Calculate total revenue share

Question

Suppose you have data such as this:

January
Total minutes of all videos watched: 50
Total minutes of video X watched: 25
Total revenue: 200


February
Total minutes of all videos watched: 200
Total minutes of video X watched: 50
Total revenue: 500

Therefore for the two months taken together:
Total minutes of all videos watch: 50 + 200 = 250
Total revenue: 200 + 500 = 700

I am confused about how to calculate the total amount earned by video X, if we assume that a video earns revenue based on the number of minutes it has been watched.

Method 1:
Total minutes of video X watched: 25 + 50 = 75
Revenue earned = 75 * 700 / 250 = 210

Method 2:
January revenue = (25*200/50) =  100
February revenue = (50*500/200) = 125
Revenue earned = 100 + 125 = 225

Please help me wrap my head around how to think about this.

Answer 1

Your method two is correct.

In january, one half of the revenue was generated by video X, since half of the total watch time was spent looking at video X. This means that video X earned 100, half of the total amount.

In february, the video earned one quarter of the total amount, meaning it earned 125, making a total of 225.

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But why does the first method return different results? Well, in the first method, you make the mistake of making the january watch-time minutes equally valuable as the february ones. For example, in january, each minute watched generated a revenue of 4, while in february, it only generated a revenue of 2.5. Therefore, saying that the video X was watched for a total of 75 minutes is correct, but saying that each of those minutes was worth 700 / 250 is not. Some of those minutes were worth 200/50, the others were worth 500/200.