Measuring a podcast appearance
The honest answer to what an appearance achieved is usually partial, and a partial answer stated plainly is worth more than a confident one that is invented.
What the numbers can and cannot say
Download counts are the figure most often quoted and the least informative one available. A download records that a file began transferring to a device. It does not record that anyone listened, how far they listened, or whether the device was a person's phone or a caching server. Comparing download counts between two shows measured by different providers compares two different definitions of the same word.
Completion and drop-off data, where a host will share it, says considerably more. Knowing that most listeners left during the third segment tells you something actionable about the third segment. Knowing that a file transferred eleven thousand times tells you almost nothing you can act on.
Observable effects
The effects that can actually be observed after an appearance are narrow but real. Direct traffic to a specific page mentioned in the episode, measured against the days before, is observable. Search interest in an unusual phrase used during the conversation is observable. Enquiries that arrive citing the episode are observable, though only the ones that bother to cite it.
Each of these undercounts, and each undercounts by an unknown amount. That is a reason to report them as what they are rather than to inflate them into a total. An appearance whose effect is described as "a visible rise in direct traffic to one page for four days, and three enquiries that named the episode" is more credible than one described with a single confident number.
The long half-life
Podcast audiences accumulate slowly and continue accumulating. A back-catalogue episode may be discovered a year after release by someone working through a show from the beginning, and by then the episode page and its transcript are doing more of the work than the release week ever did. Measurement taken only in the fortnight after release systematically misses this, and the miss grows over time.
The practical consequence is that a measurement window of two weeks is a measurement of the release, not of the appearance. If a longer window is not available, that limitation belongs in the report alongside the figure.
