A day that started with the game delicately poised ended with it bearing all the competitive elements of a firing squad. Suffice to say, England aren't the ones with the guns.

Barring a miracle, India will have wrapped up this series by the time people in England are bracing themselves for a chilly commute or dark school run. A 3-0 scoreline will mean England have lost four of their last five Tests and five of their last seven. That is a run of form that, in other sports, might have consequences.

It is natural at such moments to look at what has gone wrong and demand change. It gives us a sense that we are correcting errors and making progress. It provides the illusion that things might be better next time.

A current theme that appears to gathering momentum is the captaincy of Alastair Cook. James Anderson was the latest to be asked about it in the post-play press conference on Sunday - unsurprisingly, he was supportive, though he did admit he had "no idea" if he was going to continue - underlining the sense that it is becoming the thing to blame for this defeat.

But that's simplistic. Cook has never been a great orator or inspired tactician. Like most modern Test captains, he is cautious and like most modern Test captains, he can appear formulaic. Much of the pressure, in fact, has been brought to bear by the words of his own coach, Trevor Bayliss, whose call last week for a more "positive" approach from England's batsmen was at clear odds with Cook's more adhesive style.

But he has other skills. Most importantly, he leads by example and has, on the whole, absorbed the demands of the job without it ruining his own game. He has captained sides that won in India and South Africa and, only a few months ago - had a result or two gone their way - England would have briefly regained the No. 1 Test team ranking. His record, as player and captain, is stronger than some would like to admit.

He also protects Joe Root. While Root might, by nature, be more in tune with Bayliss's positive message, he has very little captaincy experience and is still at the developmental stage of his career when he is coming to terms with batting at No. 3. The burden on him, as England's best batsman in all three formats of the game and bearing in mind this team's silly schedule, is already cumbersome. Adding the captaincy, just as he is about to become a parent, seems unnecessarily onerous. The time for him to take over will come soon enough, but there's no hurry.

Besides, replacing Cook with Root as captain would not have made England's spinners more accurate or more potent. Replacing Cook with Root would not have ensured England took the three important chances they squandered - all three of India's centurions were given lives; two of them before they had 50 - and replacing Cook with Root would not provide any greater answer to the problem England's bowlers have with dismissing Virat Kohli. Disconcertingly for England, there have been times this series when India's seamers - notably Mohammed Shami - have looked more potent than any of England's.

We can argue with Cook's tactics on day four. But Jake Ball had dismissed Cheteshwar Pujara early on day three and Adil Rashid has been England's most effective bowler in the series. It was reasonable to turn to them, it just didn't come off. We can argue that there should have been more flexibility with the batting order, with a case being made to rest Moeen Ali, who had bowled 53 overs, for a little longer before he batted. But there is an equally good case for some consistency in the batting line-up and providing Moeen with some certainty over his position. And we can argue with the selection of the side, but it is naïve to think that the inclusion of either Gareth Batty or Liam Dawson would have made the difference. Not all decisions are right or wrong; many just come off, or don't.

That does not mean we're not about to have a change in the captaincy. It may well be that Cook, after a long and demanding period in the role, has lost a bit of hunger for it. It may well be that, once he gets back to England and has time to reflect, he decides it is time to move on. And it may well be that Root proves himself a more instinctive leader.

But we're fooling ourselves if we think that replacing Cook would have led to England winning in India.

The reality is that England keep missing chances in the field, that they still don't have, full-time, a spin-bowling, wicketkeeping or fielding coach, and that the county game is structured to prioritise the Ashes and, of late, limited-overs tournaments. If England really want to win in India, they are not going to spend every August playing only white ball cricket - as they will when ECB plans are ratified from 2020 - with the consequent marginalisation of attacking spin bowlers that will follow. The desire to embrace the T20 revolution is not wrong - it might even be essential to the sustenance of the game in the UK - but it does come at a cost.

Cook cannot control any of this stuff. He has arrived in India with an inexperienced line-up of batsmen (you could argue that, but for Cook, a certain well-known player with a pretty decent record in Mumbai might still be a member of the squad, but let's not go there) an ageing pack of senior bowlers, and spinners who have been outclassed by their opposition. India are just better than England. Cook can't change that. He may not be perfect and his form with the bat - and in the field - is a concern. But he's not the key problem here.