Neither Vince nor Stoneman escaped the general condemnation as England lost the Ashes series 4-0. Vince made attractive starts before falling to predictable modes of dismissal while Stoneman went from battling to embattled.
Both finished with averages in the mid-20s and two half-centuries from nine innings, and who you had most faith in depended upon whether you valued style or substance.
Bayliss made it clear, however, that when England announce the Test party for New Zealand on Wednesday evening (UK time) he favours them having another chance to show their worth.
"Personally I think people like Stoneman and Vince probably get another couple of games to show us what they've got," he said. "I think at times during this series, against probably close to the best bowling attack in the world in their home conditions, they have shown they can play a bit. At the top level it is about making big scores not fifties, twenties and thirties but they have shown enough that they should get another couple of games."
There was some irony in the suggestion that the batsman who might suffer for England's 4-0 Ashes defeat could be Gary Ballance, England's reserve batsman, who never got an opportunity. But England's desire to promote at least one young batsman from the Lions squad - and they have been on show to Bayliss (not otherwise a keen student of the next generation) during their time in Australia.
It was when Ballance's name was raised that Bayliss said: "With all of those guys the decision to make is when it is time to move on. Whether there are three or four good young batters in that Lions squad. At some stage I'm sure some will get their opportunity but we have to work out exactly when the time is right to blood them and give them experience."
England's problem is that none of the Lions contingent is making an irrefutable case for selection. Keaton Jennings could get another go as a back-up opener, but much as England like the cut of his jib he has not scored heavily since he lost his Test place. Liam Livingstone, his team-mate at Lancashire, is a batsman of presence but his own county captain, Ryan McLaren was not alone last season when he observed that Livingstone was still discovering his game. Joe Clarke's undoubted talent has also been sporadically shown at best, although he is coveted by several big-spending counties, among them Nottinghamshire where the England selector, Mick Newell, is director of cricket.
As for Ben Duckett, who was all the rage a year ago, his reparation will be extensive after his naïve, not to say juvenile, beer-throwing episode in Perth caused England's Ashes party such upheaval. Small-time misbehaviour perhaps that would have passed unnoticed in another era, but all England wannabes should remember that when influential people start discussing shots it is advisable that they are discussing the quality of your strokeplay.
The manner of Vince's dismissals have not escaped Bayliss: they have barely escaped anybody. "Yes, we have all seen it," he said. "He has looked as comfortable as anyone in the runs he has scored here but just makes a mistake and gets out. They have been similar each time and that frustrates him more than any of us here. It's probably a little bit technical but a lot of it is the mental side of it, knowing which balls to leave and when to attack and when not to."
As for Stoneman, Bayliss rejected suggestions that his confidence - and indeed footwork - suffered from the aftershock of being struck on the helmet by Josh Hazlewood during the third Test in Perth.
"Not outwardly - it didn't seem to affect him around the squad or practice," Bayliss said. He preferred to put it down to the exhaustion of Test cricket at the highest level. Players like Vince and Stoneman declined whereas Alastair Cook, so much at sea for much of the series, then dredged out the little matter of 244 not out.
"Both those guys in the first three games with Dawid Malan were probably our best-performing batters. Whether it was the pressure and the longevity of five Test matches pretty close to each other or whether there was a fatigue and they dropped off in the last couple of games, it being their first big five match series…
"So I think they have done enough without anyone really pushing them from behind. They probably deserve another opportunity."
That would all entail few changes to a squad that has just lost 4-0. It would not be the first time England have approached a New Zealand tour with calls for experimentation, but a challenging Kiwi attack lies in wait.
"Do we pick a second XI against these teams," asked Bayliss. "Then we are copping criticism for leaving some of these other blokes out. In the end it is down to these guys to put their hand up and score runs.
"If we do go down the track in New Zealand, or in the summer, of picking some new young batters, everyone at home in the UK has got to expect that the results might not be quite what we would like.
"Personally, I love the Test cricket more than the white-ball cricket. I'm more of a traditionalist. But with our white-ball team we've actually got a group of guys who are more suited to the way the white-ball game is played, than possibly some of the players that we've had in Test cricket.
"We've been looking for those last two or three or four spots and nobody's been able to grab hold of those spots until Malan. It's a case of searching for some of those guys to fill those last two or three spots that we need filled to compete with the best teams away from the UK."