# What’s your best email frequency? Here’s the math

Some weeks ago, I asked my subscribers: What does sending more emails mean to you – more revenue or less subscriber lifetime value? The answers have been 50/50. And surely, there is a lot of evangelism on both sides. Some literally praise to send more for years. Others raise their subscribers permission shields and warn that such attitude in the market might kill email in the long run. All in all, both don’t help marketers that much in finding their optimum email freq, do they?

Yesterday, I stumbled across an article from John Foreman, data scientist at MailChimp. He showed how to determine the best emailing frequency in an objective manner. I liked that. So here is what he found – plus a little add-on:

### Optimum frequency: The revenue side

Sending more emails per month – say 25 campaigns instead of just 6 ones – increases the number of clicks during that period. However, the click rate per single campaign worsens with each increase in frequency. This is what the blue line in the above figure tells us. It cuts through some sample campaigns. For instance, 6 sends per month yield about 2% click rate each, 25 sends yield only 0.5% each.

If you sum up all the clicks per campaign and display them in a graph, you will get a curve like the one in the below figure. For example, our 25 sends à 0.5% make a total of about 12.5%. That’s some sort of your email revenue – not measured in euros or dollars, but measured in clicks per month:

As you can see, it may make sense to increase frequency. But this works only to a certain tipping point, at which CR per month (the revenue) has its maximum. You can calculate its exact value by taking the first derivative of the curve’s formula, and then looking at where it becomes zero. Geometrically, this would be the point, where the dashed light blue line gets negative values (< 0.00):

To sum it up: The optimum send frequency for this sender would be about 15 to 16 campaigns per month. That is, if we just look at his revenue side – his clicks.

### Add-on: Accounting for costs, too

However, sending more emails also comes at costs. In fact, getting too many emails is the top reason, why people unsubscribe. Only some quit explicitly by hitting unsubscribe. Most of all unsubscribes happen implicitly. You can’t reach those subscribers anymore, although they are still on your list.

When deciding, which frequency to choose, one must also account for list churn (aka list fatigue). So, let’s add this to our plot. We assume that higher frequency causes steadily increasing churn rates (red line, churn = 0.01 * f):

Now, the picture changes a bit. Sends are profitable within the area, where the red line lies under the light blue curve. By profitable we mean here: achieving more clicks than suffering unsubscribes. (You could easily extend this model to represent sending revenues and sending costs in €/\$. Think of conversions and cpm or subscriber value for instance.)

What would be the most appealing frequency in that area? It would probably be the one, where the gap between clicks (curve) and unsubscribes (red line) becomes largest. The exact location is difficult to spot with your eyes alone. Luckily, we can calculate it.

Math tells us to look at where the 1st derivative of the click curve’s formula equals the 1st derivative of the churn line’s formula. Graphically, this would be the intercept point between both lines. At the same time it’s the point, where the red line would just touch the curve, if we would just move it up. Put in a formula, it would look like “click_intercept – churn_slope / (2 * click_slope)“.

Et voila: The optimum frequency goes down from 16 (blue dot) to 9 (red dots) sends per month, if we want many clicks AND loyal subscribers. 9 is calculated as 0.025 – 0.01 / (2 * 0.0008).

### Final thoughts

This model itself is simplistic (short-termed, just one revenue and cost component, no retention rate…). Also, for practical implementations, one would make churn and clicks better comparable. E.g. by using average subscriber lifetime values and conversion rates plus average order values. Here we assumed that 1% click rate and 1% churn rate both have the same absolute value from a marketing perspective. Nevertheless, it’s a good framework for some further analysis.

There are other ways to address churn. For example, we can include a retention rate into the click rate formula. Churn rate and retention rate add up to 1. So the retention rate shows, what percentage of subscribers stays with us from send to send. The effect would be the same: If you don’t just want to go for clicks but also for retention, the point of best send frequency wanders to the left:

#### Note

German readers might want to check out my more detailed frequency posting on emailmarketing.de. It also covers how to fit a linear model like the one that John applied.

 More info on when and how often to send your emails? Sign up for free, I'll keep you posted with email marketing news: (archive♞) Yes, I accept the Privacy Policy ♞Delivery on Fridays, 5 pm CET. You can always unsubscribe.It's valuable, I promise. Subscribers rate it >8 out of 10 (!) on average.

### 6 Responses to What’s your best email frequency? Here’s the math

1. Inspiring new take on email frequency from @John4man http://t.co/ksFDf0Dvd8 + a way 2 incl unsubs http://t.co/Jn3yrsWcLo ?

2. What’s do you think is the best frequency to send out email campaigns? http://t.co/3mzO2Fjxqq

This site uses Akismet to reduce spam. Learn how your comment data is processed.