The most talked about EverNote numbers on freemium conversion shows, 3% paying customers and 97% free users (freeloaders and hopefully some Do-Gooders).

When a user signs up, if we use priors as an indication of posterior, the probability this user will upgrade to the paid version is 3% (will not upgrade is 97%).

Let us assume the Lifetime Value of a User is $250. Since all the infrastructure costs are sunk and the marginal cost to serve an additional user is $0, there is no cost in serving the free user.

So the expected Lifetime Value of this user is $7.5 (3% * $250). Since this a positive value, it would appear that there simply is no downside to sign up another user for free.

However, what about users who would have upgraded had it not been for the free version? This could be either due to the $0 reference price or the value they get from free is good enough (See: value step function). This is the opportunity cost.Let us assume the same conversion numbers and assume that an additional 3%  would have upgraded had it not been for the free version. The value you would have gained is a forgone opportunity and hence coded as red. This brings the expected Lifetime Value to just $0.225.   Model this for different forgone opportunities, does Free look attractive any more?

You could argue that not all of the 3% who pay now would not have upgraded had it not been for free.
You could argue that it isn’t another 3% that was forgone.

You are correct on both aspects. However,  if you do not know how many will pay for your product or if your prospects do not value the product enough to pay for the value they get, isn’t that a bigger problem?