Being a golfer, with a math degree and a mathematical job, this subject is near and dear to me. IMO, statistics are often wrongly interpreted, or rather, the USE of statistics can be wrongly interpreted. I think you can use them to compare pieces of your game, maybe describe yourself as a player (i.e., low FH and GIR % but low PPH = "scrambler"), or compare yourself to others. But my statistics don't seem to really ever surprise me. I know I miss fairways and greens way too often, but that I pitch and chip well, and my putting is very good. Say I scramble at around 40%. One could say, 'raise that to 75%, and you could drop four strokes a round.' Well, yeah, I know that. I know every time I don't make the par saver that I just cost myself a stroke. And even if I do make a few more, and my scramble % goes up, the fact remains, if I hit more greens (likely through hitting more fairways as well), I may not have to scramble as much, and that would drop strokes, too.
I also think sometimes statistics puts the cart before the horse. Now on the Tour, you'll see an immediate stat pop up, while Goosen is over a 15 foot put: "Chances of making 15 foot putt: 41%" or something, based on Goosen's actual statistics. Well, every 15-footer is different, and those stats don't know if his misses were off by 3 feet or not. A statistics from past results is not a looking-forward probability. Still useful if you're betting with your buddies, I guess, but it's not like Goosen would say, "hmmm, gee, I really need to get that statistics up to, like, 55%." He just looks at (nearly) every 15 footer and says, "I want to make this."
Which brings me back to the elegant simplicity of golf. Sure, after a round, if you hit 11/14 fairways, 15/18 greens, 1.8 putts per hole, you'd think, 'damn good round!' But, you'd probably know it was a good round the second it ended. And it's not like you'd look back and say, "gee, I wish I only hit one more green," you'll likely really have wished you hit three more! The fact is, the large majority of us aren't capable of hitting a ton of greens or fairways, or putting lights out, but that's the beauty of golf psychology. With very few exceptions (really difficult holes, unreachable greens, etc...), you'll be on the tee thinking, "I want to hit the fairway." On your approach, you want to get on the green. If you don't hit the green and you're around it somewhere, you're thinking, "hit this up there somewhere close to get a chance to make a putt." Lastly, unless you're truly in 'lag-only' range, you should be over a putt thinking, "let's drop this thing."
Basically, regardless of your stats, I believe in (I should trademark this phrase) "one shot, this shot" philosophy. That has a binary result: success or failure. Hit a fairway or don't. Hit the green or don't. Make the putt or don't. You don't tee it up and think, "let's hit 70% of this fairway," or get over a putt and go, "let's get down in 1.80 putts." Ok, my little rant is over...