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Valve's API unintentionally leaks Steam player numbers

Valve
Team Fortress 2 characters sitting around a poker table
Team Fortress 2

Resorting to some serious number crunching and incredibly clever employment of statistical analyses, developer of The End Is Nigh Tyler Glaiel has basically leaked Steam's player numbers for 13,000 most popular games on Valve's platform.

Glaiel got the general idea from an analysis by Barter.vg, who've been crunching the numbers on achievements so as to extrapolate player numbers from actual percentages.

If achievements have "50% of players achieving it, that would imply at least 2 players. 33% implies at least 3. If a game has both of those, it implies at least 6 players (3/6 for the 50%, 2/6 for the 33%)", Glaiel said.

Valve's mathematical rounding has made such analyses just about impossible but where there's will, there's way. Glaiel resorted to using Steam's API, which provides 16 digits of precision, brute forcing his way to find that Barter's results were surprisingly accurate. 

The analysis was still flawed once you tried to calculate results for PUBG and other bigger games. However, mathematics prevailed once again and Glaiel started comparing his computations to 16 decimal figures spat out by the Steam API.

Lo and behold, it turned out that the new method was actually much more accurate than the old ones, which were chiefly relied on by SteamSpy and similar sites. Moreover, it extrapolates data from actual snapshots, rather than collection of data over time, which is more convenient as well.

Glaiel contacted Sergey Galyonkin, who has made the analysis work on SteamSpy but Valve have since plugged this "hole", ensuring that Steam's API rounds up numbers as well. So Valve sort of killed SteamSpy. Again.

Thankfully, not all was lost, quite literally, since Glaiel and Galyonkin have treated us to a historically quite a unique snapshot of Steam's service, providing more accurate estimates on 13,000 games than anything we've had so far.

Team Fortress 2 leads the pack with more than 50 million players, followed by Counter Strike Global Offensive with 46 million, PUBG with 36 million and Unturned with 27 million.

ValveTeam Fortress 2 characters sitting around a poker tableCounter Strike: Global Offensive - text changes

If you're interested in the full list of these 13,000 you can find it on ArsTechnica, while Glaiel's blog about his mathematical acrobatics can be found here. The first 20 games on the list are as follows:

        Game                     Player Est.      Steam App ID

  • Team Fortress 2     50,191,347     440
  • CS GO                   46,305,966     730
  • PUBG                    36,604,134     578080
  • Unturned               27,381,399     304930
  • Left 4 Dead 2        23,143,723     550
  • PAYDAY 2             18,643,807     218620
  • Garry's Mod          18,576,379     4000
  • Warframe             16,332,217     230410
  • CS S                    15,001,876     240
  • Paladins               14,371,946     444090
  • Skyrim                 13,235,488     72850
  • Terraria                13,132,545     105600
  • Portal 2                13,062,700     620
  • Civilization V       12,701,498     8930
  • GTA V                 12,604,123     271590
  • Borderlands 2     11,218,936     49520
  • Robocraft           10,145,493     301520
  • Rocket League  10,110,342     252950
  • Portal                  9,971,481     400
  • War Thunder      9,536,732     236390