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On the game entry page for each game, a list of recommendations is generated. These recommendations are based on user ratings and user collections. The strength of the recommendation is calculated into a score, and the games that get the highest score are listed on the game page.
How it works
Take a game, call it GameX. Say that game is owned by 1% of people. Take another game, GameY, which is owned by 300 people. You'd expect about 3 of them to also own GameX. If many more do own GameX, that suggests that people who like GameY enough to own it like GameX enough to own it more often than most. Now, if only 4 people own it, that's not such an anomaly. If 30 people own it, that's a dramatic factor of 10. In contrast, another game, GameZ, owned by 10 people, you'd expect no one (well, 0.1 people) to own GameY. But if a single person does, that's also a factor of 10, but it isn't as genuine of an anomaly. To correct for this, the algorithm adjusts for the relative obscurity of the game.
A similar process is applied to game ratings, and these two rates, along with the obscurity correction combine to produce the score.
The algorithm is far from perfect, but produces pretty good results. It does have some known behaviors which are worth noting.
Same Year/Publisher Effect
Because games that come out in the same year are likely to share owners and raters by virtue of simultaneous availability, the system tends to be biased towards games that came out at the same time. This is to be expected; If you like rail games, you're likely to buy more rail games. Similarly, if you started buying games in 2001, you're likely to buy more games in 2001 than 1991. Also one time raters (be they never returning BGG members or not) will create a snapshot of the games that are in vogue during their data entry time frame
The same issue causes games by the same publisher to be frequently recommended. Of course, publishers often publish similar games to others they've published, to "play to the base", so is even less of an issue.
For reasons not yet entirely obvious, the algorithm seems to have some "favorites", or games that get recommended a lot. You'll see Showmanager and Medici, for example, on a lot of lists.
New games typically only recommend other new games. This is because people who own new games have often placed a recent order, and have anomalously high ownership/ratership of other new games. Once the game becomes more widely available, this tends to go away.
Games which were only available at a particular very limited time or place have the same problem to some degree.
Very Popular Games
For games that are extremely popular and nearly universally well liked, such as Puerto Rico (yes, there are those that don't like it; I said "nearly"), the system can't give anything other than very weak recommendations. Saying "If you like Puerto Rico, you'll also like..." is (statistically) very hard to discern, because, well, the first part ("If you like Puerto Rico") includes nearly everyone, therefore there's nothing characteristically different about "everyone".
Poorly rated/unowned Games
As is probably obvious from the "how it works" section, if a game is owned by a very small sample of people, or liked by a very small sample of people, it is difficult to provide recommendations. There simply aren't enough other people who like it to come up with a fair generalization of what you will like "if you like Poorly Rated Game". This isn't really much of a problem, in that weak recommendations are still generated, and the effect is only severe under games that almost no one actually likes, so there are few who will say "I like this. What do you recommend?"
Previous Game Recommendation system
This algorithm replaced the previous recommendation system which was user-entered (pre-2005).
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