Barnes set his world record 23.12m in Los Angeles in 1990. It was in a dark age for sport and Barnes' record was one of many largely discredited due to doping offences. He was banned for life in 1998, having already served an earlier two-year ban in the year he set the world mark.
Stevenson believes there's a group of throwers who could nail the mark, and Walsh is surely at, or near, the top of that bunch. It is among the more notorious world records still sitting in the books with an asterisk beside it.
"If we don't believe that, then we're not really giving ourselves a chance to do it," Stevenson said of toppling Barnes' mark. "I think there's a small handful of guys who are as capable as any in the history of the sport."
Walsh yesterday erased East German Ulf Timmerman from the championship record books, and his mark that was set in 1987, five years before Walsh was born.
"It's nice to have that one under Tom's belt and he's deserved it," Stevenson said. "There's no great secret there's a few throwers around who have set aspirations at the No 1 all-time mark and want to get some of those dirty marks, those with asterisks next to them from the '80s and '90s, and put them under the name of the guys who are flying the flag for the sport now."
The absence of Americans Ryan Crouser and Joe Kovacs, the only two who finished ahead of Walsh at the Rio Olympics, didn't diminish the victory. Neither competed at the American trials, with Crouser also having an untimely hand injury.
Stevenson's hunch about yesterday was based on Walsh's formidable lead-up work.
"We've known for the last two or three weeks that Tom's horsepower is as good as it's ever been.
"He's right up with the best power output he's ever had.
"But what had been missing was timing, calibrating all that to put into the shot when it matters. Anything less than 22m would have been a real disappointment."
Walsh punched out 22.13m on both his first and third efforts, comfortably eclipsing his previous indoor best, had three no-throws before his booming finale. Walsh won by a ripping 87cm yesterday from two-time world outdoor champion David Storl of Germany, with Czech Tomas Stanek third.
Walsh's 22.31m added 7cm to Timmerman's mark, and 10cm to his Oceania and New Zealand records.
It was the highest calibre indoor event ever.
The eighth-placed finisher recorded 20.99m. Medals have been won with that distance.
"There's a tide shifting in our sport. It's a pretty exciting time to be a male shot putter in the world right now," Stevenson said.
Walsh was chuffed for getting one over on his coach, too. Large sideburns are soon to adorn the cheeks of Stevenson, courtesy of a pre-event water.
"I had to PB and win for him to have mutton chops for nine months," Walsh grinned.
The Timaru builder said the bets are a way to relieve the pressure of competition.
"When I throw well, I know I need to be relaxed and not amped and very low key, and that's what I did so well [yesterday]. I was in a great rhythm, great timing," he said.
His final put moved him to fourth on the all-time indoor list.
"The first two 22m throws were easy and that's always a good sign but that one there, I got a little bit more juice behind it and it just felt great off the hand and it was just a great feeling," Walsh said.
Stanek bemoaned his failure to get up to win the silver, but tellingly said: "I do not think I would beat Tomas [yesterday]. He was so strong."
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