Technical director Mike Coughlan is confident that its new car has delivered a step forward in performance, and believes that huge uncertainty about tyres will give it the chance to overcome its main rivals.
Speaking to AUTOSPORT about whether he felt there were prospects for Williams to triumph again in 2013, Coughlan said: "Yes I do.
"Obviously what we don't want is a lottery. We want to ensure that when we win, we win on merit.
"But we've worked hard; we've worked hard to understand the tyres and we got on with [testing] programmes to understand that.
"Melbourne, and indeed the first couple of races, will be where the person who really gets a handle on the tyres will certainly be in a position to be on the podium.
"Ultimately we've got to ensure that when we have an opportunity we fulfil it.
"There were so many times last year when we were in a position to score significant points or a podium and we, as a team, let ourselves down.
"We have to close them all out. You have to make sure that when the opportunity arises you deliver. That is the final piece in the puzzle."
Coughlan believes the new FW35 has built on the strengths of last year's car, but has also made big strides in addressing the aerodynamic weaknesses of its predecessor.
"We feel at least as competitive as we were, maybe a little bit closer to the cars in front," he explained.
"We've looked at the data and all we can say is that we had a car last year that was reasonably competitive. It had some problems, and we've addressed those problems.
"The drivers have confirmed we are at least as good as we were in the areas we were good last year and we are significantly better in the areas we struggled in last year.
"They have both commented on that and we are happy."
Coughlan also reckons a winter staffing reshuffle - with Xevi Pujolar being promoted to chief race engineer following the departure of Mark Gillan - has brought positives that should help its competitive situation.
"I've changed the structure a little bit and said that I don't want him [Pujolar] looking at the nuts and bolts of the construction of the car; I want him to concentrate on performance.
"I will look after the build of the car, the running of the car, and the reliability of the car.
"His brief is simple: you get the most out of the car when it arrives at the circuit."
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