free apps

[CMU App Store Study]

I found your info on CMU's site and would like to ask you a question on your recently published paper.

 

I have been referencing your research "Inferring App Demand from Publicly Available Data" for a project I have been working on. I have been testing the model successfully (for Drp) on a small sample size of paid apps. I have tried to use the model for free apps but the outcome (for Drf) seems disproportionally large. For Free, I have used the formulas you have in the Free section of your paper, a theta set to below 1, Bg based on total free daily downloads and Drf=Bf*Rf^-Af.  I must be doing something wrong. Would you have any advice?

 

DR, New York

(1/7/2013)

[Rajiv Garg]

 Thanks for your comments on the paper. I am glad that you were able to verify the paid app demand using the model in the paper.

Before I begin, please note that all of the models are estimated for 2011 and scale parameter (b) will be change as the demand for apps changes. The shape parameter (a) may exhibit some change but in general should be consistent.

Coming to the free apps if you look at the model for iPhone:

Df = Bf*Rf^(-0.45)

You can see that the Bf needs estimation from the total daily downloads with the approach suggested in equation 9. Or as an alternative you can just use data from a few apps to estimate the Bf = Df/ Rf^(-0.45) and then use Bf to estimate demand for apps at other ranks. I am assuming you did all of this and still find the estimates for free apps off. There could be some reasons like:

1. Free app demand is much more dynamic and thus could impact the Bf on a daily basis. Are you finding the estimates to be off within a day or is it across multiple days?
2. The shape parameter for free apps could be impacted by entry to large number of apps with in-app purchase option. Since the percentage of in-apps in 2011 is very different from now, could you suggest the timeline you are using in the data?

RG

[Rajiv Garg]

I have an Af=0.50, but have been calculating Bf=Bg*10^(Beta0*Ag)/Theta, with Bg and Ag taken from the paid formula and Beta0 and Theta estimated. The numbers change completely if I take formula 9, replacing Ap with Af, Rp with Rf and Dp with Df. They are much closer to what I would expect. But doesn't this make Theta's effect no longer relevant?

 

DR, New York

(1/9/2013)

[Rajiv Garg]

Assuming you are estimating the values of beta0 and beta1 in a regression on your end and that you are considering only the free apps that have a presence in the grossing app list. Also assuming that you are taking the log of ranks in base-10 and thus are using the base-10 in the Bf formula.

 

Effect of theta is relevant but the value of theta could vary over time and I am sure it has changed during the last few years (with more emphasis on in-app purchase option). Theta provides an estimate of the revenue stream from in-app purchase and you may need to re-estimate theta from paid app list to correctly estimate the Bf using the formula Bf=Bg*exp(Beta0*Ag)/Theta.

 

You modified the equation 9 correctly; equation 9 is an easier way to estimate the scale parameters as the market size changes over time. Since you have data, you could use the equation 9 for various time periods and see how it has been evolving as a function of time. This will be very valuable in predicting/inferring the future of app store and its revenue potential.

 

RG

[CMU App Store Study]

I have 3 questions/comments after reading your email:

 

1. I have actually been using, as you used in the Bf formula, exp rather than base-10. I wrote it initially with base-10 to go with the formula in your paper.

 

2. Using equation 9, I do not understand how theta comes into play. It is not in equation 9, or in the calculation of Af, Rf or Df. Do I need to add it somehow to equation 9?

 

3. Just to double confirm, I am correct in assuming that for formula 9 to estimate Bf I am using for Df the total number of downloads for Free Apps that are ranked?

 

Thank you for your patience in answering and all your help.

 

DR, New York

(1/25/2013)

[Rajiv Garg]

2. theta is not part of equation 9. Estimation of theta is on page 19 where the model becomes non-linear. You need to rewrite eq 3&4 with theta and re-estimate the model parameters.

 

3. Yes, you are correct in modifying the eq 9 to recover the bf using the actual Df values.

 

RG

[Rajiv Garg]

As for 2, I believe that I understand: I would need to re-estimate the Beta0 and Beta1 (Beta2 being irrelevant since the price is 0). If so, I will look further into this and email you if I have follow up questions.

 

DR, NY

(2/6/2013)