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Not sure if this is the right place to ask, but I'll try:

What's the right way to calculate the average open rate of mails:

  • simple average?
  • average of averages?

For example, if we have:

  • First mail, that was sent to 100 contacts, and opened by 10 contacts
  • Second mail, that was sent to 1000 contacts, and opened by 500 contacts

We get:

  • simple average: $\frac{10+500}{100+1000} = 0.46$
  • average of averages: $\frac{ \frac{10}{100} + \frac{500}{1000}}{2} = 0.3 $

Is there a "right" answer, or is it depends on something?

HeyJude
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  • The simple average is the correct way to average in this case. Averaging averages only works when each average has the same "weight", but here the second experiment has more "weight" than the first one, because it has a larger sample space. – HappyDay Dec 11 '22 at 15:02
  • The two calculations are both meaningful and tell you different things. What do you mean by "average open rate"? What are you trying to evaluate? – Karl Dec 11 '22 at 15:14
  • @Karl I was waiting for this kind of comment! I had a sense that it measures two different things, but I can't put into words what are those things. To answer your question, I'm ok with Wikipedia's definition: "The email open rate is a measure primarily used by marketers as an indication of how many people "view" or "open" the commercial electronic mail they send out." - To me, it says it all. What else could it be? And so, if we have multiple "open rates", I'd like to find their average. What am I missing? – HeyJude Dec 11 '22 at 15:28
  • It sounds like you want the average of averages then. Or do you want to give an email a higher weight (contribution to the average) if it was sent to more recipients? Or maybe there's some other non-uniform weighting you want (e.g. based on the importance of the campaign). It's up to you. – Karl Dec 11 '22 at 15:31
  • @Karl so you disagree with HappyDay's comment? They say that the "simple" average fits here because each email already has a different weight. But you suggest they don't? – HeyJude Dec 11 '22 at 15:47
  • Yeah, I disagree with that comment. If you're trying to measure (say) the quality of your email writing, it doesn't seem right for the open rate of one email that went to a million people to completely dominate the average when considered along with many other emails that each went out to a hundred people. (But maybe you do want to ignore emails with too few recipients to get a reliable open rate.) – Karl Dec 11 '22 at 18:48
  • Very related: https://math.stackexchange.com/questions/2518560/average-bias-of-coin-factory – Karl Dec 13 '22 at 22:15

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