Brown will continue to trust primarily in tactical planning and disciplined teamwork to conjure a comeback which would prove that Lazarus was a Scotsman. Yet the gravity of Scotland's situation is such that even their endlessly pragmatic manager would welcome a modicum of magic, outrageous good luck or divine intervention.
Wembley itself may just help nudge the balance back Scotland's way. Brown has witnessed from the terraces the galvanising impact this ostensibly shabby stadium can exert on his country's players and fans. He also points optimistically to the pressure a home crowd tends to put on its team to press forward, leaving gaps to exploit. And, in a spot of psychological warfare, he reiterated yesterday his belief that certain members of Kevin Keegan's team struggle at the so-called Venue of Legends.
Speaking en route to the Scottish squad's base near St Alban's, Brown noted that Tony Adams and Martin Keown did not find Wembley's "wide open spaces" to their liking when faced with sharp, mobile opponents in Arsenal's Champions' League "home" fixtures.
Clutching at straws? After 48 hours of Caledonian doom to test the gloomiest Calvinist, this was tantamount to fighting talk. Brown also claimed, contrary to popular opinion, that Scotland did enough on Saturday to prove all is not lost - provided they could score first.
That is where theory and reality collide like Don Hutchison crunching into Paul Scholes. The Scots have no natural finisher to compare with Shearer, Owen, Cole or Phillips, let alone Scholes. They must also find width and ways of getting behind the defence which were not evident at Hampden, where England were content to let them play in front of them.
Kevin Gallacher's suspension could be a blessing in disguise, forcing Brown to go for a pacier, if less canny, striker. Although both Mark Burchill and Gary McSwegan fit the bill, and Hutchison's height would be useful, Neil McCann's natural talent for pulling wide and isolating a defender makes him the likeliest partner for Billy Dodds.
Scotland's predicament means they will probably need all of them at some stage. They have to score three in London for the first time since Jim Baxter's game in 1967. Even if they matched the striking feats orchestrated by the artist formerly known as Slim Jim, they would also have to stop Keegan's men scoring; Catch 99, you could say. The last time they left Wembley with a result that would suffice was in 1949, by 3-1.
Brown takes heart from the more recent past, notably the fact that Scotland have yet to lose twice in a row in his reign, which completes its sixth year tonight. The last two times they were badly wounded, by Costa Rica under Andy Roxburgh and against England during Euro 96, they responded within days with rousing victories over Sweden and Switzerland respectively.
The regularity with which they find the net on their travels, against higher-ranked nations than England at that, also encourages Brown. But, in truth, Scotland managed but a single goal away to the might of the Faroe Islands this year and none in Lithuania and Estonia.
England have not lost by three at Wembley since Hungary's 6-3 romp in 1953. Summoning all the aforementioned powers of the imagination, only a tartan super-optimist will picture the admirable Dodds, despite his pedigree with the Maryhill Magyars (aka Partick Thistle), spearheading a spree to emulate the original version.