a golf course and broke par. Now THAT is a true natural athlete.
I look at putting as every missed putt is like duffing a tee shot, since it cost the same stroke. The worst part of my game that first year was my short game and mostly chip shots. When I started out, I was hitting it back and forth over each side of the green.
I solved that problem by grabbing a typical buck and putting it about 15 feet away in the yard with 20 golf balls and just practiced trying to chip it into the bucket. doing this 3-4 times for an hour + solved that problem. The bucket is important because most yards are nothing like a typical green so you practice/work on the "in air" accuracy, and then work on the roll when you are at the practice green before a round.
I also find if I practice for 15 minutes on the practice green before going out, I can shave 5+ strokes off my game. This is important to help judge the speed of the greens on that particular day. The speed can easily change with the weather so this is VERY important to improve your putting.
I hope this can help some fellow duffers.
