Estimating App Sales From Rankings – Part 2

In an earlier post I showed a graph of Oz Weather’s daily sales levels versus its ranking in the Australian iTunes app store, and then extrapolated the findings to get a very rough estimate of global sales versus iTunes US app store rankings.

Australian Sales vs Rankings

As Oz Weather has now been selling for more than 3 months, and has had an extended period ranked #1 in the Australian store, so I am now in a position to make an enhanced analysis. But note that there were some anomalous sales figures over the Christmas period (24th Dec to 31st Dec) due to three unusual circumstances:-

the surge in overall Christmas sales
the fact that I discounted the app over that period
thirdly due to a major loss of sales when the app store broke down temporarily

The graph below shows the entire history of sales, minus that week’s worth of “anomalous” sales data.

Sales Rankings Australia

I tried fitting logarithmic, exponential and power curves to the data – the power curve gave by far the best fit, with the approximate equation

Daily Sales = 425 * Ranking ^ -0.5

This equation can be used to give a reasonable estimate of sales of paid apps in the Australian iTunes app store using the overall ranking (not the ranking in any individual category such as entertainment, lifestyle, weather etc). However note that there is a wide range of variation about this mean trend line on a day to day basis. For example while Oz Weather was ranked #1 sales varied between about 260 and 620, and at rank #2 from 190 to 420.

World Sales versus Rankings

We now have a good idea of the apponomics of the Australian store, but what about world-wide sales? To begin to answer this, I have gathered as much data as I could find giving US store app ranking versus daily sales. The main sources I found were

Using data from these sources – some real sales figures and others inferred and estimated, I constructed the following graph.

Sales Ranking World

The main assumption here is that US rankings reflect Worldwide rankings reasonably well, which although not necessarily true for specific apps, is probably true on average. Also note that, to clarify the picture, I did exclude some of the higher figures given for #1 ranking – up to 50,000 or more supposedly. I suspect that sales at the #1 spot will be much more variable than lower ranked slots, so it seemed sensible to include only the lowest figures that resulted in a #1 ranking, for this purpose.

As before I tried fitting logarithmic, exponential and power curves to the data – and again the power curve gave by far the best fit, with the approximate equation

Daily Sales = 15000 * Ranking ^ -0.75

This equation can probably be used to give a reasonable estimate of sales of paid apps in the US iTunes app store using the overall ranking. It roughly confirms my earlier guess that world sales were typically 30 times more than Australian sales. In fact, for the given equations, the World/Australia sales ratio varies from 35 (#1 ranking) to 13 (#50 ranking).

Given that there is no reason to suspect any major difference in sales dynamics, one might have expected the ratio to remain similar at all rankings (ie. the power factor to be the same in each equation). However, note that the Australian curve is based on data only going down to #17 ranking, whereas the US curve has data down to #100 ranking. I therefore suspect that the US curve power factor is more realistic for the long tail, and that the drop-off in sales levels for Australia well below the #20 ranking might be somewhat less than that predicted by the given equation.

So there you have it – the best that I can do with the available data. As more data becomes available I will add it in to the mix, to see how much further this can be refined.