It would be interesting to do a correlation between optimum statistic and handicap. GIR for me. It means I've either not wasted an FIR or played a good shot from the tee/rough. More often than not it's a two putt par and five or six of those on the card is gravy. That said if I was a lower handicap I bet it would be scrambling!!!!
Not actually sure on what scoring depends on as you don't know what you've got until you miss it, but I voted fairways because it's the one thing that would lower my scores for sure how I'm playing now.
I put scrambling down as that is where I get my scores at the moment. I miss a lot of greens (only hit about 33% on a GOOD day) and getting up and down a few times can make a real difference to the score.
I would like to think that if I hit more GIR my score would improve even further, but the thing that really gets me points at the moment is definitely scrambling.
I keep a track of many stats on my rounds and putts are OK as long as you combine them with the likes of GR and scrambling. The likes of driving distance is irrelevant and accuracy is nice but depends on the course.
As for the Open venues, St.Andrews has so much history, it can detract from other venues which are harder and more a test of golf. Going to the Old Course every five years is the right time span and the right thing to do.
I've had the privilege and pleasure of playing most of the other venues and would call Muirfield the fairest and Carnoustie the hardest.
I went for Turnberry - it has some great holes and the scenery is second to none. Disappointed not to see any votes for Royal Troon though. I'm lucky enough to have friends who are members of both courses and play them both reguarly. In my opinion R Troon is the tougher track by a fair margin but this obviously doesn't make it a better course than Turnberry (it aint as pretty).