Of American-English origin, the expression fudge factor denotes a factor speculatively included in a hypothesis or calculation, especially to account for some unquantified but significant phenomenon or to ensure a desired result.

This expression occurs, for example, in Seconds out: Man and nature have always clashed over the order of time, an unsigned article published in the Evening Herald (Dublin, County Dublin, Ireland) of Thursday 28^th February 2008:

Why do we need this calendrical hiccup every four years? What, exactly, is the point of it? “The leap year is basically down to humans trying to make sense of natural rhythms,” explains David Rooney, curator of time-keeping at the Royal Observatory in Greenwich. “If you’re trying to run a calendar by the natural cycles of the Sun and the Moon, it doesn’t work and you have to intervene. The technical term for this intervention is ‘fudge factor’. The leap year is a fudge.”
[…]
“When the atomic clock was invented in the Fifties, we discovered that time-keeping based on vibrating atoms was more accurate than the Earth,” adds Rooney.
“It was slightly embarrassing. When clocks diverge, it isn’t good. By the Seventies, we needed another fudge factor. So, the leap second was introduced to push together Earth rotation time and atomic vibration time.”

The earliest occurrences of the expression fudge factor that I have found are as follows, in chronological order:

1-: From Question: How Big Is C.R. Today?, by Bayne Freeland, published in The Cedar Rapids Gazette (Cedar Rapids, Iowa, USA) of Sunday 4^th May 1947:

How big is Cedar Rapids?
That’s the problem, and you won’t find the answer in the back of the World Almanac. As far as the U. S. census taker is concerned, we are frozen at the 62,120 souls he counted here back in 1940 and there will be no recount for another three years. Meanwhile, how many people actually are crammed within the corporate limits?
It’s a topic of intense interest to businessmen and civic officials. The best answer that can be achieved is only an approximation, and the accepted method of attack involves a curious combination of simple arithmetic and hog-wild guesswork. […]
[…]
Method of solution varies with the individual. In general, however, here’s the way to go about it: Suppose you are a merchant who controls the sole Cedar Rapids distributing rights for a product which remains fairly constant in demand—toothpicks, for example. They’re not a class item and may be considered to be spread over the population as a whole.
In 1940, when the population was 62,120, you disposed of 1,000,000 toothpicks within the city limits. Present sales indicate that you will distribute 1,209,693 toothpicks here this year. From this point it is a matter of simple proportion, thus: 62,120 is to 1,000,000 toothpicks as X is to 1,209,693 toothpicks. The inescapable answer is 75,000 persons. Right on the nose.
But—and this is where the problem leaves mathematics for metaphysics—you haven’t taken into account that mysterious quantity which some amateur stastisticians [sic] call the “fudge factor.” At this point you must abandon cold figures and depend on the imagination.
You, as a toothpick tycoon, may estimate that your current sales would run higher if it were not for the shortage of seasoned timber, hence your population guess is low. On the other hand you may conclude that some people, with more money in the bank than they had in 1940, are buying two toothpicks where they used to make do with one. This is a minus revision. Further, a portion of your wealthier clientele may have abandoned pine in favor of lifetime ivory picks with gold heads. This is a plus.
When you have synthesized these and any other remotely pertinent factors which come to mind, apply your correction.
[…]
Prior to the war, the gas, light and telephone companies were able to work a simple proportion problem based on the number of their connections, and the answers were fairly reasonable. Today, however, many families have doubled up; moreover, some connections have lagged behind demand. A plus fudge factor is indicated, and from there on it’s anybody’s guess.
Last estimate by postal authorities was in October, when carriers counted the families on their routes and multiplied by about 3½. The answer came out about 69,000 but Supt. of Mails Robert T. Lubbock acknowledges that some Cedar Rapids areas are not yet served by carriers. Many rooming house residents, too, may have escaped the count.
M. H. Morrison, manager of the Cedar Rapids telephone exchange, estimated 71-73,000—“but it’s just a guess.” At the light company, Manager Earle G. Nichols said several executives had guessed between 70,000 and 75,000, “but we haven’t an accurate measure any more.”
Figuring four persons per family and one family per meter, District Manager E. E. Hahn of the gas company estimated population at 73,000. “But our meters haven’t caught up with the fringes of the city,” he added, and no fudge factor to compensate for shared meters was added to his estimate.

2-: From an article by Bill Broom about the launch of a V-2 rocket at White Sands Proving Ground, in New Mexico, published in the El Paso Herald-Post (El Paso, Texas, USA) of Thursday 23^rd August 1951:

There are 16 bachelor of science degrees on the firing crew alone.
Alley, regarded by his buddies as a “wonder boy,” was co-ordinator in the control room. Days before the shoot, he computed what would happen. He missed the maximum height by a mile and a half, hit the rest of the data on the nose.
“The computations involved a few fudge factors,” he said. “Fudge factors are things we aren’t quite sure about, so we just fudge a little. Fortunately, all the fudge factors turned out right.”

3-: From Hundreds Of Factors Figure In Determining Assessments, by Joseph A. Cooley, published in The Times Record (Troy, New York, USA) of Wednesday 18^th June 1952:

It may be years since you’ve eaten a piece of candy but that doesn’t mean the field crews for the Wood, Dolson Co., Inc., won’t find fudge at your house. The Wood, Dolson Co., is the firm of real estate specialists which is making the Troy property revaluation survey.
When the property revaluation crews speak of fudge, however, they’re talking about those features about your property which can’t be measured or don’t show on the surface but they do have a definite bearing on the value.
For example two houses exactly alike may stand side by side. One is built on solid ground, the other is built on a filled-in section which may shift and damage the foundation. This is a “fudge” factor which reduces the value of the second house.
[…]
After the pricing has been done and an allowance included for depreciation, Raymond B. Crawford, chief appraiser for the project and his staff, will […] check each piece of property to see it has been placed in its proper class and that full account has been taken for any factors above or below standard as well as for “fudge” factors.