There is a scene in an early episode of The Simpsons that says quite a lot about sports fans in general, and fans who gamble on sport in particular. Krusty the Clown and his accountant are watching a basketball game on TV. “Let me get this straight,” the accountant says. “You took all the money you made franchising your name and bet it against the Harlem Globetrotters?” To which Krusty wails: “But I thought the Generals were due.”

The Globetrotters crossed the line between a spectator sport and scripted entertainment. Outside Springfield – where it was the local Mafia don who laid the bet – no bookie will offer odds on a match where the result has already been decided. Some degree of uncertainty is an essential ingredient in a betting market, whether it involves a football match, a horse race or any of the other three dozen or so sports that are listed by most major bookmakers.

Uncertainty, in its other guise as competitiveness, sells tickets, media rights packages and armchair subscriptions to sports bundles and so, in one sense at least, Premier League executives should be delighted that their competition is a wildly popular gambling medium around the globe. If foreign betting firms are paying big money for shirt-sponsorship deals, say, it is, in its way, a sign that they are doing something right.

But the bewildering array of gambling brands associated with modern sport in general, and Premier League football above all, also fuels concerns that bookmakers are getting too cosy and close with the events that are their raw material. It can feel as though every half-time commercial is for a bookie pushing its latest in-play odds and as if every player is a walking billboard for a betting firm. Are they trying to test how much exposure to Ray Winstone and the latest in-play odds the average viewer can stand?

As high-profile sports are reminded on a regular basis, however, gambling comes with baggage attached and can dump it in your lap at a moment’s notice.

Tennis and cricket have endured several betting-related corruption scandals in recent years and the latest dose of negative PR for football arrived this past week, when Simon Stevens, the chief executive of the NHS, expressed his concern that eight of the nine gambling firms that sponsor Premier League shirts have failed to contribute a penny to a fund set up to raise £10m annually to fight gambling addiction and the social problems it creates.

Gamble Aware, the charity that administers the fund, added its support, saying it is “seriously concerned that the relationship between sport and gambling has reached a tipping point” and that it “would like to see all clubs, leagues and broadcasters who profit from gambling work with us to help fund treatment for this hidden addiction”.

Stevens concluded by saying that the NHS will “work with the Premier League on how we persuade these foreign gambling companies to do the right thing”. Hopefully, they will succeed. But to do so, they will need to work on the commercial instincts of the companies concerned. A simple appeal to their better nature will not be enough, because while the failure of the eight firms to pay into the fund is certainly short‑sighted, their contribution is at least roughly in line with their presence in the British betting market, which is on the low side of almost nil.

Instead, 99.9% of the customers that firms such as Fun88 (Newcastle), LaBa360 (Burnley) and ManbetX (Crystal Palace) are trying to attract will never watch a Premier League match in person or even in the country where it is being played. They will be betting, watching and supporting their favourite teams in south and east Asia, where Manchester United, Chelsea, Liverpool and others have put so much effort into building up their support. It is not just the ownership of these gambling companies that is, as Stevens said, foreign. So is their actual business and when, inevitably, some of their customers suffer the mental or social afflictions associated with gambling addiction, it will not be the NHS that pays to pick up the pieces.

Betting on English football has always been popular in south and east Asia but it has exploded since moving online to the extent that Britain is no longer the biggest market for betting on English football. These days, it is the British odds that respond to moves in the Asian prices in the minutes before a big match and not vice versa, which shows where the real strength in the market lies.

This means shirt sponsorships are highly prized by Asian gambling operators trying to carve themselves a bigger share of the bounty. It is that value the Premier League will need to target if it is serious about getting Fun88 and the rest to contribute to the treatment of British gambling addicts, because simply asking them to do the right thing is unlikely to cut any ice.

The Premier League does not have a reputation for leaving much behind when it comes to exploiting its product, but, at the same time, the long list of Asian-based betting firms sponsoring shirts, in the Premier League and the Championship, leaves little room for doubt about the immense value of English football to Asian betting markets. If they pitch it correctly, the hold-out eight firms will almost certainly cough up and they will do so because it makes sound business sense.

That would at least help to push the Gamble Aware fund towards its £10m target to assist problem gamblers in Britain. For problem gamblers in Asia, it will do nothing at all.