Television's voice of golf knows a thing or two when it comes to assessing a player's qualities, but his inclusion of the popular Price in such ceremonious company, ostensibly for his social graces, smacks of faint praise. No slight was intended, though, and Alliss is quick to talk up the 40-year- old Zimbabwean's prospects this week at Augusta. "Nick is a wonderful ball striker, and he seems to be putting very well at the moment," declares the veteran commentator. "On that basis, he is always going to be in contention."
Having travelled a long road and weathered many setbacks since his salad days on the European Tour in the late 1970s, Price rose to become the undisputed world No 1 for two and half years from the middle of 1992. During that period he won two USPGA Championships, the 1994 Open at Turnberry and 12 other titles, and twice topped the US money list. At the time, he had no apparent weakness. His driving was long and straight, his iron play crisp and accurate, his temperament sound, and his short game the stuff of dreams.
Then came an abrupt decline during which he could so easily have hidden behind the cri de coeur monotonously familiar to followers of Monty, Faldo and Woosie, about a recalcitrant putting stroke. Erratic health in the shape of chronic sinusitis also played its part, but instead of moaning or petulantly blaming the media for his misfortunes, the unassuming Price quietly prescribed his own cure with a little help from golf's spin-doctor- in-chief, David Leadbetter.
After three months of 1997, the treatment seems to be working. In seven starts since ending last year with a succession of high finishes in Africa, he has chalked up two victories, two second places, a third, an 11th and a creditable level-par tie for 24th at the TPC last weekend.
The wins, boosting his career tally to 32, both came in South Africa - the Dimension Data Pro-Am at Sun City and the Alfred Dunhill PGA at Houghton - while four of his other five outings were in the United States. Not surprisingly, he is back in the world's top 10 and bristling with renewed enthusiasm.
"Confidence is everything in golf and its what I've lacked over the last few years," said Price. "You notice it particularly on the greens. I suppose I'm holing at least two extra putts a round than I was before. I was striking the ball no worse than I am now, and I was hitting the same number of greens in regulation, but at last the putts are dropping. I knew it was the main problem with my game and I've worked hard to correct it. Now, when I'm under the gun, I know what I'm doing."
To golfers, this mental state is the equivalent of Nirvana, a promised land only fleetingly experienced, if ever. But long before his present burst of form and the sustained thrill of those previous anni mirabili, Price had already tasted this rare feeling. At Augusta of all places.
In the third round of the 1986 Masters, Price, who eventually came fifth, carded a course record 63, nine under par and 16 shots fewer than his opening effort. His score would have been even lower had either of two makeable birdie putts dropped on the final two greens. One slid narrowly by while the other hit the back of the cup and settled defiantly on the edge. Afterwards, he commented modestly: "I think Bobby Jones [the late, great champion who built Augusta and created the Masters] held up his hand from somewhere and said 'that's enough, boy'."
Price therefore has his place in Augusta's history, but only once since has he come close there, when tying for sixth in 1992. Anoraks, though, will have already detected a pattern. Price was twice runner-up in the Open, in 1982 at Troon where the tournament returns this summer and in 1988 at Lytham. Six years later, he finally scaled the elusive pinnacle. His two promising Masters tilts have also occurred at six-year intervals, so perhaps 1998 will be his year instead?
"I don't care when it comes as long as it does. But if it doesn't happen I can't complain about what golf has given me," said Price, who has banked more than $7.5m in US prize money alone.
Like many great occasions, the Masters has its own sense of theatre - witness Ben Crenshaw's tearful triumph just a week after the death of his mentor Harvey Penick in 1995. After last year's dramatic collapse, Price's great friend, fellow colonial and Floridian neighbour, Greg Norman, would be a sentimental winner.
But with his long-serving caddy Jeff "Squeeky" Medlen in need of a tonic as he battles leukaemia, Price would be a fitting recipient of the coveted Green Jacket next Sunday in every respect. As Alliss might say, what a nice idea.