SPORTS stars deal in the singular when it comes to arithmetic.

The mantra of one game or one tournament at a time slips off their lips with an ease that suggest they have been oiled.

Yet Andy Murray can be forgiven for reflecting on the past and looking to the future as he steps on to the O2 Arena in London this afternoon to play his first match in the Barclays ATP Tour finals. The 27-year-old Scot regularly faces questions of scale: how much stress is he under, how much can he improve, how much does he want to reprise the glories of yesteryear?

Murray once sardonically replied to these sort of queries with "how do you want it - in percentages or on a scale of one to 10?" There is no doubt his will is running at a footballer's 110%. He has played six tournaments on the trot, winning three of them.

It is enough to recall the reply of John D Rockefeller's to the query of how much money is enough. "Just a little bit more," said the American tycoon. The Scot, though, has no financial ambitions to fulfil. He has made tens of millions from tennis and in what has been described oddly as a "disappointing season", he has pocketed $3 million in prize money.

His aim at the O2 is to gauge his progress and plan the journey to the next summit. A year ago he was recovering from back surgery, training at the Chelsea facility at Cobham and watching the events of the finals unfold on television.

The intervening period was initially frustrating. Murray found it difficult to progress in tournaments, his Grand Slams ending at the quarter-final stage.

"One of the things I feel like I've missed at certain times of the year has actually been patience. At the beginning of the year when maybe you're not match tight, you haven't played enough matches, or you're feeling a bit tired physically, it's easy to rush points or finish points quickly and stuff like that. I need to just make sure I make more of the right decisions, rather than making any major changes in my game."

The training block after the O2 will thus involve only "small tweaks" to his game as he works with Amelie Mauresmo, the French coach who joined him in the summer. But first there is the challenge of facing the best players in the world in London. Murray is in a section with Nishikori, Milos Raonic and Roger Federer. The top two in the section will progress to meet the best of the other group of Novak Djokovic, Stanislas Wawrinka, Marin Cilic and Tomas Berdych.

On his return, Murray had to progress slowly up the ladder, first beating top-20 players, then top-10, then top-eight competitors. He will almost certainly have to defeat either or both of the No 1 in the world and the No 2, Djokovic and Federer, to win the tour finals

"When you're away from the game for sort of three or four months, you just fall behind a bit," said Murray, now ranked sixth in the world of his rivals. "They improve. They might become a bit quicker, they might be serving a little bit better. Each player is different in that respect. It does take time to catch up when you do miss a period of time.

"I learned that this year because I'd never really been away from the game for that long a period. Everyone just gets a bit better."

This relentless tide of improvement has thrown up Nishikori on the banks of the Thames. The 24-year-old Japanese is playing his first tour finals in a year when he recorded the most stunning result of the calendar, beating Djokovic to reach the US Open final where he lost to Cilic.

Murray was not convinced playing Nishikori on his opponent's tour finals debut was an advantage. "That can always work both ways. Someone who's inexperienced can come out and struggle with nerves, the occasion or the crowd. That can happen. And sometimes it can happen the other way where people come out and just love it, play great, feed off the atmosphere, feel there's no pressure and just go for it and feel very loose and free," he said.

The Scot has achieved his "one game at a time" goal but is still involved in matters of arithmetic. "I'm not exactly where I would like to be, I still want to get four or five per cent better. But compared to where I was four or five months ago, I am much, much closer," he said.

He is now, crucially, inside the top eight and that makes progress in Melbourne at the Australian Open in January an easier proposition in terms of draw.

But what are the chances of home rule at the O2 for the pro-independence Tweeter? Murray is in London to win but one suspects he would be grateful to experience evidence of increased powers.