For the typical amateur golfer, you save strokes everywhere

and any improvement will drop you 3-5 strokes.
I use to be an 18 handicap. I worked on my short game and every chip and pitch gets really close to the hole and I have a good chance of getting up and down and saving par. That dropped my handicap about 4 strokes.
I was hitting a Titleist 975D fairly accurate, but short. I made myself an SMT Nemesis and tried different shafts until I found one that worked for my swing and average 240, 270 if I get after it. Those extra 20-30 yards means the difference between a 3 wood in and a 4-5 iron in, or a 5 wood and 7-8 iron. That would save you 3-4 strokes a round.
Combine the increase in driving, hitting easier clubs, and better pitching, and you've cut down 7-8 strokes.
Finally, work on the putting game, which is truly where the money is for everyone, and you can shave off 3 more strokes.
It's really easy for a beginner/amateur to cut strokes, since our games are so raw compared with the top amateurs and pros.
Oh yea, I've only hit a drive 300 yards once and it was down hill, down wind, and a hard fairway
