1) G.I.R.
2) Proximity to the hole
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Average putting is good enough to rank in the top 10 on the money list.
Look at the 2009 PGA Tour stats and you'll see those are among the weaker predictors of winning tournaments and money. They might be good predictors for consistently shooting your handicap or keeping your card. But to win, you need more "beta" - ability to spike low scores outside your handicap.
I would argue that separating yourself from the crowd of many talented players and winning means something like:
The ability to hit par fives in two that other players can't hit PLUS scrambling within 80 yards (Tiger kills people here - I think this stat shows ability to take chances without blowing up your score) PLUS the GIR/close to hole (which gives you a consistency measurement) PLUS ability to absolutely putt out of your mind and make almost every putt for four days within 12 feet and also throw in a few bombs. It's rare to excel in more than two of these categories. Being a streaky brilliant putter might be the most valuable of these (well, scrambling like Tiger might be close).
That last putting stat - the ability to be a streaky great putter for most of four rounds is huge -- it gives you the ability to go really low. It makes Tiger, especially because he can hit long par 5s in two and can scramble, dangerous in his ability to separate from the field (when he doesn't do it - US Open this year - he has much less margin for error). It made Brian Gay a lot of money in a few tournaments this year. Kenny Perry and Steve Stricker can be streaky good putters too, although they have a little trouble holding up under major tournament back-9 pressure.
Even among us hacks streak great putting sometimes appears and then disappears. I have played golf on Saturdays with a guy for a decade now who is a 10-11 handicap and has always been a poor putter and a good driver. I mean a bad putter. In the last month he has putted lights out and twice broken 75, which is very low for someone at his handicap (he just switched from a long putter back to his ancient bullseye). Who knows how long his run will last.
Imagine how many more events Trevino would have won if he had Nicklaus' putting ability.