In fact, this is not an impossible question to answer.

For clarity, please note these definitions:
• “reply to my e-mail”: generates any type of action; most basic example is the Receiver sending a reply e-mail; also can include Receiver talking in person to the Sender, or Receiver talking to a third person, or any other action that would not have occurred otherwise
• “not reply to my e-mail”: generates no action; most basic example is the e-mail sitting unactioned in the Receiver’s Inbox; also can include ignoring or deleting of an e-mail, whether intentional or unintentional  

First, we need to determine what the relevant factors are. Once this is established, we can then analyse each variable to estimate the probability.

Actors:
(1) Sender
(2) Receiver

Variables, ranked in importance (highest to lowest):
• i = importance of, or interest in, the subject to the Receiver (highest importance)
• I = importance of, or interest in, the Sender to the Receiver
• n = number of e-mails the sender has sent previously on the same subject
• t = time management skills of the Receiver
• N = number of other demands on the Receiver
• q = frequency in which the sender sends e-mails (lowest importance)

Putting these together, we have the following equation:
• f(probability of reply) = i + I + n + t + N + f + q

The next step is to assign a weight to each variable. This will likely vary from case to case, but in general the more important the variable the greater the weight it should have. As an example:
• f(probability of reply) = 0.3i + 0.25I + 0.15n + 0.15t + 0.1N + 0.05q

Consider two e-mails, one sent by me (a graduate) and the second Andy Green (CEO). Andy will likely generate a higher score for “I”. Consider further that Andy’s e-mail is to a senior manager and advises of an interesting article on cricket, while my e-mail is to my project manager and contains the final draft of a document for a project deliverable due in two hours. I will likely generate a higher score for “i”.

When generating a “score”, we must assign a percentage to each variable between 0 and 100.

Now we are in a position to bring this all together. Consider an e-mail that I send under the following conditions:
• subject = proposed dinner during my return to Minnesota for a holiday in May
• receiver = one of my best friends Brian
• this is the first e-mail I have sent advising that I’m returning for a visit
• Brian is extremely efficient worker
• Brian is getting married in May, and together with work, has many demands on his time
• Brian and I communicate on average once a month

Calculations to estimate the probability of a reply from Brian might look as follows:
= f(probability of reply) = 0.3i + 0.25I + 0.15n + 0.15t + 0.1N + 0.05q
= 0.3(.80) + 0.25(.9) + 0.15(.5) + 0.15(.8) + 0 .1(.2) + 0.05(.7)
= 0.72

Thus, we can conclude there is a 72% chance Brian will reply to my e-mail.

So, what does this all mean? I suggest that as we now better understand the factors determining whether or not we receive replies to our e-mails, we can focus our efforts on activities that will likely increase the score we generate for each variable.