We are under way. 

Murray, no doubt affected by the pattern on Cilic's shorts, comes second best in a baseline rally. It's 15-15.

Murray, like Kei Nishikori earlier, challenges early on his own serve. It was called out, and was confirmed out by the replay. The Japanese player won his challenges by the way.

Now then. Cilic has two break points already after a pass that landed right on the baseline.

Both are saved after a good Muzza serve and then a long return by the Croat.

'The Number One' produces another good serve that Cilic cannot handle. 

Held.

Miles Maclagan
Former British Davis Cup player on Radio 5 live sports extra

Image source, Reuters

I hate it when people try to judge a player by their walk-on but, having said that, Andy looked a little bit edgy to me. 

It's not often he does something for the first time and maybe he's a little bit conscious that we expect him to play a little bit different tennis as the world number one.

But he should try to remember how he got here, with all the scrapping and fighting he's produced over the years.

Miles Maclagan
Former British Davis Cup player on Radio 5 live sports extra

We've got he number one-ranked player up against the number one for the worst pair of shorts. They are worse than Stan Wawrinka's. They are definitely for the beach and not the tennis court!

Image source, Getty Images

Cilic, 28, is in good form going into the tournament.

He won a title in Basel last month and then ended a 14-match losing streak against ex-world number one Djokovic in Paris 10 days ago.

He is currently being coached by the rather enigmatic Swede Jonas Bjorkman, who was part of Murray's set-up last year.

Cilic said: "When a coach works with a player always you get to know more things than when you're looking from the outside.

"Definitely having Jonas on my side now is a big plus. I'm going to be able to prepare a good plan for the match. But things are not always as you expect, you always need to find a way if things go wrong.

"I have to obviously focus on myself, on my game, and implement as well a few tactical things I know from playing Andy." 

Image source, Getty Images

Murray wins the toss and will serve first. 

Worth pointing out that Cilic is wearing shorts that appear to be a tribute to Arsenal's 1992 away kit. Disturbing.

Miles Maclagan
Former British Davis Cup player on Radio 5 live sports extra

It is a huge moment for Andy Murray to come out as the world number one, as the best in your business. It's been a long road, a huge effort and massive determination with a fair bit of pain physically and emotionally.

What a pleasure to be here to witness it and on British soil too.

Andy Murray has just been introduced to the packed arena as the world number one. Soak it up Andy!

Undoubtedly, Murray isn't confusing himself with these permutations, so let's read what he has to say:

"It's an incredible feeling to have made it to world number one, and it's something I'm very proud to have achieved.

"It's important to keep taking it one game at a time to try and perform as best you can during each match and try to ignore the noise around you. 

 "Number one came earlier than I first anticipated after a hectic few months, which is great, but now it's important that it's business as usual. It will make for an exciting battle in London but also for next season."

He added: "Marin serves well. He's a big guy. I'll try not let him dictate the points."

Piers Newbery
BBC Sport in London

Image source, Rex Features

Murray might be playing within commuting distance of his Surrey home, but he has not always looked comfortable at the O2 Arena. Whether it was the slow court surface, the effects of a long season or the overwhelming star power of Roger Federer and Rafael Nadal, Murray repeatedly struggled to live up to the role of local hero.

This year feels very different. Murray arrives as the world number one and, in the absence of Federer and Nadal, takes undisputed top billing for the first time.

With the court quicker than in previous years, and backed by a partisan crowd that has been steadily building around the arena for the last few hours, it's all set up for Murray to finally excel in the ATP showpiece.

Andy Murray's just going through his pre-match exercise routine in the O2 corridor - some of it looked like what you'd see at one of those holiday camp classes in Bridlington. He's world number one, so it obviously works.

Right then. Permutations. 

This is how Andy Murray can cut the family Xmas turkey as a world number one:

• Murray has 11,185 points. Djokovic has 10,780.
• The Scot will lose 275 points gained from last year's Davis Cup final before the end of the year because those points no longer count.
• There are 200 points available for each ATP Finals group win
• If Djokovic were to win this tournament but win only one match in the group stage, he would collect 1,100 points (400 for a semi-final and 500 for winning) but Murray could stay ahead by winning all three of his group matches and reaching the final to earn 1,000 points.
• Apply the same rule again here. If Murray loses in the semi-final and Djokovic loses in the final, with Murray having three group wins to one for Djokovic, they would collect 600 points apiece. So, happy days for Murray
• If Murray wins, well, that's self-explanatory.

Tim Henman
Former British number one on BBC Two

Andy Murray has played brilliantly. We know he has won four tournaments in a row and comes in as the world number one, but Marin Cilic is in form as well. 

He is another big match player, he has won the US Open in the past, beat Novak Djokovic in Paris last week and won the Swiss Indoors in Basel. He won't be scared to win this match.

OK, now we've got a feast of a multi-platform offering for this match.

You can read the best live prose/poetry money can buy here*

And

Listen to the best radio commentary on BBC Radio 5 live sports extra, starting at 20:00 GMT.

*This game's all about opinions

Image source, Getty Images

Hello again.

Andy Murray - world number one!!!!

Now that I've got that out of the way, it's back to business for the Brit.

Because his status as top dog, head honcho, numero uno, king of the hill, chief of the tribe could be short-lived if he underperforms at the O2.

If he wins the tournament then all is well, but if he doesn't then it can get a little bit more complicated - we'll explain in a bit.

Anyway, first up for him in this round-robin group stage is Croat world number seven Marin Cilic.

Murray's record against him is 11-3, but he lost to Cilic last time they played, which was on the hard surface in Cincinnati.