Mark Paul, who worked as a jewellery salesman, killed John Lavender with one double-handed blow to the back of his head.
The Old Bailey was told the unprovoked attack occurred as Mr Lavender, 28, was walking home alone in Battersea, south London, last September. His murderer ran off to leave his victim to die - and four days later was seen playing with the murder weapon in a park game with friends.
Paul, of Granfield Street, Battersea, claimed he had only given Mr Lavender a 'tap on the head' and that he had no intention of causing serious injury. But the jury of six men and six women convicted him of murder in an 11 to 1 majority decision after deliberating for 5 hours and 17 minutes.
Paul covered his face with his hands and sobbed as the verdict was announced.
Police revealed that Paul had a history of violence stretching back to the age of 14 when he was expelled from the Magdalen College Secondary School in Northamptonshire for 'violent behaviour'. He was sent to a rehabilitation centre, which he left at the age of 16. In 1989 he moved to London, where he became the pounds 11,000-a-year assistant manager at Samuel's jewellery store in Surrey Quays, south-east London.
Since 1988, he had been convicted of two counts of assault, one of possessing an offensive weapon and one of threatening behaviour. In one attack, he hit a bus conductor over the head with his own ticket machine.
He had sobbed as he admitted running up and hitting his victim to 'show off', but denied his intention was to kill or cause serious harm. 'It was a little tap. I thought he would have a headache,' he told the jury.
The jury was told Paul ran up behind his victim and delivered a blow with such force it cracked Mr Lavender's skull like a coconut, causing numerous fractures. He ran away leaving his victim bleeding and moaning in an alleyway.
Mr Lavender's mother Mary, who sat through every day of the trial, said of Paul outside court: 'I hope he keeps on crying for the rest of his life. I would like to have 10 minutes with that young man so he knows exactly what he has done. I want him to know he has my son's blood on his hands. He should never forget that. I hope it haunts him for the rest of his life. My son was left to die. He didn't even call an ambulance.'
The jury heard the attack took place after Paul and his flat-mate Andrew Christie, of Granfield Street, Battersea, south London, had been drinking.
They armed themselves with the baseball bat and went out roaming the streets looking for trouble. Paul said they had planned to smash up cars. He had drunk about six pints of lager and smoked two or three cannabis joints. 'I was tipsy, excited, in high spirits.'
The pair saw Mr Lavender as he made his way home to Sunbury Lane, Battersea, after an evening out with a friend. They followed him into an alleyway and Paul struck the fatal blow. Mr Lavender died of brain lacerations from a fractured skull 12 hours later.
Christie, 22, a camera salesman, has admitted causing criminal damage to a car and will be sentenced later.
After the trial, the policeman in charge of the case, Detective Inspector Martin Smith said: 'It's the only case of its kind I have known. It was totally unprovoked wanton violence against a complete stranger.'
Mr Lavender, a history graduate, was described as a gentle, academic type who loved travel.
Originally from Castle Bromwich, in the West Midlands, he graduated with second class honours from Jesus College, Oxford. At the time of his death he was studying for a Masters degree in business administration at the University of London.
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