The only rule with this unique sire is that there are no rules

That's the breeding game sorted, then. Send a high-class sprinter – or, failing that, at least a fair one with an excellent pedigree – to Galileo and, hey presto, you will get yourself a Group 1 winner.

Take Churchill and Winter, who completed their Guineas doubles at the Curragh over the weekend. Both by Coolmore's phenomenal sire, the former is out of Meow, a Queen Mary Stakes runner-up, herself out of the fine sprinter Airwave; and the latter is out of Laddies Poker Two, a daughter of Choisir who landed a gamble in the Wokingham Handicap at Royal Ascot.

Tattersalls Gold Cup hero Decorated Knight, Galileo's third Group 1 laureate in two days, is out of Pearling, an exceptionally well-bred mare who finished second over five furlongs on the first of only two starts in Canada. Pearling is a sister not only to the great Giant's Causeway, but also to Cherry Hinton Stakes winner You'resothrilling - who delivered further proof of the efficacy of the sprinter "system" by giving Galileo another dual Guineas winner, in Gleneagles, as well as Irish 1,000 Guineas heroine Marvellous.

Hydrangea, third to Winter on Sunday, is out of Beauty Is Truth, winner of the Group 2 Prix du Gros-Chene over five furlongs (as is her brother, The United States, a top-flight winner over double that distance in Australia). And Deauville, third behind Decorated Knight on the same card, is out of Walklikeanegyptian, whose only victory came over the minimum trip in a Class 5 nursery at Folkestone.

Cliffs Of Moher, contesting favouritism for the Derby on Saturday, is another Galileo colt out of a winner over five furlongs. His dam, Wave, is out of Queen Cleopatra, who finished third in the Irish 1,000 Guineas and Prix de Diane and is a sister to ace miler Henrythenavigator.

That so many are being bred on this template can be no surprise in the wake of Frankel, in terms of ratings the best horse we have seen - and, of course, a son of Galileo out of Kind, a daughter of Danehill who won Listed contests over five and six furlongs.

Cliffs Of Moher is another colt whose dam won over five furlongsCredit: Edward Whitaker

Coolmore and outside breeders had always sent fast mares to Galileo, perhaps hoping to mitigate the stamina influence in a sire who seemed best over 12 furlongs on the track. As a son of Sadler's Wells and Prix de l'Arc de Triomphe winner Urban Sea, after all, it seemed reasonable to assume that he would impart staying power in abundance.

Since the emergence of so many top-notchers by Galileo out of sprinters – not just Frankel but also Adelaide, Cape Blanco and Seventh Heaven, among others; many staying far beyond the kind of distance their dams could have managed – the volume of such mares in the champion sire's books has only intensified over recent years, with speedy Group 1 winners Margot Did, Mecca's Angel and Tiggy Wiggy bought specifically to visit him.

But it should not be forgotten that Galileo-plus-sprinter is not the only formula that equals a top-class performer. Matched with Oaks winner Ouija Board, he came up with Derby winner Australia - not beaten far in the 2,000 Guineas, remember, even though his parents both won Epsom Classics.

New Approach, beaten a whisker in the Guineas before he landed the Derby, is out of Irish Champion Stakes heroine Park Express; while last year's Derby runner-up US Army Ranger is a son of Irish Oaks winner Moonstone, a daughter of Dalakhani, more often than not a strong source of stamina.

Just as putting speed to Galileo does not appear to inhibit the progeny's ability to stay Classic distances, so adding more stamina to the genetic mix does not necessarily mean a foal will lack zip.

Allegretto - one of Galileo's early stars, winning five Pattern races between 12 and 16 furlongs from 2006 to 2008 - is an intriguing case study as a daughter of Doncaster Cup winner Alleluia. Yes, Allegretto stayed well, but sending a mare who won over 18 furlongs to a Derby winner might otherwise have been expected to result in a winner of the Lancashire Chase, rather than the Lancashire Oaks.

New Approach is out of Irish Champion Stakes heroine Park ExpressCredit: Edward Whitaker

Although Cliffs Of Moher heads the betting among the Galileo battalion in the Investec Derby this week, a couple of others in Saturday's field could reaffirm the case for sending him middle-distance mares.

Chester Vase winner Venice Beach is out of Danedrop, an unraced daughter of Danehill and 1m5f winner Rose Bonbon, who owes her place in Galileo's affections to having produced Arc and King George winner Danedream; while close Derrinstown Stud Derby Trial third Capri is out of Dialafara, a winner over an extended 12 furlongs out of Prix Vermeille second Diamilina.

Moreover Waldgeist, though taken out on Monday, has clearly been treated as a rising force at this level by his respected connections - and he is out of Waldlerche, a Monsun half-sister to St Leger winner Masked Marvel and a Group 3 scorer over an extended ten furlongs.

In usual circumstances, we might agonise over whose pedigree is best suited to the Derby. Is the more speedily bred Cliffs Of Moher guaranteed to stay? Will the likes of Capri lack tactical speed, and instead put in a persuasive trial for the St Leger?

But when it comes to Galileo, multifarious breeding theories feel redundant. It is probably sufficient to say that he simply transmits sheer class, which allows his progeny to defy stamina expectations. We are talking, don't forget, about a Derby winner who raced only once at two, in late October - but who can supply two-year-olds with the precocity to shine at Royal Ascot.

With Galileo, Coolmore and other breeders who can afford his services do indeed seem to have the breeding game cracked. But despite a glut of recent evidence to the contrary, it is not solely by sending him sprinters or the speedily bred.

Mares from all walks of life produce stars over all sorts of distances with this truly extraordinary sire.