Mercedes team principal Toto Wolff says his team's chances of winning the title this year are around 20 percent after its worst start to a season for nine years.
The grim forecast is based on the opening two races of the 2022 season in which Hamilton and teammate George Russell have struggled to come close to matching the pace of rivals Ferrari and Red Bull.
Mercedes, which has won the last eight F1 constructors' titles, is currently second in the championship, but only because both Red Bull cars failed to finish the race at the opening round in Bahrain.
"I think we are on the back foot," Wolff admitted after qualifying for the Australian Grand Prix on Saturday. "If I look at it from a mathematical standpoint and probability I would say the odds are 20/80, but this is motor racing and in motor racing anything can happen.
"Teams can DNF and if we unlock the potential of the car we are right back in the game. So as a racer I would say it's probably 40/60 and as a mathematician I would say the odds are worse against us.
"But it's the third race of the season and we are not going to write the title off, so it's just the current status quo -- we are 0.9s off."
On Saturday, Hamilton and Russell qualified fifth and sixth for this weekend's Australian Grand Prix and were roughly a second off the pace of Ferrari's Charles Leclerc on pole. The laps of the Mercedes drivers offered a visual explanation of the team's issues as both cars bounced dramatically on the straights and through high-speed corners.
"You can see many other teams, like Ferrari, still have some bouncing but they have done many other things right that we missed out on or didn't perform very well with," Wolff said. "It was the same for Red Bull, their car got quick from one to another in Bahrain testing by bringing the update.
"Our bouncing is worse [than Ferrari's] because we carry it into the corners and the high-speed, so you can see where we lose performance. When you look at the overlay in sector one we are very competitive, sector two we are competitive and then in sector three, through Turns 9, 10 and 12 we are losing all our margin -- it's almost like a second through a couple of corners.
"So is curing the bouncing going to miraculously unlock a second within the car? No, for sure not. But there are many other little improvements we can make on weight and other things we can optimise and we just need to chip away the small gains while understanding the car.
"I'm optimistic that eventually we will get there, whether it is two races or five ... we need to stay humble and my time horizon is not a race weekend or a year, it is more like ten years and I want to look back and have a competitive team and there will be more difficult years and this is one of them."
Wolff explained that one of the reasons Mercedes has struggled to get on top of its issues is because it is impossible to accurately replicate the bouncing in the team's wind tunnel and simulations.
"This car is very difficult to correlate because you can only move the car with a certain frequency in the wind tunnel where it is limited and on track it does something completely different, so this is a new way of analysing aero data and correlation between the simulations and the real world, which needs to be understood.
"We believe we have the tools and the people to understand that, but we haven't found that yet."