Understanding Convexity in LTV Modelling

As trends in mobile gaming move towards longer LTV games where players stick around for longer, it’s more important than ever to understand their behaviour over time. In this post, we're going to explore the issue of convexity in understanding LTV curves, and how to correctly factor this into your wider UA and growth planning models.

What is Convexity of an LTV Curve?

When looking at cohort behavior, players of f2p mobile games typically exhibit a path of greater spending in a shorter period of time, which then flattens out over time, and if you're lucky continues on an upward trajectory. The term convexity refers to the shape of the curve, and the fact that the journey to LTV is not a straight line. Here we have two example LTV curves, one more convex then the other representing different player behaviours, perhaps across different genres of game, but over the same time period.

In both examples, it takes 360 days to achieve 100% of the LTV of the game.

The first example profile achieves a total of 75% of LTV after just 90 days, indicating a more convex LTV curve, steep at first, then flattening off quickly.

Contrast this with a less convex example which returns 75% of the LTV after 180 days which has a much less convex curve as it takes longer to earn revenue from players.

The more convex LTV curve game is accruing revenue at a faster rate early on than the less convex curve.

As the LTV is realized, it is chalking up revenue faster, which will in turn be turned into cash more quickly when the platforms ultimately payout 15-90 days later (depending on their payout terms). This becomes an important consideration if this revenue is going to be reinvested into additional user acquisition, as it will impact the rate at which reinvestment into more UA can occur.

Another way to look at it is that if a business is investing heavily in a long LTV game with a less convex LTV curve, it will have to rely on a lot more external capital to fund its scale up plan, as the LTV takes longer to recover.

When looking to calculate financial returns over time, UA managers typically look at the profit achieved from the UA cycle (LTV minus CAC), and represent this firstly as an ROAS percentage, then divide it across the time period to get a monthly return on capital invested into the UA cycle. This assumes however the return is generated on a linear basis, which of course it is not.

It’s more accurate to look at the returns on a monthly incremental basis so that the benefit of the convexity can be better factored into the UA calculation, such as in the example below. This does make the modelling more complex, but if a studio is looking to spend significant sums of capital on UA for longer LTV games it's worthwhile taking the time to do this, as it can significantly impact the financial models and capital planning requirements.

When scaling the studio can further reduce its reliance on external capital by using a revolving credit facility to provide further leverage. By being able to borrow against platform receivables (AR) of IAP and ad revenues, as well as the projected residual value of existing cohorts, this can give the studio significant further firepower to reduce its reliance on external capital to achieve its scale-up plans. UA managers can take advantage of the more rapid revenue accrual of convex LTV curves, and turn it into cash using revolving credit facilities.

The rule of thumb is The greeter the convexity of your LTV curve, the more you can leverage your AR in order to reinvest faster into UA to scale faster.

As VC funding across the tech sector starts to tighten up, this trend will inevitably spill over into the mobile gaming sector, hence it’s very important for CFOs and UA leads to understand the impact of convexity of their LTV curve in their capital planning as they look to scale their games in a leaner funding environment.