They are jacks of most political trades and masters of the remainder. They can absorb the detail without losing the big picture.
Crucially, they enjoy a level of political seniority which allows them to bang heads together (metaphorically speaking) to make things happen.
Their reward is invisible, yet palpable - ever-increasing influence as the power behind the throne.
Jim Bolger had Bill Birch, someone whose political acumen, understanding of the bureaucracy and relentless work ethic meant he could sort out most foul-ups thrown in his direction.
Helen Clark had Michael Cullen, whose considerable intellect was tapped to do the almost impossible - come up with a lasting solution to the foreshore and seabed imbroglio.
Joyce has likewise been handed the hospital pass from hell. The problem had become bigger than National had earlier anticipated. Junior minister Craig Foss was struggling over how to stem the never-ending flow of payroll errors.
You only have to read the catalogue of woes in the Ministry of Education briefing paper written for Joyce to understand how daunting the challenge is.
The document gets to the nub of the problem - that Novopay was designed with the assumption that 90 per cent of school administrators would be using it online, not the little over 70 per cent in actuality.
Worse, some aspects of the payroll - such as submitting timesheets for part-time teachers - could not be done online.
The result was schools submitted pay forms by email. Talent2, the Australian-based company which owns Novopay, hadn't devoted enough staffing to cope with the deluge. Existing staff weren't trained to answer the schools' queries.
The ministry said Talent2's performance had been improving, but this was so slow and incremental that it was virtually invisible to schools who had largely lost confidence in the new system.
If nothing was done, it would take 18 to 24 months before the system was delivering at the level expected of it, let alone generating the extra benefits promised of it.
Not surprisingly, Joyce has recoiled in horror at such a timetable. He certainly warned that there was no quick fix. But that was much to avoid unduly raising expectations among teachers and parents that his appointment would mean rapid progress in sorting out the mess. Joyce would rather adopt the standard approach that it's better to under-promise and over-deliver.
At the same time, he cannot be sanguine about time. The pressure is on him to institute measures which see a substantial reduction in errors and which has the double plus of taking the pressure off waiting times for teachers seeking answers from Novopay's and the ministry's call centres.
Joyce's inclination is to stick with Novopay simply because things are so far down the track that it would be even more disruptive to switch to a back-up provider.
But he has to be absolutely sure Novopay can be fixed. That is the priority. He has, accordingly, instituted a technical audit to find out if Novopay can be "stabilised" or if the project will have to be ditched. That's expected to take three to four weeks.
Until then, he won't foreclose on any options, such as discussing contingency plans with Datacom, the previous supplier.
Among a host of other initiatives designed to be inclusive of sector groups, Joyce has instituted a separate ministerial inquiry which will assess all aspects of the Novopay project from go to whoa.
That will take in the at times fractious dialogue between the ministry and Talent2 which saw the project's "go live" date twice delayed and the ministry threatening breach of contract. Given problems were apparent at least three years ago, one of the more delicate questions will be how much ministers knew of all this and how much the ministry kept them in the dark.
One plus for Joyce and National is that Labour is implicated in this sorry saga by virtue of having signed the contract with Talent2 back in 2008.
The then Cabinet went with the cheaper option of outsourcing all aspects of the teacher payroll, rather than keeping some critical elements in house in the ministry.
That now looks to have been a false economy. Talent2's failure to meet deadlines and its inability to respond fast or adequately enough to the crisis of its making has seen the ministry necessarily retain control of some elements of the project and assume new ones where Talent2 has left a yawning gap.
This is likely to lead to negotiation of a variation in the contract which would see the project looking far more like the more expensive option Labour ministers rejected.
But that doesn't make Joyce's job easier. The ministry is already pouring extra funds into the project to try and get it back on the rails. There will probably have to be more.
Joyce hardly needs telling that there's not a lot of political upside in New Zealand taxpayers having to bail out an Australian enterprise which has displayed little remorse for its failure to deliver on its contract or the consequent disruption that has caused to many teachers' lives.
But then there isn't a lot of upside for Joyce in all this. Success is simply expected of him; failure will be a major blight on any higher ambitions. So far it's been textbook stuff from the fourth-ranked Cabinet minister. In short, so far so good. But there's a long way to go before he and National can finally breathe easier on this one.