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A recently discovered hole in Valve's API allowed observers to generate extremely precise and publicly accessible data for the total number of players for thousands of Steam games. While Valve has now closed this inadvertent data leak, Ars can still provide the data it revealed as a historical record of the aggregate popularity of a large portion of the Steam library.
The new data derivation method, as ably explained in a Medium post from The End Is Nigh developer Tyler Glaiel, centers on the percentage of players who have accomplished developer-defined Achievements associated with many games on the service. On the Steam web site, that data appears rounded to two decimal places. In the Steam API, however, the Achievement percentages were, until recently, provided to an extremely precise 16 decimal places.
This added precision means that many Achievement percentages can only be factored into specific whole numbers. (This is useful since each game's player count must be a whole number.) With multiple Achievements to check against, it's possible to find a common denominator that works for all the percentages with high reliability. This process allows for extremely accurate reverse engineering of the denominator representing the total player base for an Achievement percentage.

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