
Darren M
Canada Fort Vermilion AB

Looking at the BGG Top 100 games and the ranking system in general here on BGG... there is almost unanimous agreement that the games in the Top 100 likely aren't the "optimal" mix of games for a diverse and varied group of gamers.
Yes, they are the highest rated games on BGG but many agree that within the highest ranked BGG 100 games there are too many derivative games, too many heavy games, not enough "fun" games, not enough party games etc etc.
There is no ranking system that will suit every gamer and game group but looking at a gaming collection as a "portfolio" is a good start.
Here's some stats on the current BGG TOP 100:
Average user rating 7.7562 Average Bayesian rating 7.5175802 Average Standard Deviation 1.3674696 Average ratings 2107.35 Average Weight 2.955508
So if we were to use the BGG top 100 and the BGG ranking system in general as a template for a portfolio of games for a collection that's what the stats for that collection of games would look like.
One way to make a diversified portfolio is to first separate games into different "classes". One method we can use to do this on BGG is by weight. We know that comparing a game like Caylus with a game like Gulo Gulo for example is definitely apples vs oranges... yet that's what the current BGG rankings try to do.
It's much easier and useful to first divide up the database into equalized divisions by looking at the weight ratings for each game and coming up with the "best of breed" for each class.
One way to do this is simply rank all 3696 games by weight rating from highest to lowest and sum up all the times each game has been rated. Currently that total is 967488 ratings.
To make a balanced portfolio of games we can give equal priority to each weight class of games by using for example 5 weight divisions. This basically aligns with the Heavyweight, Medium Heavyweight, Mediumweight, Light Mediumweight, and Lightweight classes.
Each class will have 967488/5 ratings which is approximately 193498 ratings per class. So we take our list of 3596 games ranked by highest to lowest weight ratings and sum from the top down until we have 5 classes with a roughly equalized number of ratings in each.
The classes end up looking like this:
Heavyweights: 2.92235 weights 194411 ratings 691 games Medium Heavyweights: 2.35192.9203 weights 196652 ratings 588 games Mediumweights: 1.91162.3514 weights 191230 ratings 682 games Light Mediumweights: 1.50001.9091 weights 191746 ratings 618 games Lightweights: 1.0001.5000 weights 193449 ratings 1017 games
Now, with each weight class equalized... we pick out the "best" games from each class for the portfolio. We could use any number of variables and averages to pick out the best but I'll stick with the Bayesian average here on BGG and make one simple modification.
For each game take the Bayesian average and subtract its standard deviation * 1.28155 to get the Bayesian average at which 90% of gamers rate the game. I think this is a good adjustment and helps show which games are potentially the most widely acceptable to the most diverse groups of gamers/nongamers.
Here's what the Top 50 games are using this method per weight class:
Heavyweights: 1 Puerto Rico 2 Power Grid 3 Twilight Struggle 4 Tigris & Euphrates 5 El Grande 6 Princes of Florence, The 7 Shogun 8 Caylus 9 Goa 10 Railroad Tycoon 11 Taj Mahal 12 AmunRe 13 Die Macher 14 Wallenstein 15 Hammer of the Scots 16 Age of Steam 17 Struggle of Empires 18 War of the Ring 19 Louis XIV 20 Maharaja: Palace Building in India 21 Hannibal: Rome vs. Carthage 22 Imperial 23 Leonardo da Vinci 24 Traders of Genoa, The 25 La Città 26 Wilderness War 27 Bonaparte at Marengo 28 Ys 29 Combat Commander: Europe 30 Reef Encounter 31 Torres 32 Antike 33 Antiquity 34 Dune 35 Game of Thrones, A 36 Löwenherz 37 Paths of Glory 38 Princes of the Renaissance 39 Up Front 40 Blood Bowl: Living RuleBook 41 Twilight Imperium 3rd Edition 42 Liberté 43 Roads and Boats 44 Rommel in the Desert 45 In the Shadow of the Emperor 46 EastFront 47 Through the Ages: A Story of Civilization 48 Descent: Journeys in the Dark 49 Friedrich 50 Medina
Medium Heavyweights: 1 BattleLore 2 Samurai 3 Commands & Colors: Ancients 4 Ra 5 YINSH 6 Modern Art 7 Pillars of the Earth, The 8 Tikal 9 Keythedral 10 Yspahan 11 Settlers of Catan, The 12 Santiago 13 Vegas Showdown 14 DVONN 15 Acquire 16 Mykerinos 17 A Victory Lost 18 Domaine 19 Hacienda 20 Notre Dame 21 Union Pacific 22 San Marco 23 Attika 24 Web of Power 25 Hansa 26 ZÈRTZ 27 Primordial Soup 28 Vinci 29 Space Hulk 30 Fury of Dracula 31 St. Petersburg 32 Mexica 33 Arkadia 34 Oltremare  Merchants of Venice 35 Tichu 36 We the People 37 Elasund: The First City of Catan 38 Mü und Mehr 39 End of the Triumvirate, The 40 GIPF 41 Aladdin's Dragons 42 Capitol 43 Star Wars  The Queen's Gambit 44 Shadows over Camelot 45 RoboRally 46 Runebound Second Edition 47 Kreta 48 Pueblo 49 Tycoon 50 On the Underground
Mediumweights: 1 San Juan 2 Ticket to Ride  Märklin Edition 3 Ticket to Ride Europe 4 Ingenious 5 Memoir '44 6 Carcassonne  The City 7 Hollywood Blockbuster 8 Battle Line 9 Thurn and Taxis 10 Through the Desert 11 Blue Moon City 12 Jambo 13 Lord of the Rings  The Confrontation: Deluxe Edition 14 Nexus Ops 15 Carcassonne  The Castle 16 Hive 17 Mr. Jack 18 Lord of the Rings  The Confrontation 19 Razzia! 20 China 21 Citadels 22 Medici 23 Meuterer 24 Battle Cry 25 Atlantic Star 26 Alhambra 27 Edel, Stein & Reich 28 Taluva 29 Colossal Arena 30 Showmanager 31 Evo 32 Manila 33 Wings of War  Burning Drachens 34 Big City 35 Cleopatra and the Society of Architects 36 Blokus Trigon 37 Ta Yü 38 Expedition 39 O Zoo le Mio 40 HeroScape Master Set: Rise of the Valkyrie 41 Palazzo 42 Sticheln 43 Blue Moon 44 Roma 45 Elfenland 46 Masons 47 Marracash 48 Havoc: the Hundred Years War 49 Formula Dé 50 Afrika  2nd Edition
Light Mediumweights: 1 Ticket to Ride 2 Carcassonne 3 Blokus 4 Schotten Totten 5 Carcassonne  Hunters and Gatherers 6 Lost Cities 7 Ark of the Covenant, The 8 Travel Blokus 9 Winner's Circle 10 Rumis 11 Downfall of Pompeii, The 12 Bohnanza 13 High Society 14 Wyatt Earp 15 Mystery Rummy: Jack the Ripper 16 Daytona 500 17 Fearsome Floors 18 Wings of War  Watch Your Back! 19 Survive! 20 Odin's Ravens 21 Wings of War  Famous Aces 22 Um Reifenbreite 23 Kupferkessel Co. 24 Cartagena 25 Fairy Tale 26 Sieben Siegel, die 27 Basari 28 Mystery Rummy: Al Capone and the Chicago Underworld 29 Fjords 30 Boomtown 31 Kingdoms 32 Niagara 33 Flaschenteufel 34 DetroitCleveland Grand Prix 35 Bang! 36 Ubongo 37 Emerald 38 Fugger, die 39 Queen's Necklace 40 Polarity 41 Caesar and Cleopatra 42 Qwirkle 43 Get the Goods 44 StreetSoccer 45 Frank's Zoo 46 Money! 47 Ingenious: Travel Edition 48 REco 49 Around the World in 80 Days 50 Cribbage
Lightweights: 1 For Sale 2 Hey! That's My Fish! 3 Coloretto 4 No Thanks! 5 Crokinole 6 PitchCar 7 Gulo Gulo 8 Category 5 9 Wits & Wagers 10 Turn The Tide 11 Diamant 12 Time's Up! 13 Balloon Cup 14 Liar's Dice 15 Pitchcar Mini 16 Bausack 17 Loopin' Louie 18 Loco! 19 Ave Caesar 20 Can't Stop 21 Hamsterrolle 22 TumblinDice 23 Pick Picknic 24 Saboteur 25 Circus Flohcati 26 10 Days in the USA 27 Tier auf Tier 28 Poison 29 Ca$h'n Gun$ 30 Nacht der Magier 31 King's Breakfast 32 Mamma Mia! 33 Monstermaler 34 Viva Topo! 35 Schildkroetenrennen 36 Chicken Cha Cha Cha 37 Maus nach Haus 38 Light Speed 39 Villa Paletti 40 Loot 41 Cluzzle 42 Werewolf 43 Ausgebremst 44 Relationship Tightrope 45 10 Days in Africa 46 Beyond Balderdash 47 Bucket King, The 48 Tanz der Hornochsen 49 Knights of Charlemagne 50 Flowerpower
We then can take an equal amount of games from each class to make up a balanced portfolio of games for a collection. Adding games in sets of 5 to any collection (1 from each class) keeps the collection balanced in terms of it's diversity and weight.
A portfolio of the top 100 games (20 best from each class) would look like this: 1 Puerto Rico 2 BattleLore 3 San Juan 4 Ticket to Ride 5 For Sale 6 Power Grid 7 Samurai 8 Ticket to Ride  Märklin Edition 9 Carcassonne 10 Hey! That's My Fish! 11 Twilight Struggle 12 Commands & Colors: Ancients 13 Ticket to Ride Europe 14 Blokus 15 Coloretto 16 Tigris & Euphrates 17 Ra 18 Ingenious 19 Schotten Totten 20 No Thanks! 21 El Grande 22 YINSH 23 Memoir '44 24 Carcassonne  Hunters and Gatherers 25 Crokinole 26 Princes of Florence, The 27 Modern Art 28 Carcassonne  The City 29 Lost Cities 30 PitchCar 31 Shogun 32 Pillars of the Earth, The 33 Hollywood Blockbuster 34 Ark of the Covenant, The 35 Gulo Gulo 36 Caylus 37 Battle Line 38 Tikal 39 Travel Blokus 40 Category 5 41 Goa 42 Thurn and Taxis 43 Keythedral 44 Winner's Circle 45 Wits & Wagers 46 Railroad Tycoon 47 Through the Desert 48 Yspahan 49 Rumis 50 Turn The Tide 51 Taj Mahal 52 Blue Moon City 53 Settlers of Catan, The 54 Downfall of Pompeii, The 55 Diamant 56 AmunRe 57 Santiago 58 Jambo 59 Bohnanza 60 Time's Up! 61 Die Macher 62 Vegas Showdown 63 Lord of the Rings  The Confrontation: Deluxe Edition 64 High Society 65 Balloon Cup 66 Wallenstein 67 DVONN 68 Nexus Ops 69 Wyatt Earp 70 Liar's Dice 71 Hammer of the Scots 72 Acquire 73 Carcassonne  The Castle 74 Mystery Rummy: Jack the Ripper 75 Pitchcar Mini 76 Age of Steam 77 Mykerinos 78 Hive 79 Daytona 500 80 Bausack 81 Struggle of Empires 82 A Victory Lost 83 Mr. Jack 84 Fearsome Floors 85 Loopin' Louie 86 War of the Ring 87 Domaine 88 Lord of the Rings  The Confrontation 89 Wings of War  Watch Your Back! 90 Loco! 91 Louis XIV 92 Hacienda 93 Razzia! 94 Survive! 95 Ave Caesar 96 Maharaja: Palace Building in India 97 Notre Dame 98 China 99 Odin's Ravens 100 Can't Stop
Now, is this set of 100 games derived from this method "better" than what's currently in the BGG Top 100? Everything is of course subjective but looking at the statistics for this portfolio of games we find these numbers:
Average user rating 7.528972 Average Bayesian rating 7.3328078 Average Standard Deviation 1.2344927 Average ratings 2023.79 Average Weight 2.244344
Now look at the stats for all the games currently ranked on BGG (30+ratings) with at least 1 weight rating (to have an idea how heavy/light the games are). As noted above there are currently 3596 games with 30+ ratings and 1+ weight rating(s). We can calculate a weighted statistic to try and determine what the "optimal weight rating" may be for a basket of games in a collection.
If we take every game weight and multiply that by how many ratings that game has we come up with an idea of what the average weight of all ratings entered for the entire (ranked and weighted) population of games on BGG.
So for every game we do something like this:
Puerto Rico (weight*ratings) 3.3609*8593 = 28880.2 Tigris & Euphrates (weight*ratings) 3.5955*5224 = 18782.9
We then sum up the totals for all 3596 games and divide by the total ratings(967488). This average weighting comes out to 2.22938.
This result shows that of all games being rated on BGG... there is quite a wide discrepancy between the average weight of the games in the BGG Top 100 versus the average weight of the population of games in general.
If we do a comparison of the stats from the BGG Top 100 versus a balanced portfolio of 100 games we get the following:
BGG Top 100: Average user rating 7.7562 Average Bayesian rating 7.5175802 Average Standard Deviation 1.3674696 Average ratings 2107.35 Average Weight 2.955508
Balanced Portfolio: Average user rating 7.528972 Average Bayesian rating 7.3328078 Average Standard Deviation 1.2344927 Average ratings 2023.79 Average Weight 2.244344
Doing some comparisons between the two baskets of games:
Games in the BGG Top 100 are 3.0 % higher rated than in the balanced portfolio.
Games in the BGG Top 100 have a 2.5% higher Bayesian average than the balanced portfolio.
Games in the BGG Top 100 have a 10.8% higher standard deviation than the balanced portfolio which is an indicator of the variance of the ratings in each collection of games.
Games in the BGG Top 100 have 4.1% more ratings than in the balanced portfolio.
Games in the BGG Top 100 are 31.7% heavier than in the balanced portfolio of games.
This last statistic is probably the most interesting as it exposes probably the biggest bias in the BGG Top 100.
Medium/Heavyweight and Heavyweight games dominate the BGG Top 100. They are certainly the games that the community here gravitates towards and rates highly... but when you look at the entire database we find that the weighted average of all game weights for the (ranked and weighted) games on BGG is 2.22938.
So effectively... of all the games actually being played, bought and rated in tens of thousands of collections here on BGG... the average game weight is much more in line with a balanced portfolio approach rather than what we see as the top ranked games on BGG.
So this long winded approach is a way of saying "Buy a more balanced mixture of games and we won't hear so many complaints of repetitive and similar playing games in people's collections."
We may give up a little in terms of the "quality" of games in the balanced portfolio approach as we see an approximate 3% drop in the average ratings but the lower standard deviation combined with an average weight rating that's much lower (and more in line with the average of all games) in a balanced portfolio should make for a more diversified, flexible and adaptable collection of games to play with diverse groups of gamers.
The fact that we can see some statistical basis behind this though is relevant as we can directly see that what people play, rate and have in their collections is not necessarily the same as the BGG top ranked games.
Ideally I think this type of ranking system would be much more useful to new users on BGG as they would see a much wider spectrum of games ranked highly and not just an elitist and often derivative view of what boardgaming has to offer.

Eric Brosius
United States Needham Heights Massachusetts

Hmmm. I suspect most players are willing to tolerate heavier "weight" in their favorite games than in the ones they only play occasionally. After all, you spend more time playing your favorite games, and as you do so, the "weight" doesn't seem like such a barrier.
If we are trying to pick a Top 100 that provides almost every gamer with some games he or she really likes a lot, the current approach is probably better. On the other hand, your approach might be better if we are trying to pick a Top 100 such that almost every gamer likes all the games.

Joe Grundy
Australia Sydney NSW

I'd be happy to see a myriad of rating scales on BGG. Pick the scale that most suits your taste!
(Actually, we already have that. Go to Advanced Search, apply all the filters you want, and list the results sorted by Bayesian Average.)
Perhaps all that's needed is a disclaimer at the top of the "main" ratings list: "Note: Your favourite games are likely to be found here amongst the top games, but most of the top games are likely to not be your own personal favourites. That's why we also have game descriptions, reviews, and the Advanced Search."
It all comes down to what the purpose of a "Top 100" might be. Your analysis is true to your headline.
Some food for stats analytic thought...
I note that one effect of this approach is that new games arriving on the database at ratings far below the top 100 games could still substantially change the top 100 list. eg a group of games get their first weight ratings and are all lightweight. The weight boundaries shift a little, and there's a chaotic reaction in this Top 100.
nexttothemoon wrote: It's much easier and useful to first divide up the database into equalized divisions by looking at the weight ratings for each game and coming up with the "best of breed" for each class. This does still penalise games in each weight class that lie near the boundary that's furthest away from the "BGG Weight Sweet Spot". An alternative would be to regress the average ratings to the weight and adjust every game by that continuous function. But then you'd have to make assumptions about the shape of that function.
nexttothemoon wrote: For each game take the Bayesian average and subtract its standard deviation * 1.28155 to get the Bayesian average at which 90% of gamers rate the game. Generally you would either use a Bayesian drag or subtract multiples of the standard deviation, rather than doing both.
nexttothemoon wrote: of all the games actually being played, bought and rated in tens of thousands of collections here on BGG... the average game weight is much more in line with a balanced portfolio approach rather than what we see as the top ranked games on BGG. It's true that lighter games see more ratings. Perhaps that's because they see more players and playings. Whether that would mean they should get a leg up in the ratings is an interesting question... perhaps the many ratersoflightgames are still personally more interested in some specific heavier games that get less table instances merely because they take longer, and less new players merely because they're less "accessible". And perhaps a purpose of the top 100 is to provide a guide into these more engaging but less accessible games?
Or perhaps not. But it all comes down to purpose.

Darren M
Canada Fort Vermilion AB

Thanks for the comments everyone.
This indeed could be taken as a potential solution to a problem that may/may not exist (All depends on what the BGG top ranked games are supposed to show and how people want to use the database on BGG).
As a stats dork I like looking at different ways to look at portfolios and collections and ways to rank and rate items. This is commonly done in the markets with different asset classes as well and that same idea in general has applicability here as well... in producing diversified portfolios (in this case of boardgames) which are better suited to a wider audience. In the markets we want several asset classes in a portfolio to smooth the ups and downs in volatile times and to actually decrease the variance of our returns... the comparison in a boardgame collection is to have various games in different genres and weight classes to better suit diverse gaming groups, play lengths, gaming situations, player ages etc.
Quote: I note that one effect of this approach is that new games arriving on the database at ratings far below the top 100 games could still substantially change the top 100 list. eg a group of games get their first weight ratings and are all lightweight. The weight boundaries shift a little, and there's a chaotic reaction in this Top 100.
The weight classes are reasonably slow changing... weighted by the number of ratings each game has so a new game with 30 ratings with a weight of 5.00 for example would only have a current weight of 30/967488 in the grand scheme of things so the weight classes evolve very slowly and are quite stable. Remember that all games in the database are continually adding ratings(several thousand per day in total) so the effects of any new games entering the rankings are more than balanced by continual ratings added to games already ranked in the database.
Sometimes a game on the edge of one weight class will drop down/move up to another weight class as it's weight rating moves ever so slightly and that can make a difference for that game as some classes have a stronger set of highly rated games in it's class. So for example a game may be 20th best in it's weight class and with just a slight increase in it's weight rating can find itself 30th best in a higher weight class. The opposite also holds true. Such is the nature of a somewhat "quantum jump" system such as this where there are hard (but very slowly evolving) boundaries for each weight class.
Quote: Generally you would either use a Bayesian drag or subtract multiples of the standard deviation, rather than doing both.
I actually used the Bayesian average because it's what is used here on BGG and for simplicities sake it does still illustrate that any average or method can be used to come up with various classes for portfolio selection. I actually don't prefer the Bayesian average method (I use other methods of adjusting the averages for my own use) and think it is a rather poor method of adjusting the raw ratings BUT it's here, it's the standard since BGG began (I think) and it works well enough for Aldie and the Admins so I doubt we'll see it changed anytime soon.
I do believe using an average that adjusts to the 90% (1.282*SD) or 95% level(1.645*SD) is a useful stat as just viewing a raw average is basically like looking at a coin flip. A game rated at an average of 7.5 has a 50% of being liked more or less than that level... which doesn't really tell you much when you have 10 gamers in your group and the game has a standard deviation of 2.00 and you want the game to be liked by most in the group... not likely.
I would also say that since the Bayesian does nothing with standard deviations... it only adjusts for the "popularity" (number of ratings) of each game... so it isn't redundant to apply a standard deviation adjustment to the Bayesian average level.
A bit tangential and VERY ARCANE statistical jabber... but as a replacement for the Bayesian average I personally use the raw average for each game minus the standard error mutiplied by (Square root of each games # of ratings divided by the square root of the ratings of the most rated game on BGG (Settlers currently) minus 1.645*SD (Standard deviation levels also adjusted for standard errors by same method). I find this to be a much better indicator of games which have widespread appeal than the current Bayesian method used currently on BGG. This average takes into account the raw average rating adjusted by both standard deviation AND # of ratings. The "4th element" of this whole method being the weight rating classes which gives a total view of what comprises the "best games" on BGG.
To non stats freaks this is undoubtably a very goofy and a very complicated way of picking Gulo Gulo and Die Macher in the same gaming collection but it works for me (and is only a few cut and pastes and clicks in a spreadsheet) ... so there is more to this than just theory and mumbo jumbo... I actually put it into practice by making purchases using this method.
I do agree it all does come down to utility and what each person wants when they look though and filter out thousands of games in the database. I personally feel the way the top ranked games on BGG shake out is not a particularily diversified and useful list of games for many gamers... especially new gamers looking for a start to a gaming collection... many are indeed brilliant games but if the purpose is to showcase and highlight the best group of diversified games across a broad cross section of boardgaming... it is less than adequate (though again that's in the eye of the beholder).

Mark McEvoy
Canada Mountain Ontario

nexttothemoon wrote: For each game take the Bayesian average and subtract its standard deviation * 1.28155 to get the Bayesian average at which 90% of gamers rate the game. I think this is a good adjustment and helps show which games are potentially the most widely acceptable to the most diverse groups of gamers/nongamers.
Lightweights: 1 For Sale 2 Hey! That's My Fish! 3 Coloretto 4 No Thanks! 5 Crokinole
I'm not entirely sure what this arithmetic acrobatic is supposed to be accomplishing, but if it propels "No Thanks!" ahead of "Crokinole", I must say I'm feeling skeptical.

Darren M
Canada Fort Vermilion AB

Hey... 5th place among a group of hundreds of light games is pretty good. Crokinole has a higher standard deviation which is what kills it somewhat in terms of the 90th percentile stat. (It also has only about half the ratings of No Thanks! probably simply because it's a lot easier to throw a little card game into an online shopping cart and ship it across the planet than a Crokinole board.
Look at it this way.. Crokinole is 25th best overall under this method and 37th on BGG... so now which do you prefer.

Evan Stegman
United States Minneapolis MN

I like to see the game ratings broken down by weight. When I am deciding what games to suggest for a particular group of players (or to add to my collection so there's more available to suggest), that is the first thing I look at.
There was a similiar geeklist that I added to my favorites that covers the same topic:
http://www.boardgamegeek.com/geeklist/18172

hugo mocc
United Kingdom Leeds United Kingdom

Hi,
I find your approach very interesting, but to me it is based on a very weak premise: Game weight.
I understand that this is BGG ratings according to game weight but ultimately, game weight will be very subjective. For instance, I may find Hey! That's My Fish! a medium/light game where others will think it's just light.
Or where do you put Go in terms of weight?
I'd rather see a rating according to either Matthew Gray's gamers clusters (http://www.boardgamegeek.com/geeklist/18879) or BGG's own game categories (http://boardgamegeek.com/browser.php?itemtype=game&sortby=ca...) to make for a truly eclectic mix of games.

Eric Jome
United States Franklin Wisconsin

A valiant effort...
Unfortunately, weights are pretty much irrelevant in terms of categorizing games in my opinion. Weight is only "how hard is this to play"... this is largely meaningless. If Chess, Puerto Rico, and Advanced Civilization are heavyweights, does that say anything to you about which to play or that they are interchangeable?
When I choose different games, I want games that actually play differently. I don't need 10 auction games, I need 1 really good auction game or perhaps 2 pretty good auction games. I don't need 15 different awesome historical simulations set across the last 5000 years, I need one pretty good historical simulation of WWI.
How do we categorize games so that we get the top 10 by different genres? When we look at IMDb, we see that films and tv are categorized into areas and each film can be shown on a list. That's what we should be striving for here  different genres of games viewable by ranking right from the front page with a pop up description of what the genre is... and the genre's need to be very intuitive.

Ben .
United Kingdom Unspecified Surrey

I tend to agree that by focusing on game weight, you are only identifying one differentiating parameter. For me,
 mechanics  weight  play time  theme  number of players and, of course, rating
Are all factors in determining the relative quality of a game within a "portfolio".

alan beaumont
United Kingdom LONDON Unspecified

Quote: . . .if we were to use the BGG top 100 and the BGG ranking system in general as a template for a portfolio of games for a collection ** One way to make a diversified portfolio is to first separate games into different "classes". One method we can use to do this on BGG is by weight. 2 points: First you have to care about diversity. There are some games I would play to kill time and keep the table happy, but wouldn't dream of owning, so your answer is produced from a premise that I don't care about and is therefore, from my own 'objective' point of view, wrong. The heavy weight games are floating to the top of the list because the audience is disposed to enjoy the heavyweights. So it goes. Second and more critically I believe you have left out a crucial factor that distorts lists and that is novelty. I suspect new games tend to rate higher, especially in the light of youthful enthusiasm, given that there is a tendency to rush into print with a favourable opinion, rather than comment on one which left you cold. (Although a really bad experience is also really motivating!) If you could filter out this initial effect I would have a lot more confidence in the listings. As it is I think you should consider adding date of publication to directly indicate which games truly stand the test of time. Impressive effort, but lost the will to read very quickly.

David desJardins
United States Burlingame California

There's something pretty wrong with a weight system in which Puerto Rico, Power Grid, Euphrat & Tigris fall into the "heaviest" category.

Jared Heath
United States Dallas Texas

DaviddesJ wrote: There's something pretty wrong with a weight system in which Puerto Rico, Power Grid, Euphrat & Tigris fall into the "heaviest" category.
Yeah. Does that mean ASL holds the uber heaviest level? It does, afterall, have a rulebook that must be purchased independantly of the game itself

Eric Jome
United States Franklin Wisconsin

jaredh wrote: DaviddesJ wrote: There's something pretty wrong with a weight system in which Puerto Rico, Power Grid, Euphrat & Tigris fall into the "heaviest" category. Yeah. Does that mean ASL holds the uber heaviest level? It does, afterall, have a rulebook that must be purchased independantly of the game itself
ASL = Unlimited Class Weight Competition! The Mightiest of the Mighty!
Sunday. Sunday! SUNDAY! We're going to turn the floor of the BGG Colessium into a mud pit! Come see the fire breathing monster game, Advanced Squad Leader crush the competition...

Darren M
Canada Fort Vermilion AB

Valid points raised as of course everyone has different views. I personally think game weight is a useful stat as at a glance we can see what people feel is the depth/complexity of a game. The advantage is that almost every game has a weight rating and a consistent 15 scale is applied just like the rating system itself so at least there is a consistent means of comparison between one game and another (subjective as that comparison may be).
Using categories/mechanisms/themes as diversification classes is just as valid... or better yet combine weights and those categories as well and have the portfolio diversified even more thoroughly. The fact is though that the category/mechanism definition system on BGG is inconsistent and incomplete... many games are categorized "questionably" (or not at all) and I think that's an area where more input should be made by the community to better classify the mechanisms and categories which games belong to.
The point of the whole idea of a "portfolio" approach as I see it is to diversify across a broad range and find the "best of all genres" that are playable with the largest possible audience. If that's not what a particular person wants then this is of course meaningless... but this approach is based on having a theoretical/practical view of having a ranking system in place which is the most efficient at helping to choose games which can satisfy the maximum number of gamers/nongamers/newbies etc.

Darren M
Canada Fort Vermilion AB

Each of the five "weight divisions" has an equal number of ratings and ASL belongs in the heavyweights... If we wanted further granularity in classes we could make 10,20,30 etc weight divisions but taking equal amounts of games from a larger number of classes doesn't result in a necessarily "optimal portfolio" as the overall average rating of the games in the portfolio begins to drop too much... offsetting the advantages of increased diversification of the portfolio. There's basically a point of diminishing returns.

Darren M
Canada Fort Vermilion AB

Just to illustrate the "diminishing returns" point for comparison:
Here's what the portfolio stats look like when we diversify by 10 weight classes (Top 100 with 10 games per class):
Average user rating 7.5067 Average Bayesian rating 7.3212 Average Standard Deviation 1.23217 Average ratings 2094.32 Average Weight 2.2317
Compared to the previous 5 Weight classes (Top 100 with 20 games per class):
Average user rating 7.52897 Average Bayesian rating 7.3328 Average Standard Deviation 1.23449 Average ratings 2023.79 Average Weight 2.2443
When using 10 weight classes there is a further drop in average user rating and the average Bayesian rating of the portfolio while the average standard deviation drops only very slightly and the average weight moves slightly closer to the overall average "weighted" weight of all the games "ranked and weighted" on BGG (2.22938).

Alan Kaiser
United States Aurora Colorado

DaviddesJ wrote: There's something pretty wrong with a weight system in which Puerto Rico, Power Grid, Euphrat & Tigris fall into the "heaviest" category.
In addition to games like Dune and War of the Ring being lumped into the same weight category as Louis XIV and Torres. None of those I'd categorize as heavy and I'd certainly not put Dune and Louis XIV in the same group.
And Battlelore and C&C: Ancients fall into the medium heavyweight category!

David desJardins
United States Burlingame California

nexttothemoon wrote: The advantage is that almost every game has a weight rating and a consistent 15 scale is applied just like the rating system itself so at least there is a consistent means of comparison between one game and another (subjective as that comparison may be).
It's not really consistent, because more popular games have more ratings from more players, who tend to be players of lighter games. Puerto Rico receives a weight much higher than really makes sense in the BGG system (i.e., much higher than other games of similar length and rules complexity) just because it is so popular.

Michael Leuchtenburg
United States Cambridge Massachusetts

nexttothemoon wrote: Medium/Heavyweight and Heavyweight games dominate the BGG Top 100. They are certainly the games that the community here gravitates towards and rates highly... but when you look at the entire database we find that the weighted average of all game weights for the (ranked and weighted) games on BGG is 2.22938.
So effectively... of all the games actually being played, bought and rated in tens of thousands of collections here on BGG... the average game weight is much more in line with a balanced portfolio approach rather than what we see as the top ranked games on BGG.
You've measured here the games which exist on BGG, not those "being played, bought and rated". If you normalized by one of those stats (plays, users owning, ratings)  or better yet, all of them  that average weight would be a more convincing picture of the BGG populace's inclinations.

Michael Leuchtenburg
United States Cambridge Massachusetts

nexttothemoon wrote: A game rated at an average of 7.5 has a 50% of being liked more or less than that level
This is not correct. The average rating is a mean, not a median. Say we have a game rated by 10 users: 10, 10, 10, 10, 10, 10, 10, 10, 10, 1.
The average rating would be 9.1, but clearly there is not a 50% chance of liking it more than that level vs. a 50% chance of liking it less! An example for an average of 7.5 is: 9, 9, 9, 9, 9, 9, 3, 3
Again, the mean doesn't equal the median.
For this particular data, the ratings are a truncated bell curve. I'm not sure what that implies about the relationship of the mean to the median, but my intuition tells me that they won't be equal.
I also strongly agree with Joe that taking the Bayesian average and subtracting a multiple of the standard deviation is a strange thing to do. It seems meaningless. It certainly doesn't tell you what rating 90% of people would rate it higher than.

David desJardins
United States Burlingame California

dyfrgi wrote: For this particular data, the ratings are a truncated bell curve. I'm not sure what that implies about the relationship of the mean to the median, but my intuition tells me that they won't be equal.
It will be pretty close.

Virre Linwendil Annergård
Sweden Stockholm
Forza Bajen!
... and still sober

It's a nice effort, but gameweight as said is not good to base categorys on. This is due to the fact that some games change with who plays it. As I realised when I played Hey that's my fish! with adults, the game is verry different and much heavier then when you play it with children.
(I hope I am not repeating something, someone else already have said)

Darren M
Canada Fort Vermilion AB

Quote: You've measured here the games which exist on BGG, not those "being played, bought and rated". If you normalized by one of those stats (plays, users owning, ratings)  or better yet, all of them  that average weight would be a more convincing picture of the BGG populace's inclinations.
I'm not sure what this means... but I have to assume the games that exist on BGG are actually being played, bought and rated or else there's a whole lot more shilling and ghost ratings than we ever thought.
Yes.... I have normalized by the # of ratings... and the average weight for all those weighted by # of ratings is ~2.229.
Interesting suggestion to do the same weight calculation for measuring the "played" games... unfortunately that's tough to do for thousands of games with the way the database is set up on BGG. Someone with better access to the raw database than I have should be able to whip up that figure quite easily.
As a proxy though I've calculated the average weight for the 100 games with the most plays recorded on BGG.
The average weight for all those plays for the 100 most played games is ~2.244
I would expect the average normalized weight if we did a calculation based on all games owned for the ranked games would be fairly highly correlated with the average weight based on total ratings for the ranked games as they are highly correlated statistics.
True the mean is not the same as the median and I was speaking generally as there are always cases where you can show any distribution of numbers that show exceptions... but generally speaking we will have roughly half the ratings below the mean and roughly half above the mean.
Puerto Rico: 4987 above the mean 57.92% 3623 below the mean 42.08%
Tigris & Euphrates 2616 above the mean 50.02% 2614 below the mean 49.98%
Power Grid 2236 above the mean 48.57% 2368 below the mean 51.43%
As to the Bayesian average... well we are are talking degrees of meaninglessness here as the Bayesian is a basically "cracked" stat to start with... remember it uses fake average ratings and adds them to every game in order to manipulate ratings up and down so bad games look "better" and good games look "worse" until they get enough ratings to make the effective "Bayesian shill/shillbuster" ratings moot. You certainly could interpret the situation by saying every ranked game here has 100 shilled ratings in it (and you'd be exactly right) when you look at the Bayesian averages. It IS one method though of adjusting for different levels of "confidence" in the ratings and it's what is used here so that's that.
Taking away some multiples of standard deviations from the Bayesian average breaks no laws of statistics... no more so than using the same method on the raw user average. Using a standard deviation reduction simply tries to find a level where some % of gamers may agree that the game rates at or better from a parametric point of view. I think it's a useful stat when applied consistently across all games to get a comparison of which games have higher variance in their ratings.
2 games with average user ratings(or Bayesian averages for that matter) of 7.00 but with very different SD levels... one of 2.00 and the other with 1.00 will have much different variances in their appeal to a diverse group of gamers. That's all that simple adjustment to the Bayesian average tries to achieve.
Without this standard deviation deduction and just using the Bayesian average without adjustments we have the following portfolio as the Top 100 balanced portfolio (again 5 weight classes with the 20 best Bayesian average games per class):
1 Puerto Rico 2 BattleLore 3 Memoir '44 4 Ticket to Ride 5 Crokinole 6 Tigris & Euphrates 7 Ra 8 Ticket to Ride Europe 9 Carcassonne 10 For Sale 11 Power Grid 12 Commands & Colors: Ancients 13 San Juan 14 Lost Cities 15 Time's Up! 16 Caylus 17 YINSH 18 Ticket to Ride  Märklin Edition 19 Blokus 20 PitchCar 21 El Grande 22 Samurai 23 Lord of the Rings  The Confrontation 24 Carcassonne  Hunters and Gatherers 25 Hey! That's My Fish! 26 Twilight Struggle 27 Settlers of Catan, The 28 Lord of the Rings  The Confrontation: Deluxe Edition 29 Bohnanza 30 Werewolf 31 Princes of Florence, The 32 Modern Art 33 Battle Line 34 Schotten Totten 35 Coloretto 36 Die Macher 37 Tichu 38 Ingenious 39 Travel Blokus 40 Liar's Dice 41 Age of Steam 42 Acquire 43 Through the Desert 44 Winner's Circle 45 No Thanks! 46 Shogun 47 DVONN 48 Hollywood Blockbuster 49 Ark of the Covenant, The 50 Can't Stop 51 War of the Ring 52 Pillars of the Earth, The 53 Carcassonne  The City 54 Rumis 55 Wits & Wagers 56 Goa 57 Tikal 58 Thurn and Taxis 59 Downfall of Pompeii, The 60 Category 5 61 Paths of Glory 62 Union Pacific 63 Hive 64 High Society 65 Loopin' Louie 66 Hannibal: Rome vs. Carthage 67 RoboRally 68 Blue Moon City 69 Daytona 500 70 Ave Caesar 71 Wallenstein 72 Web of Power 73 Battle Cry 74 Wyatt Earp 75 Gulo Gulo 76 Railroad Tycoon 77 ZÈRTZ 78 Citadels 79 Mystery Rummy: Jack the Ripper 80 Diamant 81 Go 82 Santiago 83 Medici 84 Bang! 85 TumblinDice 86 Taj Mahal 87 Yspahan 88 Carcassonne  The Castle 89 Survive! 90 Bausack 91 Twilight Imperium 3rd Edition 92 Space Hulk 93 Jambo 94 Fairy Tale 95 Balloon Cup 96 Hammer of the Scots 97 Shadows over Camelot 98 HeroScape Master Set: Rise of the Valkyrie 99 Um Reifenbreite 100 Turn The Tide
The stats for this portfolio are as follows:
Average user rating 7.5531 Average Bayesian rating 7.3721 Average Standard Deviation 1.2984 Average ratings 2188.59 Average Weight 2.2541
Compared again to the current BGG Top 100:
Average user rating 7.7562 Average Bayesian rating 7.5175802 Average Standard Deviation 1.3674696 Average ratings 2107.35 Average Weight 2.955508
So we see even this balanced portfolio has a much lower average weight (more inline with the weights of all the rated games on BGG), and a lower average standard deviation. This is also a vast improvement over the current BGG Top 100 in my opinion. I prefer the standard deviation adjustments as well... but certainly the "portfolio" method of selection is robust enough to work with basically any average or calculations you throw at it... the key is "strengthening by diversification" and reducing redundancies and redundancies are what we have in abundance when you have a "classless" ranking method like we currently have on BGG.

David desJardins
United States Burlingame California

nexttothemoon wrote: As a proxy though I've calculated the average weight for the 100 games with the most plays recorded on BGG.
The average weight for all those plays for the 100 most played games is ~2.244
You need to weight them by game length, otherwise you are skewing strongly toward lighter games just because they are shorter and therefore get more individual playings.



