Ninety-nine per cent of occupants of the dozens of double-decker carriages bound for a single location were supporting the same team, but the stern-faced individual patrolling the Patriots train was targeting the others.

“Any Dolphins fans here?” he demanded as he entered the carriage my son Sean and I were occupying – we wondered briefly whether there was some sort of segregation issue – before his gaze alighted on a hapless soul.

“Ah, here we are . . . Come on then, who’s your starting quarter-back today? Come on, surely you know? Do you want to phone a friend?” he taunted, to general merriment.

“OK, you don’t know that one, so you might struggle with this. Can you remember the last time the Dolphins were four and O at the start of a season? That’s what they have to do if they’re going to win today. Nah . . . actually looking at you, you probably weren’t even born. No idea? It was 1985 . . . Do you really think it’s going to happen today?”

It was a one-sided exchange that might have sparked serious trouble had it taken place on a train bound for a football match in Europe, but the Miami Dolphins fan was never going to take exception. Even if the man doing the goading had not been a gun-toting transit cop, the victim was in on the joke and, bizarre as it seemed that the only harassment an away supporter suffered was delivered by a policeman, that, too, spoke to an atmosphere which was all about enjoyment.

As the name on the back of thousands of shirts being sported indicated, the vast majority on board were paying homage to "the GOAT", a quarterback who has earned that "Greatest Of All Time" acronym by re-writing the record books since being repeatedly overlooked by every team in the National Football League in the Millennium year draft. Yet, as we headed to Foxboro Stadium for the first of two visits in five days, doubt was growing about whether the now 41-year-old Tom Brady still had the capacity to add to his peerless achievements.

Such is the short, sharp, leave-them-begging-for-more nature of the NFL season, our week-long visit would let us attend a quarter of this year’s New England Patriots regular season home matches and they had the potential to be pivotal. In the course of those meetings with the Dolphins and the Indianapolis Colts, Brady would seize the chance to stimulate hope that much more is yet to come.

In the build-up to the first, the announcer let us know he would have a new target in the shape of Josh Gordon, a fine talent with a troubled past that had resulted in a number of suspensions for use of recreational drugs, the latest of Patriots coach Bill Belichick’s risky redemption projects. Brady could, we were told, set yet another new NFL record by connecting with Gordon to send a 71st different receiver into the end zone.

Admittedly there was momentary concern when an impressive opening drive stalled, but by half-time the contest was over, a final scoreline of 38-7 ensuring Dolphins fans would literally cop it once more on the way home.

Four nights later and our exemplar of law enforcement unorthodoxy was at it again: “Any Colts fans in this carriage? Great . . . come on who’s your quarterback? Can you believe I had a Dolphins fan on here the other day who had to phone a friend when I asked him that? Luck you say… that’s right. Luck, that’s what you’ll need tonight.”

Once again, not a suggestion of any offence taken as his target took the razzing in good spirit and Andrew Luck was to do a pretty decent job of leading a threatening comeback, until his counterpart intervened as only Brady can.

So much about the game’s key moment spoke to greatness on a night when the pre-match message had been that Brady needed only three more touchdown passes to become just the third quarterback in NFL history to reach the 500 mark. Once again, the Patriots had dominated to lead 24-3 at the interval, but that change of Luck in the third quarter had narrowed the gap to within a score to transform the dynamics. Now there was real pressure as, 34 yards out, Brady scanned for receivers and for a split second he seemed to have got it wrong, the pass heading into the end zone where two Colts were covering a solitary Patriot until Gordon seized his chance. As his 6’3” frame soared athletically skywards, the defenders were removed from the equation and Brady joined the 500 club by separating himself from the rest in yet another way by finding that 71st receiver.

Perhaps it was sheer opportunism, but beyond that it felt like a statement was made as he effectively told the newcomer how much faith he has in him. To be anointed that way by the GOAT could prove a turning point in terms of much more than this match, our pleasure in the moment amplified by the selection of soundtrack, The Proclaimers adding a Scottish element to proceedings as “500 miles” belted out around the stadium.

With running backs Sony Michel and James White also adding an extra dimension to the Patriots offence, a previously ineffective unit suddenly looked to be bristling with menace, Gordon and the ever dangerous, but fragile, Rob Gronkowski joined as receiving targets against the Colts by the return of another fan favourite.

Admittedly, as addressed in my column earlier this week, Julian Edelman’s reintroduction after a ban for a different type of substance abuse to those that have blighted Gordon’s career introduced a less savoury dimension. The warmth of the wide receiver’s reception after missing the first four weeks of the season after testing positive for performance enhancing drugs spoke to some very different views towards what is permissible within elite sport on the other side of the Atlantic where professional sport has evolved rather differently with the need to do what is required in the name of entertainment and putting bums on seats providing the main impetus in American sport.

Yet, whatever we think of some consequences of that, there is much to learn from the emphasis placed on a sense of enjoyment that allows the local polis to join in the fun, contrasting as that does with the open hostility towards friend and foe that is so often central to the European football experience. Reservations of a different sort there may be, but few who get the chance to jump aboard the Brady Train are likely to be deterred.