Your Favorite Analytic to Prove Improved Fitness

That is an very interesting question and the answer also depends on your specific goals.

In general I would say a sign of improving fitness is the ability to produce a higher power at the same heart rate (or to have lower heart rate for the same power).

To visualize this I really like the Power vs. Heart Rate curve under the Compare tab where you can compare periods in time.

Shifting the curve lower/to the right is better.