Roberts, who was the first NRL player to come out as gay in 1995, went into acting after retiring in 1998 and told the BBC that he struggles to learn his lines.
"In the last five years I've noticed my recollection of things has slowed down and my memory isn't as sharp as it was. I first realised it at rehearsals for plays because my ability to learn lines has deteriorated. I'm just not as sharp as I was in the past."
"I was fully aware there was something wrong with me, but to be told I had scarring on the brain was surprising. It's irreversible damage."
The study, performed by neuroscientist Dr Alan Pearce and Melbourne's La Trobe University last year, involved 25 former rugby league players who were asked to perform five tasks relating to memory, short-term learning and attention, reaction time and fine motor skills.
The results were compared with men of similar ages who did not play professional sport.
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