Bangladesh will almost certainly not win this World Cup. They will, of course, come considerably closer to winning it than England, who can only dream of being in a position to almost certainly not win a World Cup, rather than being in the position of having confirmed that they will definitely lose yet another one.

Bangladesh face a Titanic quarter-final challenge to overcome the renowned iceberg of Indian batting, and the slightly less renowned but thus-far impressive back-up iceberg of Indian bowling. Whatever happens, however, they will leave this tournament with individual and collective reputations enhanced, and in considerably better spirits than when they exited the last World Cup.

Four years ago, Bangladesh departed as humiliated co-hosts. The vibrant enthusiasm of their support for their team and the sport, and a gripping win in a low-scoring error-strewn cliffhanger against England, had been deadened by a second horror skittling - 78 all out against an under-strength South Africa, following their earlier 58 all out versus West Indies, an anti-performance that had catapulted them towards the top of the All-Time Batting Incompetence Charts, and provoked some stroppy rocks to be hurled at an innocent bus.

Bangladesh were only the third team to be dismissed for under 100 twice in a World Cup, and the first to be bowled out twice for less than 80 in the same tournament.

Those two hyper failures were not merely the struggles of a still-new cricketing nation against the established powers of the game. They were abject capitulations against decent but hardly unplayable opposition. Kemar Roach's pace took three wickets for West Indies, but the remaining seven fell to Suleiman Benn and Darren Sammy for 39 runs in 13 overs. South Africa had rested Morne Morkel and Dale Steyn - Lonwabo Tsotsobe and Robin Peterson took 7 for 26 between them.

Even in victory over England, a middle-order collapse of 5 for 14 left them on the brink of defeat, until a ninth-wicket stand of 58 by Mahmudullah and Shafiul, aided by an almost heroic 23 wides in the innings by England's not-entirely-accurate-then-either bowling attack, saw them to victory. This was a team that seemed to have reached a plateau of minimal elevation, and played with such fragility that a well-timed growl or an accurately-directed frown seemed enough to take a couple of top-order wickets.

In 2015, Bangladesh have had plenty of chances to collapse in a jibbering heap, 2011-style. They were 119 for 4 in the 30th over against a fired-up Afghanistan, fueled by the passion of the World Cup debut, in a game that could have set Mashrafe's men off on a disastrous course. They conceded 319 against Scotland, raising the live prospect of a tournament-wrecking defeat. They were 8 for 2 against England, then 99 for 4, with their quarter-final hopes on the line. Against New Zealand today, they were fortunate to be 8 for 1 after 7 overs, then 27 for 2, having significantly underutilised the middle of their bats and played the swinging ball like an overworked submarine fleet - they were all at sea.

But this Bangladesh has not surrendered, panicked, folded or otherwise failed. Shakib and Mushfiqur snuffed out the Afghan fire with 114 in 15 overs to establish a winning platform. They chased 320 to beat Scotland with ease and assurance. Against England, they reconstructed their innings so effectively that their final score of 275 was something of a disappointment. Against New Zealand, they counterattacked, consolidated, then flourished, to post 288, the largest total New Zealand have conceded in the last two World Cups.

Even in the heavy defeat against Sri Lanka, after their bowlers had been cauterised by Tillakaratne Dilshan and Kumar Sangakkara, their batting did not capitulate, reaching 240, after being 100 for 5.

This 240 is, so far, their lowest score of the tournament. They surpassed that score only once in 2011 (283 for 9, against India, in a futile pursuit of 371), once in 2007 (251 for 8 to beat South Africa, their only score over 200 in that World Cup), and not at all in 2003 or 1999. This has been, largely, a batsman's tournament, played under batsman's rules, and their abandonment against Australia spared them trial by pace, but the improvement is nonetheless marked, in the score book and in the flesh.

Mahmudullah, a useful chipper-in from the middle order until recently, has led the way. His hundred today in an excellent, fluctuating match in Hamilton was, after an early escape when dropped by Corey Anderson at slip, a masterpiece of increasing authority and brilliance, of poise, pacing, dancing feet and snapping wrists. He currently averages over 150 as a No.4 in ODIs - admittedly, this is after only seven innings, with four not outs, but those are some numbers that would have Don Bradman rattling his abacus in admiration in his grave.

The bowling, brilliant at decisive moments against England, remains relatively blunt. New Zealand's wickets all fell to careless strokes, but the bowlers remained focused and competitive throughout, supported by fielding that was almost flawless - even the one major flaw, Nasir Hossain's drop of Vettori near the end, came after a 25-yard sprint and dive as if trying to save a priceless vase dropped from a careless getaway helicopter after a museum robbery. In their last two matches, Bangladesh have looked like a team who can challenge, if not yet beat, the best.

What makes their performance in this tournament all the more heartening and impressive is their unfamiliarity with Australio-New-Zealiac conditions. Since the last World Cup, Bangladesh have played the grand total of three ODI series outside Asia - two in Zimbabwe, one in West Indies - totaling 11 matches, only six of which have been played in the last three-and-a-half years. They last played international cricket in New Zealand in February 2010, and their only experience in Australia since 2003 was a three-game ODI series in Darwin in 2008 (further evidence of cricket's powers welcoming their less lucrative cousins to their bosoms like a cantankerous ichthyophobe mothering a goldfish).

Andy Zaltzman is a stand-up comedian, a regular on BBC Radio 4, and a writer