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They’re the questions that vex leisure travelers across regions, languages, origins and destinations: When will I find the best fare? Should I buy that plane ticket now or wait?

Websites are increasingly responding to these universal questions with tools that predict whether a price will rise or fall during a consumer’s online search. Though Bing has been at the game for a few years (including back when the travel-forecasting system it was known as Farecast), Kayak launched its version of the technology earlier this year.

The prediction tools do a few things. First, and most important, they advise users on whether to hit “buy” while sitting at the computer. They also express their confidence in their recommendations in the form of a percentage.

For example, on a hypothetical trip from Chicago to Los Angeles in May, Kayak turned up a low fare of $248 and urged me with 73 percent confidence to buy it immediately. Bing found the same fare and said with 80 percent certainty that I should hit purchase.

What those percentages actually indicate is the websites’ confidence that the fare will rise or fall in the next seven days. In the case of that LA flight, Kayak said its “model has been 73 (percent) accurate on forecasting whether these fares will rise or stay within $20 of the current price over the next (seven) days.”

Both websites also offers charts with their predictions that show the recent price fluctuations in a desired route. Bing’s looks back three weeks; Kayak’s goes back three months. Again, in the case of that flight to LA, Kayak’s chart showed my price recently hovering at about $250 before taking a recent spike up and then coming back down to its current price. Kayak’s best guess, therefore, was that the price had reached its floor.

Where does all this knowledge come from? In the case of Kayak, it comes from statistical models and data crunching led by the company’s “chief scientist,” Giorgos Zacharia, whose background is in math and computer science.

Zacharia said the project was the product of two years of watching airfares and trends and is simply “driven by the strength of pattern.” That is, Kayak uses its billions of searches to reach its conclusions and predictions. Many factors are weighed, including recent price fluctuations, how far a search is made from the date of travel, origin, destination and time of the year and day of the week for the travel.

“The importance of each factor depends on each search,” Zacharia said. “There are no absolutes.”

That said, the most important factor, he said, is how many days out it is from the trip. The industry’s universal school of thought (which is consistent with Kayak’s annual findings) is that the ideal time to book a ticket is about 20 to 30 days in advance for domestic fares and slightly longer for international trips.

If Kayak (or Bing) doesn’t have enough data to make a confident prediction, it will say as much. The most popular trips — to Orlando, Fla., or Las Vegas or during spring break — therefore see the strongest predictions.