In some of the other stats threads, folks have occasionally wondered how many dimensions there are underlying the game ratings. What do I mean? Think of politics: we all understand that there's a left-right dimension in politics that has something to do with economics, but there are also other dimensions. For example, people's views on abortion don't necessarily track with their views on economics. So there are at least two dimensions in politics that vary fairly freely with regard to each other: economics and abortion.
The following analysis is like that but for games. I have taken all of the games with more than 1500 ratings (except Carcassonne: The Expansion because it's an...expansion) and downloaded the ratings of all of the players who have rated all twenty of them, and there happen to be exactly twenty such players. I then put this data into Hierarchical Clustering Explorer 3.0, a freeware tool designed originally for identifying dimensions in genetic data (which I once used to dimensionalize human rights in my dissertation).
The way this works is that the program first identifies the most highly associated pair of games, then hierarchically identifies the most highly associated game with the initial cluster of two, and so on. If any pairs of games that have not yet joined the initial cluster are as similar or more similar than the growing cluster, then another cluster starts building alongside the first.
Where to set the line for distinguishing the number of clusters/dimensions in the data is more art than science,* so I decided to distinguish dimensions (starting from the top of the list, in which all the games are clustered together) to the point at which one game would be on its own. This left five dimensions, with a minimum similarity of 0.66 (using the simplest approach to measuring simultaneous similarity: Pearson correlation).
See
http://www.analytictech.com/networks/hiclus.htm for a fairly clear explanation of a more intuitive kind of hierarchical clustering, and
http://www.cs.umd.edu/hcil/hce/ for the freeware Hierarchical Clustering Explorer software.
The question here is what the games in each cluster have in common that would distinguish them from the other four clusters. I look forward to your speculation.
The dimensions are (highest rated game pictured -- that is, highest rated by BGG, not necessarily by the sample):
* There are significance tests for dimensionalizing data, but there are probably too few gamers here for any of these clusters to be statistically significantly distinct.
Posted Mon Apr 11, 2005 2:01 am
Mt. Vernon
Iowa
I also note that my taste in pictures has only one-dimension: zoomed-in-ness.
San Francisco
California
Basically I think it taps into my desire for the "ratings correlations" to come back. I still wish we could use the correlations with other users to predict what games I would like. This is sort of along the same lines.
Carpentersville
Illinois
1) This is the High-Low rating lifecycle category. These are games with great wow factor, but that show themselves to be lighter (or at least more random) with repeat playings.
2) This is the High-High rating lifecycle category. These are games with great wow factor that even with repeat playings remain difficult to solve (are deep)
3) This is the Low-High rating lifecycle category. These are the games that while fun initially take on a whole new level when serious time is invested in learning them. They also are the games most likely to impress by watching more experienced players play them.
4) This is the diffuse category. In this case the rating for scrabble depends more on the unrelated skill of depth of vocabulary. Deep game theory is not the issue.
5) This is the Low-Low rating lifecycle category. These are the games that are not popular with the folks that rate games. Its possible that this is a member of category 1, but since everyone left the high ratings stage so long ago that doesn't show in the data.
Unspecified
Unspecified
All geeklist, by me , have the right to exist here on BGG.
This said, am I the only one that finds Statistical geeklists incredibly boring?
Mt. Vernon
Iowa
And back to the boring: Ray, your comments seem pretty plausible. It's sometimes hard to remember when you're analyzing clusters that you're looking for consistently different voting patterns for games rather than consistently different voting patterns by gamers. If you were taking my research methods class right now, you'd be doing well.
Aldie has again proven what a wonderful web genius he is by adding an option to the stats tool to permit downloading all of the people who've rated any one game in a set of games. Note that he had to put some value in for missing games, and he picked zero. So depending on what program you're using, you should replace all of the zeroes with the missing value marker for your program or tell the program to ignore zeroes, or any calculations will be wildly off the mark. I already have the set for the top 50 rated games (except expansions), and it has 8,866 people in it. I'll see what it has to say later today or tomorrow.