The monosyllable was more expressive than you might imagine. It seemed to convey a kaleidoscope of emotions: relief that the election - which had delivered a second-round victory for Bach, the red-hot favourite - was behind him; satisfaction at an ambition fulfilled; a dawning realisation that life would be different now; and perhaps just a dash of trepidation at the size of the job.

I very much doubt, however, if even in his wildest pre-electoral dreams the ninth International Olympic Committee (IOC) President imagined all the slings and arrows that outrageous fortune was set to fling at him over his first decade in charge of this unwieldy, globe-spanning sports empire.

The harsher economic climate in the rich, industrialised countries of the global West, yes, that he could - and I think did - foresee. This was 2013, after all, and the slow-motion fallout from the financial crisis of 2007/2008 was already impacting those of us in the real world. Bach’s new fief was still insulated by the particularly lucrative Vancouver 2010-London 2012-cycle broadcasting rights deals that had been negotiated. But you did not have to be Nostradamus to comprehend that 50 per cent growth was not going to be sustainable in this increasingly tetchy new climate.

The gathering storm-clouds over Rio and its 2016 Olympic and Paralympic project were also plainly apparent. And I suppose if you are going to stage a Winter Olympic Games in South Korea, prudence ought to dictate the formulation of some sort of back-up plan lest tensions with the North began to spiral.

But a raging global pandemic? Even if the wisest national Governments and their scientific advisers were aware that eventually humanity’s recent luck on this score was likely to run out, Bach would have had little reason to anticipate that the contagion would strike in the middle of his watch, blighting a Summer and a Winter Games.

Nor can the German realistically be expected to have foreseen that Vladimir Putin’s Russia would be a cause of almost constant problems for the Movement during his stint at the helm. Indeed, the early signs - up to and including the Sochi 2014 Winter Games a few months after Bach’s election, which were initially felt to have passed off splendidly - might have led us, and him, to expect the opposite.

By comparison, Bach’s predecessor Jacques Rogge - whose approach to the Presidency, admittedly, could not have been more different - had things rather easy.

All of which is a preliminary to saying that even if, like me, you think that the Olympic Movement is in a worse place today than it was on that bright confident morning 10 years ago in the Argentine capital, it does not necessarily follow that Bach has been doing a poor job.

Raising money to keep the Olympic ecosystem - including some of the minor sports on the programme - going is these days one of the Games’s key functions, and here Bach has performed well.

His early sealing of a $7.65 billion (£6.1 billion/€7.1 billion), three-cycle, broadcasting deal with NBCUniversal, locking the US network into screening the Games until 2032, has come to look more and more astute with the passage of time, as the traditional media rights model that enriched sport has come to look ever more precarious.

More than that, he somehow managed to plot a path through the COVID-19 emergency without incurring either a significant hit to IOC revenues or a damagingly substantial escalation of IOC costs. While handouts to some of the bodies that depend on the IOC have scarcely risen since that buoyant 2010/2012 quadrennium, things could have been so much worse. Bach and his team deserve credit for staving off what might have been a real disaster for the wider Movement.

In management terms, the chief hallmark of Bach’s decade has been the centralisation of power. On this I have very mixed feelings.

The IOC did need to become nimbler in an ever faster-paced world. This has been achieved by shifting more onus onto professional, mainly Lausanne-based, officials - the IOC’s civil service - at the expense of members, who are spread around the world (obviously), meet only occasionally and mainly have busy portfolio careers.

In spite of an initial display of collegiality, this centralised, often secretive approach has been evident since the Bach regime’s early days. The path towards that landmark NBCUniversal deal began at a New York dinner attended on the IOC side, by just Bach and two top officials. “We kept it among the three of us,” as the German subsequently confided.

But efficient execution in an organisation whose aspirations are as universal as the IOC’s needs to be accompanied by a consensual, understanding approach when seeking to address the many delicate, potentially divisive matters that will arise.

Too often, I think, Bach’s personal management style has appeared disappointingly intolerant of criticism and sincerely held differences of opinion. Under his leadership, I would say that the IOC’s treatment of individuals such as former International Paralympic Committee President Sir Philip Craven, former World Anti-Doping Agency (WADA) chief Sir Craig Reedie and former IOC doyen, the massively well-respected Richard Pound has sometimes seemed unappealingly petty.

As Pound himself told me: “I paid the price for publicly expressed opposition to the IOC’s decisions, through my removal as chairman of Olympic Broadcasting Services, as director of Olympic Channel Services and from the Legal Affairs Commission.”

There is a problem here. For one thing, once it is known that individuals of even Pound’s stature might pay a price for speaking out, it becomes hard not to take any reference to the “unity of the Olympic Movement” with a pinch of salt.

For another, in this devilishly complicated world, no one individual is going to be right 100 per cent of the time. On those occasions when a prominent leader is about to err, he - and the organisation he leads - needs someone with a firm grasp of the situation to talk straight to him. If the internal culture discourages this, you increase the risk of a damaging blooper.

Changing the Olympic motto to “Faster, higher, stronger – together” was, I believe, one such blooper, though I suppose it is not especially damaging and easily rectifiable.

Another important mistake, in my view, was to reform the selection process for Olympic Host Cities.

The IOC has two chief products: one - the Winter Olympics - is struggling, with global warming now coming, increasingly insistently, to add to its list of problems; the other - the Summer Olympics - remains broadly in reasonable health.

It could certainly be argued that the time has come to rotate the Winter Games around a small number of hosts with the required infrastructure, including the specialised sports facilities.

The Summer Games selection process - admirably transparent and suitably demanding, as it was, for those involved - should have been left well alone.

One of the old system’s abiding virtues, from the Movement’s standpoint, was that it kept the Olympics firmly in the public eye - not always in a good way, admittedly - during the long intervals between Games.

With football an ever more dominant rival for the week-in, week-out attention of sports fans all over the world, this is an increasingly critical issue, and one Bach’s IOC has yet to find a convincing alternative way of addressing.

Of course, under the old method, while their choices had generally been reasonable if sometimes surprising, IOC members had demonstrated a repeated reluctance to select another US city to follow in the footsteps of Atlanta, which hosted the 1996 Summer Games.

With US corporations contributing so heavily to the health of IOC finances, this was becoming a problem for the leadership - one rectified by the simultaneous choice of Hosts for the 2024 and 2028 Games.

With no unblemished Olympics or Winter Olympics yet staged under Bach’s Presidency, these 2024 Games in Paris have become fundamental to the legacy the German will leave behind. This means he simply has to get Russia right.

He has a point when, like the clever lawyer he is, he draws attention to “the other 70 wars and armed conflicts in the world”. After all, if we are to exclude Russian athletes from the Olympic Games, even in neutral guise, we really ought to be able to explain why athletes bearing the passports of the aggressors in at least some of these other conflicts are not similarly excluded.

However, those who argue, like Bach, that the Olympic Movement’s mission is to “unite the world in a peaceful competition” and those who point out, as Bach has done, that the Olympic Charter does not allow "a total isolation of people with a specific passport" face an inconvenient truth. This is that the staunchest support for Ukraine tends to lie in countries whose corporations are the source of a high proportion of IOC revenues.

A Paris 2024 with athletes who carry Russian or Belarusian passports, but with no Ukrainians, would be terrible for the Olympic brand in the rich, industrialised countries of Europe and North America. By contrast, a Paris 2024 without Russians would probably rub along just fine, much as the second Los Angeles Olympics managed to do four decades earlier.

If Paris does deliver a Summer Olympic and Paralympic Games to remember, Bach may have just enough time before his scheduled departure in 2025 to negotiate a parting gift that the Movement would have real cause to be thankful for: a new US media rights deal stretching well beyond 2032. The long-term financial security that such a deal might bring would be a real boon in these increasingly turbulent times and spare his successor the need to focus on the matter as an early priority.

It would also strengthen his hand should he decide to try and extend his Presidency beyond the 12-year maximum stipulated by the Olympic Charter.