Compute Expected Purchases and Revenue by Channel
Context
A company sells a product through three channels: online, phone, and email. For each channel, you are given:
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Impressions (I)
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Click-through rate (CTR)
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Conversion rate (CVR)
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An average order value (AOV) may be supplied
Assume CTR and CVR are provided as percentages and represent:
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CTR: probability of a click given an impression
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CVR: probability of a purchase given a click (post-click conversion)
Task
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Compute the expected number of purchases for each channel.
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Rank channels by conversion efficiency.
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Compute and rank overall expected revenue given AOV.
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List additional metrics you would request to judge channel performance more holistically.
Formulas
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Expected purchases per channel: Purchases = Impressions × CTR × CVR
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Conversion efficiency (two useful views):
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Post-click efficiency: CVR
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End-to-end efficiency per impression: CTR × CVR
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Expected revenue: Revenue = Purchases × AOV
Hint: Compare per-impression or per-click ROI when cost data are available.