The mood at both was buoyant, as tends to be the way when a new season beckons.

At Everton, hopes were high that a bright young manager, 39-year-old David Moyes, would pilot them to a position much higher than the previous year's lacklustre 15^th place.

Excitement was also beginning to mount over the potential of a 16-year-old forward called Wayne Rooney who, I reported breathlessly, "has drawn comparison with Kenny Dalglish".

Across town at Liverpool, hope was focused on the striking figure of El Hadji Diouf, whom I had watched terrorise defences first with Lens in northern France, then at the 2002 FIFA World Cup in South Korea and Japan, where he had helped propel Senegal as far as the quarter-finals.

The thinking was that the powerful forward might forge a partnership with Michael Owen potent enough to carry the Reds to their first league title since 1990.

"He can play in four positions," enthused Liverpool manager Gérard Houllier after an early-season win at Aston Villa.

The graphic accompanying the piece I wrote after my visit indicates that, at £10 million ($12.1 million/€11.85 million), Diouf was the third-priciest transfer arrival at a Premier League club so far that summer, after Rio Ferdinand and Nicolas Anelka.

History records that Everton’s pre-season optimism turned out to be better-founded than Liverpool's: the team from the blue half of Merseyside improved markedly to seventh place in the final 2002-2003 Premier League standings: Liverpool slipped from second to fifth.

Manchester City, by the way, came in ninth in their first season back in the big time.

It all seems so innocent compared to Big Football today, with its phalanxes of billionaire owners, its data-driven decision-making and its undercurrents of state-related image management.

In recent days, what may turn out to be the oddest Premier League season yet has been getting under way accompanied by the usual torrents of media coverage, notwithstanding the blazing British summer and the superabundance of more traditional first-week-of-August sporting fare - golf, cricket, the Commonwealth Games - that has been available for consumption.

The reason for the early start is the unusual timing of this year’s FIFA World Cup, to be played in Qatar between November 21 and December 18.

This necessitates a yawning gap in the 2022-2023 edition of the world’s most revenue-rich national football league.

This will wind down on and around November 12, with the likes of Fulham against Manchester United and Newcastle v Chelsea, to resume only on Boxing Day - December 26 - when Aston Villa are currently scheduled to host Liverpool and Manchester City to travel to Leeds.

The thing is though, not every Premier League footballer will be at the World Cup.

Two very noteworthy players who won’t are Liverpool’s main goal-getter Mo Salah and the newcomer widely expected to fulfil the same role for Manchester City, Erling Haaland.

When Boxing Day rolls around, therefore, these two and quite a few others ought to be fresh as daisies after a month-long break - albeit one they probably wish they did not have.

By contrast, a number of their team-mates and opponents may need time to recuperate after some of the most intense games of their professional careers.

Will this contribute to a spate of unexpected results in January and February?

You would not rule it out: indeed, "Expect Amazing", the catchphrase for the successful Qatar 2022 bid, might turn out to be more appropriate to the second half of the 2022-2023 Premier League.

Meanwhile, the BBC has taken a step that symbolises how football has changed, while threatening to open a new front in Britain’s rampaging culture wars, by dropping the classified football results, read out on radio at 5pm each Saturday for decades.

You can understand why: technology long ago advanced to permit minute-by-minute updates of whatever matches you or I might be interested in; in the heyday of football pools, moreover, the classified check offered an efficient means of telling whether customers were in line for a pay-out, a service that is arguably no longer necessary.

Beyond this though, the weekly compilation of results is an example of how professional sport, in particular football, has entered the fabric of people’s day-to-day lives.

When I was growing up, in millions of homes, the classified results - intoned for decades by the much-loved voice of James Alexander Gordon - were a part of the Saturday ritual, even for people who cared little about their detailed content.

This aspect of their significance was conveyed most movingly a few years ago in Terence Davies' cinematic masterpiece about an ordinary Liverpool family, Distant Voices, Still Lives.

In times of uncertainty such rituals, even if experienced as little more than background noise, can be a source of comfort.

Through customs like the reading of the classified football results, sport touches nearly everyone in a small but positive way.

It would do well to retain a few such touch-points, even as life races ahead in ever decreasing circles.