He made a fleeting appearance on the international scene against Australia at Trent Bridge in 1985.
Arnie had night-watchman Bob Holland lbw before a damaged toe forced him out of England's attack with figures of one for 65 to his name.
Memories of that occasion are sure to come flooding back if his son Ryan makes his debut in Thursday's first Test against Pakistan at Lord's.
Sidebottom senior is understandably proud of his son's achievement in winning a place in an England squad after once being deemed too erratic for the Yorkshire Schools side.
But he is quick to point out that his own part in Ryan's success has been a minor one, with another former Yorkshire seam bowler, Steve Oldham, fulfilling the role of mentor.
"I've tried to stay in the background because it is always difficult, the sort of father and son relationship.
"The one thing Ryan dislikes more than anything is being called the son of Arnie. It's something that really gets to him. Steve Oldham's really been the driving force behind him," Sidebottom said.
The impact of being overlooked by Yorkshire Schools was almost too much to stomach for the young Ryan.
It was then, however, that his father offered a few well-chosen words of advice.
"He came home and said 'I can't believe I haven't got in that team' - he was only 15 at the time - 'and I don't think I'm going to play again'.
"He was so disenchanted by what went on so I said - probably the only advice I've ever given him - 'Look, do you want to play sport for a living?'
"He said yes, so I said 'Well, you've got to fight back now - train, get yourself fit'.
"He went running in the woods with the dog every morning, he built a little gym in the garage and got himself fit. It's all down to him, what he has achieved."
Ryan's progress in the Yorkshire first team since making his debut in 1997 has been rapid - so much so that he was picked for the England A team which toured the West Indies during the winter.
His father, however, has seen precious little of him in action despite being part of Yorkshire's coaching staff.
"I'm here, there and everywhere. I don't get to the first team too much, but he's progressed nicely."
Arnie wants his son to "play with a smile on his face" and enjoy every minute if he gets the chance to play against Pakistan.
After all, fate can sometimes turn against you - a lesson Arnie knows all too well.