The tide turned on the third day at Ahmedabad, though the change was so slight it is impossible to spot quite where the low-water mark lay. Rather, each successive ball Alastair Cook faced that afternoon, as he opened the batting in the follow-on, his team 330 runs behind, seemed to represent another wave breaking and rolling back off his bat. England had been bowled out for 191. It was the fourth time this year they had been dismissed for less than 200 in the first innings while playing in Asia. The echoes of two spirit-sapping defeats by Pakistan in Dubai, and a third against Sri Lanka in Galle, must have been ringing around the minds of the players. England were suffering from post-traumatic spin disorder. Captain Cook had a cure.

Pragyan Ojha and Ravi Ashwin took eight wickets for 125 runs between them before Cook scored that 176 in the first Test. And they added only 21 at 47 runs each in the six innings that came after it. It was akin, if not equivalent to, the 285 not out Peter May scored against Sonny Ramadhin in 1957, which so blunted that brilliant bowler that he never quite recovered his bite. Ramadhin, of course, was better than either Ashwin or Ojha, but then May had Colin Cowdrey to keep him company.

Cook's first stand as captain was also a last stand against the ineptitude of England's batting, a repudiation of the idea that he and his team-mates were constitutionally incapable of playing spin bowling, which had become so widespread that even Michael Vaughan felt compelled to tweet that: "It's now absolutely official … This England side cannot play spin … 4-0 is definitely on the cards." Vaughan was only one of many to think, say, or write as much. He's singled out here is because he is a friend of the players, and closer to them than any other figure in the media. When even your best mates have given up on you, you know you're on your own. And so Cook was. In that innings the rest of the top six made just 78 runs between them.

Pause here to recall that when Cook was just 37 runs into this series-defining knock, he played and missed a sweep against Ojha, and was hit on the front pad flush in front of middle stump. Hawk-Eye suggested what all the watching world already suspected: he was out. But Aleem Dar, a man who was named the ICC's umpire of the year every year for three years between 2009 and 2011, did not agree. Before we begin to consider the Sliding Doors-style implications of that erroneous decision, it's worth recalling that this isn't just an exercise in contemplating imaginary alternative worlds. If the Decision Review System had been there, India would have used it, and Cook would have been out. As with so many of the fine margins in this series – the run-outs and dropped catches, for instance – India were simply reaping what they had sown, whether that was their board's refusal to use technology, or their players' reluctance to sharpen up their fitness and fielding.

So Cook batted on. And on. And on. And on. Nine hours and 16 minutes in total. It's easy to say that a player leads by example, but really, like so many other stock-phrases used in sport, those words don't mean all that much. Was there ever a successful captain who set a bad example to his players? And has there never been a poor captain who still scored more than his share of the runs? (If you're not sure about the answer to that one, just ask Geoffrey Boycott). Really, "leading by example", often seems to be a shorthand for saying that someone doesn't seem to be much cop at making speeches or setting fields, so we're not quite sure what it is they do, other than play well, of course. And that last quality is the minimum that should be expected from a modern captain.

Well, Cook's innings gave us a precise definition of this often empty cliché. He proved to his team that it was possible to play spin, and he showed his working as he arrived at the answer. "It provided evidence that runs could be scored if you use your brain, if you've got a reasonable method, if you show courage and discipline," Andy Flower said of Cook's 176. And Cook himself reckoned "after that second innings in Ahmedabad, we thought: yes, we can score runs out here."

Some players were inspired by his example, others copied his method. But the telling thing is that they followed him at all. You can't, after all, set any kind of example to someone who doesn't want to learn. The first player behind him, on his shoulder almost, was Matt Prior. But the others followed, in turn. From Prior in Ahmedabad, to Kevin Pietersen in Mumbai, to Jonathan Trott in Kolkata, to Joe Root and Ian Bell in Nagpur.

Cook has always been blessed with an ability to get on with people, a skill every bit as valuable as his immense powers of concentration. In early 2009, when all the talk was about the cliques within the team, Cook was part of the group who would congregate around the darts board, along with Steve Harmison and Andrew Flintoff. But he stayed close to the management too, and was made vice-captain when Andrew Strauss took over and Flower moved from assistant to head coach.

When Michael Vaughan took charge of the England team, he said he wanted to have 11 captains in the side. As happened to Vaughan, and all captains, Cook's form will fail him sooner or later. He cannot expect to always be setting the example as the lone bulwark of the batting line-up. Together with Flower, he needs to create an environment like Vaughan's, that cultivates a team full of captains. And on the evidence of this tour, where he allowed the bowlers to set their own fields, and brought the best out of the batsmen around him, he is inclined to do that. One benefit, or perhaps complication, of the policies of splitting the captaincy and rotating their players is that there are five men in the squad – Cook, Swann, Broad, Pietersen, and Eoin Morgan – who have led England in international cricket. Prior now has experience of the vice-captaincy, and James Anderson is the leader of the bowling attack. Having so many leaders in the ranks is the hallmark of a good side, but it can also make them a difficult bunch to lead.

Just ask Strauss, whose decision to retire when he did looks even more admirable in the light of what has happened since. He was once capable of playing the kind innings Cook produced in Ahmedabad – the two of them did it together at the Gabba in 2010 – but it is hard to imagine that he would have been capable of doing it in this series, exhausted as he was, and with the doubt about his own ability spreading through him "like a cancer". Perhaps he too had become just a touch too patrician in his approach as the years wore on, and lost touch with the strong characters in his team. That may explain how the situation with Pietersen came to be quite so messy. The other England players still call Cook by his nickname of Chef, when they are out on the field, which says something about how close they are to their skipper.

The captaincy will come to weigh heavy on Cook too, one day, but that moment is a long way away yet. It would not be that surprising if he went on to break English records in captaincy, just as he has in batting. And whatever success follows, it will all flow from that one innings in Ahmedabad.

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