Williams said of Woods: "His game hasn't been up to stretch, but he's well aware of each area and what he needs to work on.
"He hasn't putted well in any of his events. The key to playing well at St Andrews is putting. The greens are very generous so you don't miss that many greens.
"You can have a lot of 40, 60, 80-foot putts there and if you complete the week without a three-putt, you're going to be near the lead.
"Putting is the key element - that's the difference between winning and not winning - and Tiger has had a lot of ups and downs with his putter."
"Tiger's renowned as a good putter based on the fact that he holes a lot of putts when you have to, but there's been no consistency in his putting. It's been poor in every tournament he's played.
"It has been frustrating, no two ways about it. But he loves to play St Andrews, he knows how to play the golf course, he knows links style golf and he knows what he has to do to perform well. I've made it very clear to him what he has to do and that the onus is going to be on putting."
Williams watches Woods tee off during practice at St Andrews
Williams accepted it had been a troubling year for Woods, following his well-documented domestic problems, but admitted it was "frustrating" not to see the world's number one golfer at his best.
"The circumstances of 2010 are obviously well-publicised and that's made it very difficult. I understand Tiger has got a lot of problems - from a caddie perspective, you have to stand by your player and help him through these situations," he said.
"(But) when you caddie for someone like Tiger, you come to expect a lot of good things. I'm used to seeing a lot of good golf. When you're not seeing that for an extended period of time and not seeing a lot of improvement, that's what's frustrating.
"When you can start holing a few putts, that can change your whole confidence and the way you see the course. When you know you're putting well that turns everything around. When he can have a good week and start putting well that will turn the whole year around."
Meanwhile, Royal and Ancient (R&A) chief executive Peter Dawson has spoken of his "pride" at having Woods at St Andrews as Open champion.
His comments are in stark contrast to those of Augusta National chairman Billy Payne who was openly critical of Woods on his return to golf at the US Masters following the sex scandal which broke in November last year.
Golf chief 'proud' to have Tiger at Open
In April Payne said the world number one's behaviour "disappointed all of us" and added: "Certainly his future will never again be measured only by his performance against par, but measured by the sincerity of his efforts to change."
But Dawson countered: "You'll notice we haven't made such a statement, so I'll just leave that one there.
"I think Tiger regrets many of the things of the past and as he's said, he is trying to put them right, and I believe he is doing it and I believe he's succeeding actually. Let's hope this week is the week he gets his game back.
"I'm able in my mind to separate golf from other things and I think his golf and his skill of the game does make me proud that he's here.
"He is one of the finest, if not the finest golfer in history so yes we're proud to have him as champion."
Woods, bidding to become the first golfer to win three successive Opens at St Andrews, is due to tee off at 0909 BST on Thursday, in a group with England's Justin Rose and Camilo Villegas of Colombia.
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