It tells you much about the buoyant mood in English cricket at present that an England coach has had to field questions from journalists asking if he might consider staying on in the role.

Not so long ago - early 2015, in the Caribbean - the first question in the first press conference of a tour asked a player (Gary Ballance) whether the coach (Peter Moores) was "a dead man walking". Not long before that - the Ashes tour of 2013-14 - Andy Flower spent several months insisting that media reports were wrong and he had no intention of quitting at the end of the series. Then he quit at the end of the series.

Yet in the aftermath of England's success in Pallekele, there was Trevor Bayliss being asked if he might consider extending his contract as head coach. It expires in September 2019, after the conclusion of England's home season.

He won't, of course. He's said it before and, if England win the World Cup or the Ashes (or even both), he will no doubt be required to say it again.

"I'm not tempted to stay on," Bayliss said. "I've always been of the opinion - even before I started the England job - that four to five years is a good life for a coach with one team. Hopefully you take it forward and then it's up to a new voice, maybe someone of a different direction, to take the team forward. I've always been of that opinion and that's not going to change."

The fact that the question was asked is more revealing than the answer, though. Only a few months ago, some were suggesting that the England coaching role should be split, with Bayliss focusing on the white-ball formats and someone else taking charge of the Test team. Now England have beaten India, at home, and completed their first win in Asia since 2012 and their first in Sri Lanka since 2001. They are favourites for the World Cup, too. Bayliss' stock - in the UK markets, at least - is at an all-time high.

While there is, no doubt, an element of fickleness about such fluctuations - had England's tenth-wicket stands not added 101 in Pallekele; had Ben Stokes not pulled off a brilliant run-out; had Keaton Jennings not parried a catch to Ben Foakes, this series, against a Sri Lanka side in transition, could easily be 1-1- there is also an element of justification. For Bayliss and co - and it would be unfair not to recognise the role of Joe Root, Paul Farbrace and many others in the England set-up - have created an environment in which England are playing some wonderfully entertaining, joyful and increasingly successful cricket.

And, after a few false starts, it does seem a few things are beginning to fall into place. Foakes, for example, is clearly a fine player with a golden future. Rory Burns has looked every inch the Test opener England have required for months and Jennings has contributed heavily in both Tests. Bayliss himself reckons England have probably nailed down "two or three" positions they have been trying to fill. And they've started to hold their catches.

"There's no secret in the fact we've been looking for two or three, maybe even four, positions to get nailed down over the last few years," Bayliss said. "I think on this particular tour we've probably seen two or three of those positions getting nailed down.

"I think the job that Burns and Foakes have done in the two Tests they've been here - it looks like they're playing their 30th or 40th Tests. Their calmness has been outstanding.

"Keaton Jennings and Foakes, down in Galle, played fantastically positive innings. They played in their fashion in a positive manner. It was made partly easier because of the runs we had on the board and what was happening at the other end. You've got guys that can put pressure on, you've got guys that can bat around them as well. To me that's a perfect combination of batters.

"We've now got those two plus Burns in the team. We've got three guys that probably haven't quite got the shots of some of the other guys in the team and to me that's a pretty good combination.

"They say catches win matches. Well, this match goes a long way towards proving that. We haven't worked any more or less on it. Maybe it's just the volume of catches over a period of time that is starting to pay dividends. Certainly there were some outstanding catches."

Bayliss also thinks Root is just at the start of his journey as a captain. But despite seeing a batting order come together, despite seeing the catches start to stick in the field, despite seeing the spinners hold their nerve under pressure and leading England to victory, there will be no second thoughts from Bayliss. He isn't interested in taking this new improved England back for another crack at India. He'll be happy to watch on TV.

"Has he accepted his way back is as a specialist batsman? You'd have to ask him but I think he wants to do as well as he possibly can and cement a spot in the team"
Trevor Bayliss on Jonny Bairstow losing the gloves

"I still think Joe will improve even more from where he's at," Bayliss said. "Like any young captain, he'd probably like to do a few things differently. But the more you have these types of wins in these conditions that just gives the captain confidence. And it gives the players confidence in the captain. He'll just get better and better.

"We lost in India because, while he were able to score 400, they were able to make 600. We batted reasonably well.

"In this Test, our spinners didn't quite hit their proper lengths in the first innings. But there's a lot of pressure in having to bowl a team to a win on a fifth-day turning wicket in the subcontinent and I thought the way they responded in the second session was fantastic. Hopefully that's a learning curve for those guys. I look forward to watching the next series in India on TV."

It reflects well on Bayliss (as well as the individual players, of course), too, that England have left out some 'big name' players in this trip and it has not caused disruption in the dressing room. So united is the squad, so committed to the shared goals, that they have been able to manage personal disappointments in the knowledge that decisions were made in the best interest of the group. Bayliss and his staff deserve credit for instilling that dynamic.

"One of the great things that hasn't been spoken about over the last two games is Stuart Broad and Jonny Bairstow missing out," Bayliss said. "But the way they've taken it has been absolutely fantastic. It makes the feeling around the squad so much better. They are very much part of a squad and they realise that. They realise we're picking what we think is the best team to win each match and they've taken that on the chin. It's been great.

"Has Bairstow accepted his way back is as a specialist batsman? He's certainly done that at the moment. You'd have to ask him but I think he wants to do as well as he possibly can and cement a spot in the team as a batter."

But perhaps the most obvious manifestation of Bayliss' influence has come in the way England have batted on this tour. Instead of the cagey batting we have tended to see from England teams in Asia in the past, England have looked to hit bowlers off lengths and force changes in the field with their aggressive strokeplay. It is, at times, high risk. But it is also entertaining and, increasingly of late, successful.

"There's just a good feel," he said. "And when there's a good feel around the team, the environment to learn and get better is enhanced. It's a point we've been trying to get to and the two or three new guys in the team appear to have fitted into that system very effectively. What they've shown in a couple of matches is a positive sign for the future. But let's not go overboard. I'm sure we can get some scented candles out there to make things better."

That last sentence - delivered with a big smile - is a reference to criticism of Bayliss made on these pages not so long ago. The writer suggested that Bayliss, with his hands-off approach, his acceptance that he isn't really a technical coach and an admission that his knowledge of county cricket (through no fault of his own; his schedule is remorseless) limits his role in selection meetings, was of modest use in his job. "If he's just creating a relaxed environment, he could be replaced by a couple of scented candles, a yucca plant and a CD of ambient whale noises."

But although that criticism is still - up to a point - valid, it might also fail to recognise the importance of creating the right environment. For one of Bayliss' strengths is that he reduces pressure on his players, simplifies what can sometimes appear a hideously complicated game and encourages his teams to enjoy their cricket and the incredible journey their lives are on while they play the game at international level. And those are not inconsiderable qualities.

But, even as he said it, he conceded that he had not been involved in one of the key tactical decisions that defined the Pallekele victory. He was as surprised as anyone how much his players swept.

"It was a surprise," Bayliss said. "No one sat down and said 'look, we've got to sweep or play straight'. If you played across the line years ago you'd have got clip behind the ear. It just seemed that, on this wicket, both sides decided the sweep shot was the shot to go to and that it was actually easier than the straight bat. We've had criticism at times for the way we've approached the game but one thing that never gets spoken about is the skill of these guys to go out and play in that fashion and score 600-plus on that type of wicket. That was fantastic."

And that's Trevor Bayliss for you. He's hands off, relaxed, honest and even-tempered. He doesn't try to take credit for the players' success and his greatest attribute just might be what he doesn't do: fuss or spread anxiety or discontent in the dressing room. Somewhere in there, he's helped create a pretty decent team in all formats. England may well miss him when he's gone. Well, who doesn't like a scented candle?

George Dobell is a senior correspondent at ESPNcricinfo