Limits of matplotlib's 'best' legend location for reproducible figures

Answer to the specific questions

Matplotlib’s internal loc='best' scorer (found in _legend_box._calc_best_location) evaluates each corner candidate by:

• Computing the overlap area between the legend’s bounding box and the axes’ data area (the part of the axes that contains plotted lines, markers, etc.).
• Adding a penalty proportional to the amount of unused white‑space inside the axes that the legend would cover.
• The final score is a weighted sum of these two metrics; the exact weights and any threshold values are hard‑coded in the private module and are not exposed in the public API.

Because the scoring logic lives in a private module, there is no public method to retrieve or reproduce the score for a given axes configuration. Users cannot programmatically enforce the same placement without manually fixing the legend location.

Setting bbox_to_anchor to a fixed normalized coordinate (e.g., (1, 1) for the upper‑right corner) together with an explicit loc value (e.g., loc='upper right') guarantees that the legend’s relative position stays the same within the figure. However, the pixel position will change if any of the following vary:

• Figure size (in inches).
• DPI (dots per inch) of the canvas.
• Backend used for rendering (different backends may round coordinates differently).
• Layout managers such as tight_layout or constrained_layout, which resize the axes after the legend is placed.

Therefore, to obtain identical legend positions across different runs, file formats, or environments you must control those variables.

Steps for reproducible legend placement

1. Choose a fixed figure size and DPI, e.g., plt.figure(figsize=(6, 4), dpi=100).
2. Disable automatic layout adjustments: plt.tight_layout(False) and plt.set_constrained_layout(False) (or simply avoid calling them).
3. Add the legend with an explicit location and a fixed anchor, for example:

   ax.legend(loc='upper right', bbox_to_anchor=(1, 1), borderaxespad=0.)
   

4. Save the figure in the desired format (PDF, PNG, SVG, etc.) using the same dpi if raster output is needed.
5. Optionally verify reproducibility by checking the legend’s bounding box in figure coordinates after drawing:

   fig.canvas.draw()
   legend_bbox = legend.get_bbox_to_anchor().transformed(fig.transFigure.inverted())
   print(legend_bbox)
   

   Repeat the process with a different backend (e.g., switch from TkAgg to Agg) and confirm the printed bbox values match.

Missing diagnostic detail

If you are using tight_layout or constrained_layout in your script, the legend’s position may still shift because these layout managers resize the axes after the legend is placed. Let me know whether you employ either of these layout managers so I can advise on the exact steps to disable them.