LTV Crash Course: Math And Methods To Establish The Lifetime Value Of Your User

Customer lifetime value, recently crowned by VentureBeat as the “king” of app metrics — helps app developers and marketers pinpoint and measure the profitability of users and identify more lucrative customer segments. In its most basic form LTV is all the revenue a single user will generate from the time they download the app or game until they abandon the app altogether.

Arriving at this important — and quite predictive — metric is key to measuring the *true* potential of your business. But calculating your future profits with high confidence requires you to start with an equation that nails down LTV with high degree of accuracy. In this 2-part series, excerpted from my recent workshops on the same topic, I review what you can use to calculate LTV properly and recommend ways you can apply your model successfully.


Its roots go back to early subscription models where customers paid over time, not upfront. This is quite similar to the situation with F2P games, where your users pay more the more they engage with your app, but not all at once.

In the subscription model, let’s assume the business observes the average subscription length is 32 months at $7.95 / month and therefore can conclude that a subscriber is worth $250.00.

So far so good. But the key question is how can we come up with the 32 months early on — in other words, how do we calculate the lifetime of the average customer? In our subscription example, you could easily imagine a monthly service like America Online in the early days that observed retention over time, seeing it drop from 100% in the first year (since it was a 12-month contract), and then continue to go down in steps until you are left with the highest engaged users, the people that get used to using the service and just stick with it.


Picture 1: Subscription lifetime over 60 months. Credit: Oliver Kern.


Add a power curve function and it’s possible to predict — in theory — and project LTV out many months in the future. Heck, you could even use this model to figure out how many users you might have in 10 years (!) — but I wouldn’t recommend it.


2: Using a power curve to predict future retention. Credit: Oliver Kern.

This is because the longer you predict the future, the greater the risk. It’s common sense really — too many things can happen. Tastes can change, technology can change, markets can change. More variables means more uncertainty.

Imagine you had a game that does something cool with AR and geolocation. The recent launch of Pokémon Go — and its incredible popularity — have come out of nowhere to change your business for the good or for the bad. The point is: predicting the future is a risky business so avoid trying to predict too far into the future.



Basic mathematics tells us that, where you have 3 points on a grid, you can easily create a curve. Of course, it’s always better — and importantly, more accurate — to have more points in order to see the true shape and trajectory of the curve.

Here’s a bonus for those of you who aren’t aces in calculating the formula that is a must in order to identify the points: There is a cool trick in Excel options that will show you the formula once you add the trend line (to be found in “Format Trendline”).


Picture 3: Displaying equation of powercurve in Excel. Credit: Oliver Kern

In my example I used classic conversions for key points in retention such as Day 1, Day 7, and so on. The result is a graph with some gaps.


Picture 4: Mapping out a retention curve from a handful of data points. Credit: Oliver Kern

But using the cool function in Excel reveals the formula for the curve, and allows me to map out user retention further and far more accurately.


Picture 5: predicting lifetime into the future by using the equation of the powercurve. Credit: Oliver Kern.

This allows you to calculate LTV — and extract the values that allow you to lay the groundwork for an advertising strategy for your app and — ultimately — detect and address a hiccup in the revenue flow before it becomes a real problem for your business.

As I show in my workshop presentation, using the retention curve to model LTV– making the assumptions below — allows me to make a projection into the future.


Using retention curve to model LTV


ARPDAU = $o.22

Retention: D1 – 40%, D7 – 20%, D-30 – 10%, D 60 – 7%


Of course, you can calculate the value for 90 days, 120 days or 180 days (multiply 180 by $0.22 and you end up with $3.70) but predicting LTV 180 days may be a high risk depending on your game. A games app, especially some casual games, can have a much shorter life span.

But that isn’t the only challenge.

In my workshops I discuss several challenges that you need to factor into how you calculate and evaluate LTV.

First, and foremost, ARPDAU is not “flat” and not all users are alike.

Picture 6: ARPDAU is a combination of spend of new and old users. Credit: Oliver Kern.

It therefore makes sense to not only look at the retention curve for a group of users in a certain period of time, but also to understand their spending behaviour over time.

Do they spend more? Do they stick longer with your app, or not? It’s important to seek answers. It’s obviously also important to keep track of the impact of app marketing and promotions you run during the period you are tracking as that will impact the data.

It’s clearly a challenge for your model and this is a way to factor this into the equation.

LTV = ARPDAU(cohort) x days played 

ARPDAU = Revenue of a day / daily active users of a cohort

Days played = sum (retained users / total users)

It’s outside the scope of my post to show this model in action. So, if you want to dig into the data and learn how to combine the two graphs (retention and APRDAU powercurve) into an effective model to calculate LTV — then you can download my spreadsheet here and check out my full presentation here.


There are multiple models to calculate LTV. The above-mentioned one is widely used but basic. It may therefore not reflect your specific business well enough.

Flat ARPDAU is the chief challenge to calculating LTV, which is why I have adjusted the model to address this.

But you should also be aware of the other challenges that you will face as you develop the LTV model that is right for your app business.

  • Statistically meaningful cohorts (making sure the sample site is “right” for what you want to measure/forecast)
  • Factoring app improvements (accounting for new features that can boost your marketing effectiveness and attract more users to your game)
  • Factoring organic lift (accounting for virality and other factors that can boost your numbers)
  • Factoring cross promotion (accounting for the positive knock-on effect of successfully using one of your apps to promote your other app(s)

The point is: you have to start somewhere. From there it’s your task to continually add data into the model and continuously validate/adjust your projection. With this crucial tool, you can calculate and accurately use LTV to avoid business failure and — ultimately — build a brand.