Sunday, May 21, 2006

A bound for game collection size

One common discussion that comes up among avid acquirers of boardgames
is "How many is too many?", or to put it another way "How many games
can I justify owning?" I decided to take a look at this
mathematically, by defining some assumptions and analyzing some data.

Let me state my assumptions. First, I assume the vast majority of a
game collection is to be played. I don't acquire games to "collect",
I acquire them to play them. Sure, some fraction of my games may be
kept for nostalgia or other purposes, but it's probably about 10%. We
can tack that on at the end. Second, I assume I don't actually care
about whose copy of a game I play. If a game is worth playing, it is
worth owning, even if I may end up occasionally or frequently playing
someone else's copy. Third, I assume I want to have the reasonable
expectation of playing the bulk of the games in my collection every
several years. The exact value of "several" affects the collection
maximum, but not by an overwhelming amount. The exact value of "the
bulk" has a more linear impact, but it's a good number to use to
characterize how willing one is to have games you may not play in the
name of having greater selection. Finally, I assume some fraction of
titles played I will have no interest in owning.

Next, I looked at the data. The number of different games played in a
particular interval fits an impressively reliable curve. Based on the
past 6.5 years of data, I can say with high confidence that in any
given month, I will play about 32 titles. In 6 months, 145 titles,
with obviously some overlap from month to month. In a year, 250
titles. Looking at a full range of time periods I was able to fit a
curve that fits very well. Now, for any period I can give a
reasonably confident estimate of how many different game titles I
would likely play in that time period.

Next, I had to pick out the various threshholds. How many years
should I allow to play the whole collection? Well, I think 5 years is
about reasonable, but will also calculate for 50 years (the remainder
of my life, roughly) to get an absolute upper bound. Next, what
fraction of games I play am I interested in owning? The number seems
to be about 50% of those I play. Finally, what fraction of games I
own do I want to play in that period? I'd say about 70%. Having 30%
provide a buffer of selection seems reasonable. Finally, I'll add the
10% nostalgia number on the end.

So, let's do the math: In 5 years, the curve says I will play about
740 distinct titles. In 50 years, I will play about 2000 distinct
titles. Cut those in half, to eliminate the 50% I don't need to own
and you get 370 and 1000. Add in the "selection buffer" for variety
and the numbers become 528 and 1428. Finally, add in some for
nostalgia and the occasional "collectible" and you get 580 and 1571.
The good news is, in either case, I can keep buying new games.

So, in an effort to help others justify their own game collections,
I've created a tool that does all the math for
Naturally, it's a bit of an approximation, since I can't do
the full curve fit and your curve may even be different form mine, but
it's reasonable to guess that it may not be tha far off. Enjoy.

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