There is an abundance of world-class fly-halfs, but the pool of players with the speed, tactical nous and ability to break the gain line from inside centre is much more sparse.
A vacancy for the key position of inside centre in rugby
If Dan Carter is the so-called "Perfect 10" in New Zealand, the contest for the "Perfect 12" at the Rugby World Cup remains wide open.
The list of qualifications for the inside centre role is long. So long, in fact, that many line-ups are configured to a degree to compensate for the shortcomings of the man in the No 12 jersey. "You are looking at your 12 to be the perfect player," Brian Smith, the England attack coach, said. "A distributor, a potential kicking option, another organiser but also a ball carrier and everyone is trying to get their go forward through midfield, so he has to be a big defensive player.
"It's very difficult to have the complete game. [There are] Not many in the world who do."
Many teams are forced to choose between two extremes.
Wales can go for the spark and kicking game of James Hook or the line-breaking of Jamie Roberts, while England seem to have come down on the side of power after jettisoning the likes of Shane Geraghty to include Mike Tindall and Shontayne Hape in their squad.
England, France and Australia are among the teams at the World Cup without a full-time occupant for the role, but envious eyes from all quarters are cast toward the host nation.
Sonny Bill Williams, the rugby league convert, would probably walk into the starting line-up at No 12 for 19 of the 20 nations at the World Cup. Unfortunately for him, he is playing for the one team that already has Ma'a Nonu.
With 114 caps between them, Nonu and Conrad Smith form a centre partnership that Graham Henry, the New Zealand coach, is reluctant to split. Complementary in ability and understanding, they have been together more or less constantly since Tana Umaga left the international scene six years ago.
"The two centres we've got, Nonu and Smith, have played a lot of rugby together," Henry said. "They have played very well for the All Blacks and created a high standard."
That standard means that Williams - despite his superstar status and a build that makes him just as comfortable in the boxing ring - is yet to secure a regular starting berth for the All Blacks and made the two most recent of his 10 appearances as a replacement on the wing.
As if to confirm his athleticism and all-around game, Williams scored two tries in the rout of Japan and one in Saturday's 37-17 win over France.
"He looked pretty handy and defended well," Henry said. "Certainly it is of interest to the selectors the way he played there. His positional sense was pretty reasonable for a guy who hadn't played a lot there. He added to what we are doing and that can only be good going forward."
Williams did start at No 12 in the opening win over Tonga, with Nonu switching to outside centre to accommodate him. The split in the roles was almost notional, though, as the pair dovetailed and switched about.
"I liked what I saw," Umaga, the former All Blacks captain, said. "He and Nonu worked well, switching inside and out, and I think it was invaluable for the selectors.
"Everyone knows what he can do. He's a megastar and a rock star and a great athlete."
Almost every other team is still looking for the right No 12, although South Africa has the luxury of choosing between Francois Steyn, who kicked all the points in the Springboks' 2007 World Cup final win over England, and Jean de Villiers.
"I had forgotten how much more you are in the action at 12," Steyn said. "I am not sure if I am a centre or a fullback. I see I am listed everywhere as a utility back, so I guess that is what I am, whatever it means."
Gordon D'Arcy, Paddy Wallace and Ronan O'Gara have all played inside Brian O'Driscoll, the Ireland captain, at this World Cup, while France switched Maxime Mermoz from the wing to replace Fabrice Estebanez after the opening win over Japan.
As if to underline the uncertainty, Estebanez also plays fly-half.
But nowhere are the demands of the role illustrated better than in the England team.
Since Will Greenwood's final appearance a year after he won the 2003 World Cup, England have selected a total 28 players in the centres. While Manu Tuilagi is now first choice at No 13, a true successor to Greenwood has yet to be identified.
Tindall moved from outside centre to accommodate Tuilagi - returning to the No 12 shirt he wore alongside Greenwood because of his former partner's superstitious preference for No 13 - but has attracted widespread criticism from fans and media for having the bulk but not the skills.
"He is the personification of everything that is wrong with England's attack," Brendan Venter, the coach of Saracens, the English Premiership side, and a former South Africa international, wrote in a column for British newspaper The Daily Telegraph.
"He poses no threat with the ball in hand, he doesn't have a passing game and he has lost so much of the pace he used to have."
Smith even floated the option of switching Toby Flood or Jonny Wilkinson from fly-half into the role, although that is unlikely.
"Twelve is a real key position," Smith said. "You want someone who's got good distribution, ideally a kicker. But if you look globally now at the shape and size of 12s they've also got to have some bump."
The tinkering continues.