In any science experiment, every test will result in a data point. After two tests, you have gathered enough information to draw a graph. A straight line.
After running more tests, you find three more data points that do not fall on your straight line. Obviously something must be fixed. The data are irrefutable, so the graph must be redrawn. Drawn as a curve of some kind.
The more data points you have, the more accurate the graph becomes. But until you have every single possible shred of data, the graph will be slightly imperfect.
If it’s not too much of a stretch, apply this concept to character development. You see a character react in one situation (an extra is crushed by an elephant). How much do you know about him? Nothing. His life is one point. It has no arc.
Another character (Mom, perhaps) appears at two points in the story. She reacts in two situations, one at the beginning, one at the end. Her character may have changed – even a straight line has a slope – but we still do not really know much about her.
It’s obvious to see where this is going. The protagonist is the person the audience knows the most about. He provides the most data. His character arc is the clearest because we know where he’s been, what he’s done, and where he’s going. If he does something that appears completely random, something “out of character,” the graph must be completely redrawn. If this is done skillfully, it can be very effective in creating a complex, believeable character. If done poorly, we merely throw up our hands and give up trying to figure this guy out. He’s irrational in a way no human being would ever be, and we don’t want to watch movies we can’t relate to.
As a convenient example of this, consider a TV show. After running for three or four seasons, any major character will have performed hundreds of actions, hundreds of “data points” for the audience to file away. Even subconciously we construct character arcs. The more information we have to work with, the more accurate the arc will be.
However, if the data falls exactly on the curve, or as close as possible, we need fewer observations. We can construct this character accurately even though we have only seen them in a few situations. This is the struggle of a screenwriter, and this is why television writers have an easier time constructing characters. A television writer can scattergun situations, hoping that eventually (after scores of episodes) the audience will be able to piece together the character. A screenwriter, on the other hand, has to carefully search out those particular situations and actions (those particular “data points”) that will reveal the most about his chosen characters in the shortest amount of time.