When a major golfing figure decides to use the words "lucky" and "Tiger Woods" in the same sentence, in the same paragraph, in the same encyclopedia even, he had better be damn sure of his argument. As a former Nasa scientist and an unashamed numbers junkie, Dave Pelz happens to be damn, damn sure and he has all the damn statistics to back up his courageous claim.

The theory offered by Pelz, as the mentor and reinventor of Phil Mickelson, about Woods' startling success at the US Open last month surely provides a fascinating insight into Team Mickelson's thinking, not to mention confidence, as they come into this Open Championship. Many in the game declared that the Torrey Pines "one-legged" triumph once and for all removed any doubt as to the uncontested nature of Tiger's domination of the sport. The world No 2's camp clearly does not see it that way. Respect, yes; hero worship, if you must; inferiority complex, most definitely not. Not when the US Open afforded them ample proof to believe that fortune, and indeed Tiger's misfortune, played such a role in San Diego.

"I give Tiger all the credit in the world but I'm a stats guy," Pelz said at the opening of one of his renowned short-game schools at Killeen Castle in Co Meath. "I look at Mickelson's worst three drives and he made two doubles and a bogey and then I look at Tiger's worst three drives and he made eagle, birdie, par. Tiger's three-under, Phil's five-over. Tiger's drives were worse than Phil's, yet finished in better spots.

"When Phil hit his bad three woods they went in the deep six-inch rough; when Tiger hit his bad ones they went into the next fairway or the trampled-down dry dirt. So if you're going to miss, miss big and have a unique set of circumstances when your knee hurts so bad before the tournament that all you do in the build-up is putt all day, every day and go on to make 75 footers, 50 footers, 40 footers...

"That actually might not be a bad way to do it," he adds. "I mentioned it to Phil. Of course, it's not just luck. It is lucky when a 75-footer hits the hole and goes in, but it's not lucky that he hits it so near to the hole. It might have gone eight foot past but he probably wouldn't have three-putted as he was putting so fine.

"Tiger's putting was incredible. You don't make six or eight snakes in four rounds of a tournament if you're putting badly. So if you combine the bad misses with the luck and the great putting you get his head-to-head with Rocco [Mediate]."

Now some will inevitably view this as Pelz merely defending his own role in the most talked-about major in the last decade. The guru with the big hat was widely criticised in the American media for sending Mickelson out at Torrey with a driverless philosophy. Accusations of over-strategising and of strangling a natural talent flew his way but, far from ducking them, Pelz wants to tackle them head on.

"Phil simply didn't hit his three woods well and the only way the charges of overstrategising can be correct is if Phil would have hitten his driver any straighter. I don't believe that," he said. "You know, before I worked with Phil he had gone 43 and 0 in the majors. We're not doing bad as in the last four years he has won three. And to my mind that should be judged in three years as he was hurt [with a wrist injury] last year and there was no way he should have played."

Indeed, if the golfing intelligentsia is kind enough to wipe out 2007, then Mickelson-Pelz have not been performing too disastrously against Woods. The score between the 2004 to 2006 seasons was 4-3 in majors in Tiger's favour; a deficit lengthened to 5-3 after last month, but hardly the stuffing that current public perception might suggest. In fact, Pelz is prepared to shove his neck ever further over the block and declare that, despite Woods' dead-eyed excellence on those Californian greens, Mickelson has no equal when it comes to being in close proximity to the shaved surfaces.

"Phil Mickelson has the best short game I have ever seen," Pelz said. "No question. He is very creative and has no fear. The launch angles he gets are just absurd. Earlier this year he was not putting well because he had been working on his swing with Butch Harmon, but now it's the best I've ever seen. I think he's got a great chance at this Open."

Well, he should have, shouldn't he? Tiger is not in town and Mickelson is therefore the acting world No 1. If he doesn't have "a great chance at this Open", then something is seriously wrong. As it is, Mickelson's Open record suggests there is something horrifically wrong. One top 10 in 16 years is ghastly enough but when the number of other top 20s is placed alongside it – one – it enters the darker reaches of Stephen King's imagination. This is where Pelz comes in; the physicist charged with, if not quite reinventing the wheel, then at least making sure it does not veer off into the nearest links hazard.

"I have been working with Pelz on taking some spin off my short irons to control my trajectory" Mickelson said. "I've always been a high-spin player, so it's taken me a while to get the spin off. At a lot of courses we play, you fly it by the hole and the ball just sticks. Here, you've got to plan for 20 to 50 yards of roll."

And, by jove, this golfing Henry Higgins believes his Eliza might just have got it. "Phil's learning links golf all the time, but now he's nearer than ever," Pelz said. "It's all going to click one day and I hope it will be at Birkdale. I don't know, but I do know that it will happen somewhere."

The moment it does, if it does, will surely represent the pinnacle of their relationship; a completion of their work. Mickelson was always going to win a Masters on an Augusta course chiselled to his strengths, while the run-of-the-mill PGA Tour feel to many of the USPGA set-ups meant that particular major was a law, or average, waiting to prove itself. But the Open isn't, wasn't and to some never will be. Among the dunes he has resembled a little boy lost. Except at Troon, in 2004, when he finished one shot off the play-off. He had run to Pelz seven months earlier, to the guru who was inspiring a whole new generation of short-game coaches with his obvious, but bafflingly often overlooked, mantra: "How you play inside of 100 yards is the prime determinant of how you score." Unsurprisingly, the phone call that was to change Pelz's life still rings loudly in his mind.

He said: "I remember saying to him, 'Phil, why do you call me for? I heard you've got the best short game already.' 'Can you save me a quarter of a shot of a round?' he asked me. 'What's that based on?' I said. 'Well, I've finished second so many times. I've played 43 majors and never won. Now, if I took one less shot a major, then I can win some of these things.' And I said, 'Well there's not a man alive who can't save a quarter a shot a round'."

So the pair hooked up and within four months a Green Jacket had been hooked up in Mickelson's wardrobe. That came only after a defining showdown between the meticulous teacher and a pupil who had previously relied almost entirely on his extraordinary well of ability, exemplified, of course, by his trademark "Phil Flop Shot". "I asked Phil how he prepares for the majors," Pelz recalled. "'Well, I take Monday off,' he told me, 'on Tuesday I play the course. Wednesday, I play nine holes.' So I asked him why he never went early to a course. He said because he didn't have the time and knew the courses anyway. I said: 'Come early with me.' But he said, 'Are you joking, how am I going to find the time?' and he kept making excuses. So I finally said: 'How many majors have you won? You won zero of 43 doing it your way. Let's try it my way once.'"

Mickelson's famous belligerence eventually gave out. Mr Natural, the player who had always done it exactly how he saw and felt it, relented and let Pelz reveal what he had. "Believe it," Pelz laughed. "Phil's still stubborn, stubborn as a rock. But he's inquisitive as well." Pelz showed him the data of their stints at Augusta and Mickelson duly recognised that the miracle shots could be more costly than they were exhilarating.

"He's like Greg Norman in the fact that he could do amazing things," Pelz said. "But trying these amazing things would often get him in trouble. He would take a lot of double-bogeys. I never got him to change his game or his personality. He is simply now more aware of the percentage chances of succeeding, that's all."

Yet that plainly is not all. He is aware of the percentage chances of succeeding on each and every major hole. The pair's by now legendary reconnaissance missions leave no stone or bunker rake unturned. Take Royal Birkdale. "We spent 14 hours completing a round," Pelz said. "Around 45 minutes on each hole and most of that round the green."

There they stood, playing pitches, ships and lastly putts in from different angles, learning where best to come in from and, more importantly, where is worst. "Phil would often aim for trouble just to see what happened," Pelz explained. "And there's plenty of trouble out there. At one stage Bones [Mickelson's long-term caddie, Jim Mackay] threw a ball into a rough and we couldn't find it. That shows how careful you must be; particularly with the run-off areas and the greens."

As ever, every detail has been faithfully recorded by Mickelson in a little book to which he will be seen referring throughout the tournament. Nothing is left to chance; except, perhaps, the tee shots. That is Harmon's domain. "The day Phil Mickelson starts driving it in the fairway, he's going to be the best player in the world," Pelz said. That is the world containing Tiger. A fit Tiger. Maybe it is wise to see how Mickelson fares here without him first.

Close encounters: Others rescued by short-game coaches

SERGIO GARCIA

Since he sought out the help of Stan Utley earlier this year, the transformation in Garcia's putting has been obvious. Utley is a former PGA Tour journeyman who, while struggling on the Tour, found more and more of his fellow pros coming to him for advice. Utley was deadly on and around the greens and has made the transition into teaching.

LEE WESTWOOD

A year ago at the Open at Carnoustie, Mark Roe, a former European Tour colleague of Westwood's, started to help out with his chipping. It was the glaring weakness in Westwood's game and Roe, a highly rated short-game exponent, believed he knew how to fix it. Roe was right: Westwood's chipping is now unrecognisable from what it was.

PADRAIG HARRINGTON

If Harrington is able to overcome his wrist injury this week, he will probably need his putting touch to be even more clinical than ever. Fortunately, the Irishman has Dr Paul Hurrion in his corner, a man who, like Pelz, has applied science to his passion. Hurrion is a biochemist from Warwickshire who has also helped to design Harrington's shoes.

Mickelson's Open troubles

1991 Royal Birkdale – T73

1994 Turnberry – Missed cut

1995 St Andrews – T40

1996 Lytham – T41

1997 Troon – T24

1998 Royal Birkdale – 79

1999 Carnoustie – Missed cut

2000 St Andrews –T11

2001 Lytham – T30

2002 Muirfield – T66

2003 Sandwich – T59

2004 Troon – Third

2005 St Andrews – T60

2006 Hoylake – T22

2007 Carnoustie – Missed cut