Magic numbers in plotting

I’ve just started a class on making scientific plots so I’ll cover a common phenomenon: magic numbers.

What’s a magic number?

I use this definition: A magic number is a hard-coded non-obvious value. Notably, “value” includes non-numbers such as strings.

• Hard-coded: A value appearing directly in the source code. For example, in len(read) > 200 and geno = '0|1', 200 and '0|1' are magic numbers.
• Non-obvious: The reason for this specific value is not obvious from the statement itself. Often 0 and 1 have obvious reasons, such as colors[0] or for i in range(1, k+1).

My usual rule of thumb is to check for any hardcoded value that isn’t 0 or 1, and then consider each of those on a case-by-case basis.

Why are magic numbers (usually) considered bad?

Magic numbers are problematic due to readability. Plus they commonly violate DRY. For example, consider the following code which checks each alignment for quality and then tries to “rescue” the poor-quality ones:

if alignment.quality() < 10:
    poor_quality_alignments += 1
    # ...
    # 20 lines of trying to rescue alignment
    # ...
    if rescued_alignment.quality() >= 10:
        rescued_alignments += 1
        alignment = rescued_alignment

Here, the += 1 bits aren’t magic numbers. It’s obvious they’re incrementing counters. However, the quality threshold is a magic number: why isn’t it higher or lower? Is it intentional that the same threshold is used both times? A refactored version would be:

QUALITY_THRESHOLD = 10
if alignment.quality() < QUALITY_THRESHOLD:
    poor_quality_alignments += 1
    # ...
    # 20 lines of trying to rescue alignment
    # ...
    if rescued_alignment.quality() >= QUALITY_THRESHOLD:
        rescued_alignments += 1
        alignment = rescued_alignment

This code is more readable. Plus, it’s easy to change the threshold later.

So what about plots?

Plots and magic numbers are… tricky.

Technically plotting tends to involve a whole bunch of magic numbers. Figure sizes, panel sizes, axes limits, axes labels, legend position, the exact location of that one arrow you’ve been trying to get in place for ages, etc.

But unlike regular coding, I actually don’t recommend getting out the pitchforks here. Titles quite often make most sense simply hardcoded within a plot, in their native context. The Y-value of a horizontal line should probably be hardcoded in the horizontal-line function call. And for goodness’ sake, just put the legend’s position label within the legend-making function call itself.

In plotting, magic numbers are a necessary evil.

However, that doesn’t mean you shouldn’t factor out any magic numbers. Personally, when plotting, I factor out magic numbers I use more than once. If I have the same X-axis label in multiple plots, I make it a variable. If I place panels relative to a larger figure, it probably makes sense to factor out the larger figure’s dimensions into variables. Especially in a plotting context, it’s useful to know when two values are the same on purpose.