Exploring the relationship between Game Weight, Playing Time, and Ratings

I've always wondered about the relationship between game weight, playing time, and user ratings.  In a previous post, I found that game weight is highly predictive of rating.  But for me, I don't always gravitate towards the heaviest games.  Instead, I seem to prefer games that pack a good amount of depth into a small amount of complexity and playing time.  So I wanted to explore the relationship between rating and weight some more.  In particular, I hypothesized that what matters more than weight is actually weight-to-playing-time ratio.  That is, if a game can pack a lot of "weight" (i.e. depth, complexity) into a small amount of time, then it must be a good game right?  Well... let's find out.

Exploring these relationships was rather simple.  Again, I'm starting with the set of all non-expansion games published between 2004 and 2014 with at least 100 user ratings on BGG.  Then, I simply made scatter plots, which you can see below.


Based on the figure above, it seems there's almost a pure linear relationship between average rating and weight.  Moreover, the slope of the linear fit is pretty much the same regardless of playing time!  This was a bit of a surprise to me, as I thought that the slope would be higher for short games.

These are raw averages.  What about the Bayesian average, which is what BGG actually uses to compute board game rankings?  (The Bayesian rating pulls games with few user ratings towards 5.5)


We get pretty much the same story.  Although the relationship between rating and weight does not look at linear as before, we still see that the slopes of the best linear fits do not differ that much across playing-times.  If anything, it's the long games that have the steepest slope.  I suppose the way to think of this is that if you're going to spend over an hour playing a game, it'd better have at least some level of depth and complexity involved!

Anyway, based on this simple exploration of the data my hypothesis is rejected!  There doesn't appear to be any evidence that weight matters differently for short games vs. long games.  Of course, weight and playing time are themselves highly correlated.  Perhaps it would make more sense to split "weight" and "playing time" into three orthogonal components: rules complexity, strategic depth, and playing time.  But that's neither here nor there and we have to work with the data we have...


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