According to my philosophy teacher, Nietzsche says there is no one true, objective reality but plenty of fictions and those that are more effective are the ones that persist.
My teacher argues that science is an effective fiction because of its predictability power.
What does he refer to with 'effective'? How can we measure 'effectiveness'?
The central unifying concept in Nietzsche is the will to power. So effectiveness is what delivers power.
The ability to predict the behavior of the external world supports an ability to influence or control people, even if this control is very indirect or hard to see immediately.
You can measure effectiveness by your impact on the future through other human beings.
By effective he means able to persist. He calls science a "fiction" as a contrast to an objective truth, because we have no means to prove that science is able to reach this truth, but it is "effective", because it derives useful results, it is able to lead to predictions, verification of experiments and so on. So it is a kind of fiction, but not the same as other forms of fiction like belief in ghosts, which are not able to prove their usefuless, and so they are not effective.
I suppose that the notion that science is an effective fiction implies that science is believed to be effective because it has the capacity of predicting things about reality, yet is still flawed it its capacity to describe reality. Personally, I could not disagree more with that notion, as it has been demonstrated over and over that the scientific method is the ONLY reliable method we have to know anything about the objective reality we live in. And yes, we DO live in a single objective reality.
Not only did Nietzsche actually believe in the existence of an objective reality, but he considered it self-evident. However, he also believed that we have no means of ascertaining its nature that are 100% reliable. This implies that all our assertions about this objective reality are fundamentally subjective and therefore often wrong. Basically, he argues that what we perceive as objective reality is just our subjective, flawed, interpretation of objective reality.
This is precisely where science comes in. The very goal of science is to eliminate all subjectivity from how we perceive reality and therewith give us a model of objective reality that itself is as objective as humanly possible. And thusfar, no other method comes even close to the scientific method in achieving that goal.
When Nietzsche argues that there are no facts, he doesn't means that there is no objective reality, but rather that there is so absolute truth with respect to any assertion we make about this objective reality. Here are some quotes that clarify this.
Judgment is our oldest belief, our most habitual holding-true or holding-untrue, an assertion or denial, a certainty that something is thus and not otherwise, a belief that here we really 'know'...
— Will to Power
What then is truth? A mobile army of metaphors, metonyms, and anthropomorphisms - in short, a sum of human relations, which have been enhanced, transposed, and embellished poetically and rhetorically, and which after long use seem firm, canonical, and obligatory to a people: truths are illusions about which one has forgotten that is what they are; metaphors which are worn out and without sensuous power; coins which have lost their pictures and now matter only as metal, no longer as coins.
— On Truth and Lies in a Nonmoral Sense
All things are subject to interpretation. Whichever interpretation prevails at a given time is a function of power and not truth.
— Daybreak
What are man's truths ultimately? Merely his irrefutable errors.
— The Gay Science
