The decomposition:

avg_sessions_per_user = total_sessions / total_users. Either the numerator dropped, the denominator grew, or both.

Likely scenarios:

New users diluting the mean. If marketing drove 20% more signups this month, those new users (who haven't built usage habits) pull the average down. Total sessions might be growing in absolute terms. Check per-cohort session rate — has it actually dropped, or is the mix different?
Power users churning. The opposite — a small group of heavy users left or reduced usage, dragging the mean. Look at the distribution: did the top decile's sessions-per-week drop more than average?
Genuine engagement decline across cohorts. Every cohort is using the product less. Rarer; indicates a real product issue.
Definition / pipeline drift. Did 'session' logic change? Timezone issue in a recent deploy? Background-session-counting that used to inflate things?

The diagnostic in steps:

Plot sessions-per-user by cohort. If newer cohorts have lower rates, it's mix. If all cohorts dropped together, it's a product issue.
Plot the distribution, not the mean. Histogram of sessions-per-user, this month vs. last. Is the left tail (light users) fatter? Is the right tail (power users) thinner?
Segment by platform / geo / acquisition channel. Often the drop is concentrated somewhere specific.
Cross-reference with recent changes. Product ships, pipeline updates, marketing pushes, external events.

A likely finding:

"Avg sessions/user/week fell from 4.2 to 3.8. Decomposition: total sessions are actually up 8%, but user base grew 19% due to the Q2 onboarding experiment. Per-cohort analysis: the Q1-and-older cohorts' session rate is unchanged; the Q2 signup cohort is averaging 2.8 sessions/week, dragging the mean down. This is a mix effect, not a decline. Decision-useful metric to watch: 'sessions per user at week 4 post-signup' by cohort — that's the one that flags real product regressions."

What to report:

Whether the drop is real or a mix-shift artifact.
If real, which segment is driving it.
The better metric to watch going forward (usually cohort-normalized).

What senior candidates add:

Aggregate engagement metrics hide everything. A healthy product with high growth can look like 'engagement is falling' because new users haven't caught up. The right metric is cohort-normalized (e.g., 'sessions per user at week 4').
Track the distribution, not just the mean. Means hide what's happening to the tails, which often matter more.

Engagement depth is falling. How do you analyze?

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