In the last post we discussed how to calculate the lifetime value (LTV) of a player, and our paid acquisition budget.

This post continues by exploring:

• How to calculate the cost of acquiring a player across several different channels.
• How the addressable market size effects the cost of acquiring players and the affect on bottom line profit. 

The spreadsheet used to generate the graphs is available here.

Quick recap. At the end of the last post we calculated a £0.70 average revenue per user (ARPU) for our hypothetical world and with a 33% churn we had a £2.10 lifetime value. With a viral growth factor of 0.8 we calculated that each player we acquire through marketing activity is really worth:

£2.10 × 1 / (1 - 0.8) = £10.50

At this point the model looks fairly simple, if we can acquire and service players for less £10.50 we're making profit! All we need to do is figure out how much it costs to acquire a player. 

Normalizing the Acquisition Channels
There are many channels through which to acquire players, including Google Adwords, advertising networks, affiliate deals, and so on. You'll want to try lots of different channels so you understand which are the most effective for your world.

Often the channels have different pricing structures, be it cost per click (CPC), cost per thousand (CPM), cost per action (CPA). So how do we know which channel is the best value?

Of all these numbers, all we really care about is how much each channel costs us to acquire a new player. The cost per click, or per impression is irrelevant, its the final number of registers players that matters.

We compare channels with a simple table that normalizes the CPC, CPA, CPM, into a single cost to acquire a player.

In this case I've modeled three channels, Google's CPC, a generic ad network, and a targeted campaign on a gaming website. These three channels are first normalized into a cost per click. Each click takes a new visitor into our funnel. From the funnel we try to convert them into a registered player.

For the sake of simplicity I've used a single 10% conversion metric for all channels. In a fully featured model we would expect to see different conversions for each channel, and we would split the single conversion metric into the individual paths, such as landing pages, registration forms, and guest accounts.

For our hypothetical world we see that it costs us around £0.45 to get a user into our funnel, but we have to spend £4.50 to convert them into a registered player. Remember, a registered player is not necessarily a paying player.

But this is great news; we can afford to spend £10.50, but we only have to spend £4.50. So every player we buy makes us £6 profit!

To put it another way, for every £100,000 we spend on advertising we bring in £233,000 in revenue, and £133,000 in profit.

Addressable Market Size
However, common sense tells us that at some point we wont be able buying players forever. Eventually we'll have acquired every player who might actually want to play in the world! We call this our addressable market size.

Globally, there are over 200M children aged 5-19 with internet access. Your world is unlikely to appeal to all those 200M children! Your addressable market is a fraction of those 200M children - only those who will be switched on to your theme and concept.

Its tempting to go after a broad target market. After all, the larger the addressable market the greater the profit. However, the things that young boys like to do in virtual worlds are quite different to the things teenage boys want to do, let alone teenage girls.

Instead, its important that your world delights and excites a smaller core group of players. By spreading that target market too wide you risk diluting the concept and struggling to engage or retain users.

Nic Mitham said it best in this post "We’re targeting girls and boys aged 3 - 14".

I'd recommend following Nic's advice and choose a primary market with an age spread no greater than 3-4 years. This is still a very large market.

A virtual world can have an ARPU in the pounds, where as a social network might be in the fractions of pence. Your world doesn't need to have 200M members like Facebook - this is good news, its extremely hard to be the next Facebook!

Market Saturation
As more players join your world through viral growth or paid acquisition common sense tells us that our conversion rates should start to fall; our viral invites or banner ads are going to players who have already evaluated the world.

We're going to model this saturation to see how it effects our LTV, acquisition costs, and profit.

Notice that when we normalized our acquisition channels I assumed that they all had a 10% conversion to registered players. Happily, I also assumed that our viral growth conversion was also 10%. Of course this isn't terribly realistic, but its going to keep things much simpler for our hypothetical world.

Continuing in the spirit of simplicity we'll build our model from these basic assumptions:

• When we launch we've saturated 0% of the market, so our 10% conversion rate is unaffected.
• After a few months we might have reached 30% of the market, so our 10% conversion is discounted by 30%. 
• After a couple of years we might have reached 70% of the market, so our 10% conversion is discounted by 70%, an so on.

We can model this with the equation:

Adjusted Conversion = Starting Conversion x (1 - Market Saturation %)

Where:

Market Saturation % = Total Unique Players / Addressable Market Size

Example 1: Exponential Viral Growth
So lets try this out without any paid acquisition, we'll model a simple viral application, the sort of thing we might see running in Facebook. To keep the numbers small and manageable we'll set our addressable market size to 1M players, an initial base of 5,000 players, and churn of 33%.

We'll model the kind of aggressive growth that comes from those 'invite all the friends in your inbox' type applications. Lets assume that every player invites 16 friends, and of those 16 friends 10% convert - a viral factor of 1.6.

We're going to use the viral growth process described in the last post and adjust the conversion rate as the market becomes saturated.

To quickly recap. A viral growth of 1.6 means that every player who comes into your world brings another 1.6 with them. We only apply this viral factor to the new players; we can safely assume that most players will invite their friends within the first month. Take a look at the google spreadsheet to see how this works.

We see an exponential growth up to month 11 which then begins to gradually slow before leveling at 700,000 users. The growth slows as the market becomes saturated, invites start to go out to the same players, and the conversion rate falls.

Notice that even with our initial aggressive viral growth we never reach the full 1M addressable market size.

Can we use paid acquisition to sustain the growth? Up to a point. As the market becomes saturated the conversion rate falls. In the last post we defined the equation for the acquisition budget as:

Acquisition Budget = LTV x (1 - Viral Factor)

By month 18 our viral factor has fallen from 1.6 in month 1 to 0.5. If we take the £2.10 hypothetical LTV from the last post, and plug them into the equation we get:

Acquisition Budget = £2.10 x (1 - 0.5) = £4.20

But, at falling conversion rate also increases our acquisition cost. At month 18 our conversion has fallen to only 3%. If we plug the 3% conversion into our normalized channels table then we find our acquisition cost is nearly £15. Thats three times what the player is worth!

When it becomes too expensive to buy new users then we need to look at improving our product, increasing the retention, and decreasing the churn.

A wildly successful product like Facebook might see a churn around 4% - that is 4% of the active users leave every month. Lets see what that looks like.

Notice how we still only reach 700,000 users, so the churn does not effect the total users. But, we've got over double the active users, and a much more gentle deceleration. When users stay on our site longer we're increasing our LTV. So while we might have nearly saturated our market, we've dramatically increased our profits.

Example 2: Viral Growth with Acquisition Support
Lets try a model closer to a typical virtual world. Again we'll keep the numbers small by limiting the market size to only 1M players, an initial base of 5,000, and a 40% churn. However, we'll set the viral growth to 0.8 and we'll buy 50,000 impressions to our homepage every month.

Using our Normalized Acquisition Channels table we find that 50,000 impressions to the homepage cost roughly £22,500 per month. Every month we spend the same amount of cash, but as our conversion rate falls we convert few and few of those impressions into registered players.

This time the graph shows the cumulative revenue and cumulative profit. We see that at by month 32 the cumulative profit is starting to decrease. This means the cost to a acquire a new player is more than the player is worth. This hypothetical model achieve a maximum of £225,000 profit.

Lets see what happens when we increase the viral growth by 50% versus decreasing the churn by 50%.

By increasing the viral growth we can make a maximum of £650,000 profit in month 22; we've generated 180% more profit. Not bad!

However, decreasing the churn by 50% causes the world to grow much slower; it continues to grow right off the graph, eventually making a £1M in little over 60 months.

This is a perfect candidate for acceleration through paid user acquisition. In the next graph I've doubled our marketing spend, we're now buying 100,000 impressions to our homepage every month.

The result is striking, we've still reached the £1M in profit, but have done so 20 months earlier!

Of course these numbers are for demonstration purposes, and there are lots of ways to improve the model, but they point towards an important learning. Improving your product and increasing retention ultimately delivers more profit than rapid viral growth.

Indeed, growing too quickly presents the risk that you never quite have time to figure out how to retain players. Once you've blown through your addressable market it becomes very hard to bring players back. This is the type of behavior we saw in the first example: exponential viral growth.

For this reason, viral growth less than 1 can actually be an asset. Growth is controlled by the paid user acquisition. Providing your channels are optimized you should be able to keep your acquisition cost below your LTV, so when you're ready to grow faster just increase your acquisition budget. (There is more to player acquisition than just buying ads, but we'll cover that in a future post).

Conclusions

• Normalize your acquisition channels; we only care about the cost of acquiring a new player, cost per click, per thousands, are irrelevant.
• Measure your conversion rate at each step of the funnel. What gets measured gets improved.
• Understand your addressable market size. Don't try to reach everyone, delight a smaller group, there are still plenty of players.
• Understand that market saturation will effect your conversion rates. As you reach more players your conversion rate for both viral and paid acquisition will decrease. 
• Its usually better to have slower growth and higher retention. Once you've blown through your market its very hard to bring players back. Improve your product and keep them coming back for more.
• Buy players to accelerate growth.

Scale
Remember, while these numbers a broad indication of what to expect they are only hypothetical. More importantly, I've limited the addressable market size to only 1M players, consequentially our hypothetical profits never exceed £1M. Even with a narrow 3-4 year age range you can expect an addressable market of 10M+ players and significantly more revenue.

Model Improvements
There are plenty of ways to improve the model, from increased granularity in the normalized acquisition table, to not assuming all channels have the same conversion rate. However, by simplifying the assumptions I hope I've been able to explain the core concepts and their consequences.

The basic google spreadsheet that uses the formulas used in this post and the last is available here.

Lastly, I'm far from perfect, so please let me know about any typos I've made along the way!

Thanks
Matt