It is no flight of fancy to suggest it could be gold.
If she wins any kind of medal, Miley will be only the second Scottish woman to do so, and the first since Elenor Gordon took bronze in the 200 metres breaststroke in Helsinki, exactly 60 years ago tomorrow.
There is a special but fragile bond between parent-and-child athletes. It worked wonderfully for the man running these Olympics, Sebastian Coe, who was coached by his late father, Peter. Together they smashed 11 world records including three in 41 days, and won Olympic 1500 metres gold in 1980 and 1984. The fraught relationship between Damir Dokic and his daughter, Jelena, the Australian tennis player, illustrates that such relationships are not always so productive.
Patrick Miley is a former soldier and Army triathlete. He is now a pilot serving the North Sea oil industry. As a coach, he has also worked with Ian Thorpe, the five-time gold medallist from Australia, and the USA's triple Olympic champion Brooke Bennett. More than 20 years ago he invented what has become a fundamental training tool, the Aquapacer, a device which bleeps inside the swimmer's cap.
Miley defies convention and the notion that she should train in more fashionable surroundings, not least a 50m pool. Her home pool, the 25m Garioch facility, has just four lanes. Miley dismisses this: "It's all about the coach," she says. "You can have the best training facilities in the world but, if you've not got the right coach it's not going to work."
It is also about the athlete. A ferocious work ethic is the norm for the elite, but Miley has it in spades. She is up between 4.45am and 5.30am, covering 80,000 metres in her six morning sessions – the equivalent of swimming from Edinburgh to Glasgow city centre every week.
Miley has been known to hit the wall hard on turns, deliberately hurting her hand. "I just want some other part of my body to hurt," she explains. "All I wanted to do was to take the skin off my knuckles, so that the chlorine would really sting. Then when I started swimming again I would think about the stinging rather than the real pain."
In Beijing four years ago, when she reached the final, she felt like "a rabbit in the headlights". She is a real contender now.
Miley is in the fourth of five heats this morning, in the lane adjacent to world record-holder Stephanie Rice. The Australian won three gold medals in Beijing, and set the world best of 4:29.45 there. However, she has since undergone shoulder surgery, and ranks only fourth in the world this year (4:33.45). Miley is second (4:32.67), but the leading mark is by American Elizabeth "Diesel" Biesel (4:31.74).
There is a double Scottish assault on the men's 400m freestyle. Robbie Renwick (3:46.73) and David Carry (3:446.84) are ranked seventh and ninth in the world. China boast three of the four fastest, headed by Sun Yang (3:42.31) and they hope to sweep the podium.
Edinburgh teenager Craig Benson goes in the 100m breaststroke. He is 15th in the field, with 60.47. He will need to go under 60 seconds for the first time to have any hope of reaching the final. Team-mate Michael Jamieson is just behind him at 60.50. Fastest in the field and seemingly invincible is Japan's Kosuke Nakajima on 58.90. His mission is to win in memory of his late rival, Alexander Dale Oen, found dead at 26 after suffering a cardiac arrest at his Arizona training camp.
But the headline race is the start of the rivalry between Americans Ryan Lochte and Michael Phelps. The 400m individual medley is the first of two races in which they will meet. Phelps set the world best of 4:03.84 in Beijing – he has set the last eight world marks in this event, dating back to August 2002. However, Lochte beat Phelps in the US trials.
Phelps vowed he would never do the event again, but here he is, needing three medals to top the all-time list. "These are the last competitive moments that I will have in my career," he says. "It's big. There are going to be a lot of firsts and a lot of lasts this week. I won't be holding back when I am in the pool."
This, however, is about the current best swimmer in the world. Lochte can't surpass Phelps's great trawl of eight in China. He is doing "only" seven, but says he is ready: "I had a four-year plan. This is the year that I'm putting everything into it. This is what I've been working for."
He has worked harder than ever before, throwing tires and dragging chains. He claims to be the strongest swimmer at these Games. "I think that's one of the edges I have over everyone."
There's some evidence. He beat Phelps and his 200m individual medley record at the world championships in Shanghai last year, the first long-course record to go since the passing of the supersuit age.
A new era beckons, but Phelps will not surrender meekly.