A new way to rank the top 40 games
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Floyd Sherrod recently created a geeklist entitled, "What am I missing?" http://www.boardgamegeek.com/geeklist/44251, in which he filtered the game rankings by the number of people owning a game, rather than by its rank in popularity, as it appears on the BGG "Games" homepage.
I mentioned in the comments that I was going to do some simple statistical analysis with the list, and here it is.
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1. Board Game: Number One [Average Rating:7.12 Unranked]
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A ranking of number one is so subjective!
Is one game better than another just because it has sold more copies? Or because more people have given their approval of it? Or because it is easy to learn and playable with any number of people? So many criteria.

BGG has gone with the popularity ranking, and I can see its merits. If 1000 people love one game but only a dozen love another, and you're an average person with similar tastes, you're more likely to be happier with the one that the 1000 people recommended.
 
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2. Board Game: Majority [Average Rating:4.75 Unranked]
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Floyd's list was interesting to me because he discovered that a ton of us own games that we obviously

a) have regretted buying, or
b) have a soft spot in our hearts for.

I did up a spreadsheet that had the top 25 games list ranked by the most owners, and next to it I put the top 25 games on the BGG Games list ranked by popularity.
I checked the rankings of the games on each list, added up some other values, and compared the two. Interesting.
Some games appear on both lists, most are unique to only one list or the other.

To me, this says a couple of things. A lot of us have pooh-poohed the highest ranked games by popularity (I am not a sheep!), or it could be that many of those good games are either out-of-print or hard to locate. Or very expensive, maybe. Or perhaps the theme doesn't appeal. Or maybe the number of players is a big issue. Or...
 
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3. Board Game: The Analyst Game [Average Rating:6.30 Unranked]
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What I did was to list the games in order of "Most owned" and add that rank to the game's "Most popular" rank.

For instance, The Settlers of Catan is #1 on the most owned, but only #39 in popularity (at this time). That gives it a score of 1 + 39 = 40
Then Carcassonne is 2 + 59 = 61. Puerto Rico is 3 + 2 = 5, and so on.

I then ranked them from low to high based on their combined score. As you can tell, five is a pretty low total and thus Puerto Rico end up ranked as #1 on that combined score list.

Next, I took the "most popular" list and did the same thing in reverse; I added the "most owned" ranking onto those numbers.
As expected, games on both lists will have the same number after both calculations (e.g., Puerto Rico is 2 + 3 = 5 on this list and 3 + 2 = 5 on the other list).

There are 17 games on each list of 25 that do not appear on the other one, however, so the two lists are really quite different.
As an example, Twilight Struggle (#4), is down at #58 on the most owned list, so its combined score is quite high (and thus ranked lower on the combined list): 4 + 58 = 62.

Oddly, games numbered 4 through 7 on the BGG most popular list are not amongst the most owned games by the BGG users. Likewise, games 12 through 21 inclusive also do not appear on the most owned list.

As it turns out there are 42 games, of the 50 that I looked at, that occupy just one of the lists.
That leaves only 8 games on both lists. Thus, we can conclude (?) that those eight games on both lists must be popular: both by personal user ranking and by the number of people who have bought the game and were likely pleased with their purchase.
 
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4. Board Game: Carcassonne: The Discovery [Average Rating:6.50 Overall Rank:1656]
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A couple of final notes about my analysis. On the "most owned" list, Carcassonne appears (at #2) along with two expansions (Inns & Cathedrals, at #12, and Traders & Builders, at #22).
These expansions do not have a popularity ranking. However; since the base Carcassonne game is ranked, I removed the two expansions from the stats and considered them to be part of the ranking for the base game.

Because of that the raw data looks a bit skewed, since I added Catan Card Game and Acquire into spots #24 and #25 on the first list to take the place of those Carcassone expansions.

Then, because I wanted a nice round number, I dropped what turned out to be the the two obvious last place games: Scrabble and Risk.
That leaves me with forty.
 
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5. Board Game: The Game of Top Ten Lists [Average Rating:6.75 Unranked]
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Because of their presence on most popular and most owned, I think that most people would be happy with the first eight games on this list, and probably safe with the top twenty.
Where ties occurred in my ranking system, I gave the benefit of the doubt to the game that appeared highest on the most popular list.
So here it is--the new top forty:

01 Puerto Rico........................ .................................21 Acquire
02 Power Grid...........................................................22 Goa
03 Agricola...............................................................23 Railways of the World
04 Tigris & Euphrates................................................24 Lost Cities
05 Caylus................................................................25 Bohnanza
06 El Grande............................................................26 RoboRally
07 Race for the Galaxy..............................................27 Battlestar Galactica: The Board Game
08 Catan............................................28 Shogun
09 Dominion.............................................................29 Hannibal: Rome vs. Carthage
10 Pandemic.............................................................30 Commands & Colors: Ancients
11 Carcassonne (plus some expansions, likely)............31 Die Macher
12 The Princes of Florence.........................................32 Through the Ages: A Story of Civilization
13 Twilight Struggle...................................................33 Age of Steam
14 Ticket to Ride.......................................................34 Le Havre
15 War of the Ring (First Edition)....................................................35 Alhambra
16 Arkham Horror.....................................................36 Chess
17 Ra......................... .............................................37 Catan Card Game
18 Memoir '44...........................................................38 Paths of Glory
19 Citadels............................. .................................39 BANG!
20 San Juan............................. ................................40 Brass: Lancashire
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6. Board Game: Big Breakfast Vital Statistics [Average Rating:0.00 Unranked]
 
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Here are the two spreadsheet outputs that I used to make my top 40 list:
 

 
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