How does the 45 degree banking rule apply when plotting multiple data series in one chart? Cleveland's rule of thumb that the average slope of a line should be 45 degrees. But what about when a chart plots multiple data series? Is there a generalization of Cleveland's rule, or do you set the chart's aspect ratio by the "Eh, that looks good" method?
 A: The Visweek 2012 paper, An Empirical Model of Slope Ratio Comparisons [PDF] by
Justin Talbot, John Gerth, and Pat Hanrahan, attempts to generalize the question of optimal banking. Excerpt from introduction:

Despite the practical success of this guideline, its perceptual underpinnings
  remain unclear. Cleveland et al. justified the guideline with
  an experiment that showed that placing the mid-angle of two lines (the
  angle halfway between them) at 45° minimizes errors made in judging
  the ratio of their slopes. However, examination of their experimental
  design suggests that this conclusion might not be generally applicable.
  ...
  This paper seeks to improve our understanding of slope ratio estimation
  in line plots through empirical modeling and experimentation.

The experiments suggest the optimal median angle may be around 30° and that flatter is better for perceiving angle differences. Excerpt of a graph supporting the former point (observed error in black; predicted error in red):

However, like seemingly every other research paper, the bottom line is:

It is still unclear if the results derived in our studies for pairwise discrete comparisons will transfer to real plots. ...
  there remains substantial work to be done to
  build a solid understanding of aspect ratio selection.

Related papers:


*

*Arc Length-Based Aspect Ratio Selection [PDF], Justin Talbot, John Gerth, and Pat Hanrahan

*Crowdsourcing Graphical Perception: Using Mechanical Turk to Assess Visualization Design [PDF], Jeffrey Heer and Michael Bostock

