"I'm not a mathematician and you need to be at least A level standard to understand our ranking system," he said. "But there are about six players chasing the final four places. I try not to play the rankings game because it's sad but unfortunately in my position you have to."
Davis's opponent in the next round will be Michael Judge, who beat the world No 17, Dominic Dale. Dubliner Judge, a wild card in the recent Irish Masters, came back from 3-0 down to deny the 1997 Grand Prix champion 5-4.
Another Irishman, Fergal O'Brien, the provisional world No 18, survived a last-frame decider against the world No 105 Anthony Bolsover, while John Higgins began the defence of his title with a 5-0 drubbing of Wolverhampton's John Read.
"I have only been going through the motions in practice because I want to make sure I'm fresh for Sheffield," the world champion and No 1 said.
Higgins struggled only to win the final frame after making breaks of 35, 32, 59, 93 and 82. He continues his defence against Ulsterman Terry Murphy, a 5-1 winner over Mario Guedens of Belgium.Reuse content