"The best big-occasion players I see in the field would be John Higgins, Ronnie O'Sullivan and Mark Selby and that's disregarding some fantastic players", Davis said.
The 41-year-old was made to work hard by the qualifier from Wallsend, and was relieved to book his place in the second round, where he will face either Shaun Murphy or Yan Bingtao.
Mark Selby celebrates with the trophy after beating Ding Junhui in last year's World Championships final.
Ronnie O'Sullivan has launched a furious attack on World Snooker, labelling them "bullies" in an ongoing row.
"You have to have a certain level of bottle to win the World Championship - there have been many players who you wouldn't fancy winning it, but when it comes to the chase they're able to perform when they need to".
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"Mark is world No.1 and the reigning world champion - it's now his time and he's been making the most of that", said O'Sullivan, who last won the World Championship in 2013 and lost to Selby in the 2014 final.
O'Sullivan has deliberately and repeatedly given one-word answers to questions he has faced after matches, while in an ITV interview at the World Grand Prix in February he gave a series of responses in a robotic voice.
"I hope all parties can move on from this position and concentrate on the brilliant entertainment provided by players at the Betfred World Championship".
And though they have been withdrawn O'Sullivan claims he was "bullied" and "intimidated" by snooker chiefs and chose to get the lawyers involved.
"I like Barry, but I'm not being intimidated or bullied any more". I don't think I've done a lot wrong.
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Hopefully, if we accomplish the goal of winning a championship in future years, we will be back on the South Lawn again soon. But, according to the team, the picture from this year is misleading. "No team has been this good for this long".
O'Sullivan has been out of sorts ever since his Masters triumph at Alexandra Palace, failing to win back-to-back matches at the five events he has played since that tournament and his trip to Sheffield.
"Hopefully, they can relax and stop being so precious, but I'm not prepared to put myself in that situation anymore".
"I love to play and it is extra special at the Crucible".
"I have tried being open and it gets me in trouble, and I have to be in the right frame of mind to at least have a chance here". I'll definitely be playing for the next couple of years.
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