Uneven sampling plotted at even spacing distorts rates of change

What it is

Many datasets carry uneven timestamps: manual records every few days, a sampling frequency changed after a system upgrade, sparse stretches in historical data. Plot every sample at even spacing (the categorical-axis default) and the axis lies: a three-month gap and a three-day gap take equal width. The damage concentrates in rate reading — the slope between two points is read as "speed of change," and even spacing draws slow stretches steep and fast stretches flat; an acceleration can render as a plateau and vice versa. The trend's direction may survive by luck; "how fast" is necessarily wrong.

Why it happens

Slope perception is relative: the same value change looks steeper the less horizontal width it occupies. Even spacing rearranges widths (timestamp-interval information discarded), so each segment's visual slope = value change / sample-index gap, while the true slope = value change / time gap. Sparse periods (long intervals) compress to the same width as dense ones, visually amplifying their change; dense periods stretch, flattening theirs. The distortion is systematic, its direction set by the sampling pattern — monitoring data that happens to sample more densely around key events exaggerates and misplaces the event's dynamics simultaneously.

Where it stops holding

Two legitimate "even spacings" are exempt: event sequences (logs or match actions ordered by occurrence, not clock time) promise no rates; confirmed regular sampling (hourly records, truly uniform) has even spacing equal to time proportion, harmless. The check is on the data: large variance in timestamp differences demands a true continuous time axis. Mixed granularities (days and hours in one series) unify to a common granularity before plotting; where impossible, split into two charts.

Applying it

• Compute the timestamp-interval distribution (diff min/max) before plotting a time series; a ratio over 2 bans the categorical axis in favour of a genuine continuous time axis.
• Prefer data-layer repair: resample irregular series onto a regular grid (interpolate or aggregate, with the rule declared) while the axis keeps time proportion.
• Verification: sample two intervals with very different densities and ask readers "which changed faster?"; any mismatch with true rates convicts the even-spacing distortion.

Related

• Same group: U3.06.2 Gaps in a series should appear as gaps on the axis, not be skipped over · U3.06.3 Months have unequal lengths; equal-width monthly bars are not directly comparable · U3.06.4 Time zones and DST create duplicated or missing hours on the axis · U3.06.5 Temporal granularity decides which periodicities become visible
• Nearby: U3.07.2 Trend judgement depends on line-segment angle · U2.03.2 Never connect a categorical axis with lines
• Search terms: uneven sampling · temporal axis · rate distortion · time series plotting