Bayliss' inside track on Australians helped England
Bayliss' previous role before taking the England coaching job - which he only began officially a couple of weeks ago - was with New South Wales who provide 10 of the Australian touring squad now that Pat Cummins has been added as a replacement.
That list includes David Warner, Steven Smith and Michael Clarke, all of whom were targeted by England with well-defined tactics in Cardiff.
Although England have bowled against that trio plenty of times in the past - and the time Australian players spend with their state is limited - the way they were kept quiet in Cardiff had the hallmarks of detailed input.
Warner flashed to slip in the first innings and was made to work extremely hard for his 52 in the second; Smith got himself into a tangle against Moeen but, perhaps more significantly, also fell to England's plan of hanging the ball a little wider outside off; and Clarke was again troubled by Stuart Broad before driving limply to point.
Bayliss had barely a fortnight to prepare for the Ashes, which included a four-day trip to Spain, but Farbrace said his knowledge of the Australians quickly came to the forefront.
"It did help that he had an insight into a few of them," he said. "You look at their squad, and probably half of them are from New South Wales.
"He was able to talk with quite a bit of authority in Spain, when we went through the Australian team, about how people play, where to bowl at them.
"But there's so much footage these days, and everybody knows everybody so there's a pretty good knowledge of the Australian team anyway.
Farbrace also gave a further insight into Bayliss' character during his first Test in charge, revealing how he rarely showed his emotion - a levelness for which he was well known in his other coaching roles.
"You would never know, looking at him, what the score was," Farbrace said. "One or two of the rest of us, you'd probably have a good idea.
"I think you need to have that because as well as the Test match that's gone, we know there are going to be tough times during this series and over the next four years that Trev's in charge.
"He wasn't jumping around on Saturday night all excited, shouting from the rooftops. He reminded the players that they'd done very well, but that there was a game to be played in a few days' time and the Aussies will come back very hard at us.
"He keeps a very even level, and if he can maintain that over the next few years it will be a big influence on the England team."
The relationship between Bayliss and Alastair Cook - which has been helped by Farbrace's previous stint working alongside Bayliss for Sri Lanka - has appeared to blossom in its early days and Farbrace said that any concerns about how the pair would work together were soon allayed by the first few days in Spain.
"There was obviously some hesitancy going there - one, what were we going to get, and two, how would people fit in?
"What Trevor did really well was that he fitted into what we'd been doing as opposed to everyone else having to try to fit into him, or him coming in and rewriting everything and starting everything from scratch.
"He isn't that sort of a bloke. He'll do his work quietly, and pick people off one at a time. It was important he and Cookie spent quite a bit of time together, and that they seemed to be getting on very well. It's not false. I think they actually do get on very well."
Hardys of Australia, proud sponsors of England cricket. Show your support this summer with #HardysENG or #HardysAUS to win prizes
Andrew McGlashan is a deputy editor at ESPNcricinfo