The West Indies teams that ruled the roost in those days were awesomely destructive, with bat and ball, but also super-cool.
And since many of them spent the English summers playing county cricket, we came to see them partly as our own.
As Somerset supporters, for example, we were only too thrilled to welcome Vivian Richards and Joel Garner into the fold.
It was the same, no doubt, in Hampshire with Gordon Greenidge, Andy Roberts and Malcolm Marshall, Northamptonshire with Curtly Ambrose, and Gloucestershire with Courtney Walsh.
The lesson of this sustained success-story seemed plain enough: in a region like this, whose 40 million or so people are split among (according to Wikipedia) 13 sovereign states and 17 dependent territories, the route to the top lay in banding together.
Now that we live in an era when the symbol of regional sporting prowess is Usain Bolt, the best that has ever lived at one of the most individualistic events in the entire sporting canon, I can understand how perceptions might have changed.
Even so, imagine the relay teams one might have assembled over the past 10-15 years by adding the likes of Kim Collins and Thompsons Richard and Obadele to the cream of the Jamaican sprint crop.
The point of this trip down memory lane is to underline how the secrets of success in one arena do not necessarily hold good for another.
Indeed, pointers from the most important arena of all – international sports politics – suggest that far from holding Caribbean sports leaders back, the fragmented nature of the region can be one of the keys to their ascent.
Imagine there had been a West Indies football team along the lines of the cricketing model.
You might well think that sides combining the top talent from Jamaica, Trinidad and Tobago, Antigua, Grenada and others ought by now to have been capable of compiling a reasonably respectable World Cup record; certainly of qualifying for the finals on a regular basis.
But what might such a creature have meant for the political career of Jack Warner, the Trinidad and Tobago official who rose to become one of the top football power brokers during Sepp Blatter’s long reign at FIFA?
Well, had there been a West Indies Football Association, and had this become a member of CONCACAF, the football Confederation bracketing North and Central America and the Caribbean, in place of Barbados, Grenada, Jamaica and so on, the regional disposition of forces within CONCACAF would have been different, to Warner’s possible disadvantage.
It might well also have meant that fewer national associations from the CONCACAF region were members of FIFA, thus diluting the power of the potential CONCACAF bloc-vote in the world governing body’s decision-making.
Not only is the Caribbean a peculiarly fragmented region; it also happens to lie in a hemisphere of giants – the United States, Mexico, Brazil et cetera et cetera.
As far as sports politics is concerned, this creates a fascinating regional dynamic.
If weight of numbers were the only yardstick that mattered, the Caribbean – population a mere 40 or so million, remember - should nearly always be in the driving-seat: of CONCACAF’s 41 member associations, some 27 are in the Caribbean zone; of the 41 National Olympic Committees (NOCs) represented in the Pan American Sports Organization (PASO), the Caribbean region accounts for nearly half.
CONCACAF, indeed, has been led, for better or worse, by a President from the Caribbean for some 24 of the last 26 years.
Until about a month ago, moreover, there seemed a reasonable chance that Caribbean Football Union President Gordon Derrick, from Antigua and Barbuda, would emerge as the first elected CONCACAF President of football’s new post-Blatter era, in a poll to be held this week.
In the event, he seems highly unlikely to make it to the starting-line, having been declared inadmissible as a candidate by FIFA.
As a result, CONCACAF members, Caribbean and otherwise, will almost certainly be left to choose between Canada’s Victor Montagliani and Bermuda’s Larry Mussenden for the top job.
PASO, in stark contrast, has never yet had a President from the Caribbean in 76 years of existence.
Partly this reflects the simple fact that the organisation covers a wider geographic sweep than CONCACAF, since it takes in South America.
But there is also the small matter of its voting rules.
Under its long-time leader Mario Vázquez Raña, PASO operated a system giving countries an extra vote on certain types of ballot for each time they had hosted the Pan American Games.
Naturally enough, this worked to the benefit of relatively wealthy and/or powerful nations, not least his own country of Mexico, which has hosted the Games on three occasions.
Of the first 17 editions of the Games, only three were hosted by Caribbean cities.
Even now in what is as much a new era for PASO as it is for FIFA, the regional body has not deemed it desirable to implement unadulterated one member-one vote.
Instead, in what might be dubbed Vázquez Raña-lite, the organisation last week decided to allow past-Games hosts to retain one extra vote for certain decisions.
Peru, in consequence, stands to double its voting power from 2019 when Lima hosts the Games.
Presidential elections are also due at PASO in short order, and there are at present no fewer than three prospective candidates from the Caribbean region – Keith Joseph (St Vincent and the Grenadines), José Joaquín Puello (Dominican Republic) and Richard Peterkin (Saint Lucia).
While there is no obligation on countries to vote for their most local candidate - and while the Caribbean’s rich African, Dutch, French, Spanish and British cultural heritage is sufficiently diverse to make holding together a controlling block of votes a distinct challenge - the prospects of any of this trio winning are, by my reckoning, dimmer than if one-country-one-vote applied.
Instead of 18-20 votes out of 41 (depending on how you define the region) if one member-one vote applied, I make it that the Caribbean should account for 21-23 votes out of 51 under the new system, a small but potentially significant dilution.
It could be worse though.
Under the old system, it would have been 21-23 votes out of 58.
And imagine if in years gone by a West Indies Olympic body had somehow become established, covering the same geographic zone as the cricket team.
I reckon that would have cut Caribbean representation to around 12 within a PASO consisting of some 32 members.
It might have robbed us of one of the great teams in sporting history, but beyond the boundary rope, and especially in the corridors of power, there is quite a lot to be said for fragmentation, or so it seems.