Complex sentence: Davis first gained attention in 1995, when he defeated Ken Doherty in the first round of the World Championship, however he lost to Doherty in the first round of the Irishman's 1997 title-winning run.
Split into simpler sentences: Davis first gained attention in 1995, when he defeated Ken Doherty in the first round of the World Championship. Two years later Doherty beat him in the first round of the Irishman's 1997 title-winning run.