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Subject: A "Portfolio" approach for redefining the BGG Top 100. rss

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Darren M
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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: 2.9223-5 weights 194411 ratings 691 games
Medium Heavyweights: 2.3519-2.9203 weights 196652 ratings 588 games
Mediumweights: 1.9116-2.3514 weights 191230 ratings 682 games
Light Mediumweights: 1.5000-1.9091 weights 191746 ratings 618 games
Lightweights: 1.000-1.5000 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 Amun-Re
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 Detroit-Cleveland 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 R-Eco
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 Tumblin-Dice
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 Amun-Re
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.
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Eric Brosius
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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.
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Joe Grundy
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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 raters-of-light-games 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.
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Darren M
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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).
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Mark McEvoy
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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.
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Darren M
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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.
 
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Evan Stegman
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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
 
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hugo mocc
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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.
 
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Eric Jome
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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.
 
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Ben .
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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".
 
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alan beaumont
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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.
 
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David desJardins
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There's something pretty wrong with a weight system in which Puerto Rico, Power Grid, Euphrat & Tigris fall into the "heaviest" category.
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Jared Heath
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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
 
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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...



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Darren M
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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 1-5 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/non-gamers/newbies etc.
 
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Darren M
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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.
 
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Darren M
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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).
 
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Alan Kaiser
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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!
 
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David desJardins
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nexttothemoon wrote:
The advantage is that almost every game has a weight rating and a consistent 1-5 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.
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Michael Leuchtenburg
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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.
 
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Michael Leuchtenburg
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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.
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David desJardins
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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.
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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)
 
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Darren M
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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 Tumblin-Dice
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.
 
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David desJardins
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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.
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