Oppressed by Pessimists / Fueled by Optimists >> Games with personalities? (v2)
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Oops. I published this earlier but my underlying number crunching had a mistake, which of course I've now fixed.

This is an exercise in statistical curiosity... some game ratings might be dominated by a bunch of pessimists dragging it down, or a bunch of optimists giving it a boost.

There are 25,000 game raters on BGG and 3,500 ranked games. An average ranked game has 260 raters, but that's mostly because a few games have thousands. Half of ranked games have fewer than 90 raters. What if those 90 (or fewer) happen to be characteristically low or high raters, either by chance or because the game attracts mostly negative b*stards to play it?

So I thought I'd check it out. Here's the waffle, followed by the list of most affected games...

First I assigned each user a User Optimism value. This is the average value of their own rating for each game above the game's overall BGG rating. ie how much higher/lower does this user characteristically rate games than everyone else? Raters vary quite a bit in measured "optimism". (Particularly people who only rate one or two games of course.) The standard deviation across all users is about 0.7 of a rating point. The average user optimism is about +0.25 of a rating point, which happens because the more games someone has rated the lower their ratings tend to be so a few pessimistic users can drag all the ratings down. Like this:

Rates # Users Avg Opt Std Dev
1->9 10651 1.03 1.30
->99 11400 0.27 0.67
->999 2876 -0.11 0.56
->9999 10 -0.23 0.51

Then for each ranked game I found the average Optimism for the game's raters. For this bit, I ignored the Optimism rating for any user who rated less than three games, since the granularity of integers would dwarf their optimism measures AND for one-game-raters in particular we'd like to let them have some opinion other than average. Instead I assume anyone with three or less rating has the same Optimism as average everyone else on each of their games.

Then I took the average Optimism and adjusted the game's overall rating, taking into account the Bayesian calculation used on BGG. There's a slight level of approximation because I can't say how many ratings are removed by Aldie's ShillSeeker Filter (tm, pat pend).

The result was a bit of an anticlimax. But you've read this far so you might as well have a look!
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1. Board Game: Carcassonne [Average Rating:7.42 Overall Rank:163] [Average Rating:7.42 Unranked]
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(2000) City Building, Medieval, Tile Placement
Raters: 8907
Avg rater optimism: 0.10 ratings points
Rank change: #43 => #84

Outside shuffles in the top ten games, here's the biggest relative rank demotion, not quite doubling its rank but staying in the top 100. And, incidentally, winding up closer to
#62 => #87 Carcassonne: The City
#91 => #117 Carcassonne: Hunters and Gatherers
#94 => #121 Carcassonne: The Castle
 
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2. Board Game: Catan [Average Rating:7.17 Overall Rank:355] [Average Rating:7.17 Unranked]
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(1995) Civilization, Trading, Modular Board
Raters: 9302
Avg rater optimism: 0.09 ratings points
Rank change: #24 => #46

Since it turns out that on average raters of fewer games are more optimistic, games with many many ratings are more likely to be boosted with a little optimism. So it's no surprise to see the most rated game on BGG here on this list. (Puerto Rico certainly has a little optimism behind it too, but it turns out not enough to drop it from #1 when it's "corrected".)
 
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3. Board Game: Memoir '44 [Average Rating:7.56 Overall Rank:126] [Average Rating:7.56 Unranked]
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(2004) Wargame, World War II, Modular Board, Campaign/Battle Card Driven, Co-operative Play, Hand Management, Dice Rolling
Raters: 3753
Avg rater optimism: 0.01 ratings points
Rank change: #19 => #30
 
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4. Board Game: Clue FX [Average Rating:6.21 Overall Rank:4830]
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(2003) Electronic, Bluffing, Deduction, Paper-and-Pencil
Raters: 145
Avg rater optimism: 0.41 ratings points
Rank change: #1131 => #1757
 
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5. Board Game: Ticket to Ride [Average Rating:7.44 Overall Rank:157] [Average Rating:7.44 Unranked]
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(2004) Transportation, Trains, Travel, Hand Management, Point to Point Movement
Raters: 5673
Avg rater optimism: 0.03 ratings points
Rank change: #33 => #51
 
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6. Board Game: Munchkin 4: The Need for Steed [Average Rating:6.56 Unranked] [Average Rating:6.56 Unranked]
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(2005) Card Game, Humor, Fantasy, Role Playing
Raters: 119
Avg rater optimism: 0.35 ratings points
Rank change: #632 => #968
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7. Board Game: Risk: The Lord of the Rings Trilogy Edition [Average Rating:6.50 Overall Rank:1939]
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(2003) Wargame, Miniatures, Fantasy, Adventure, Movies/TV/Radio theme, Novel-based, Area-Impulse, Dice Rolling
Raters: 673
Avg rater optimism: 0.20 ratings points
Rank change: #606 => #900
 
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8. Board Game: Munchkin Bites! [Average Rating:6.01 Overall Rank:3814] [Average Rating:6.01 Unranked]
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(2004) Card Game, Humor, Fantasy, Science Fiction, Horror, Trading, Role Playing, Dice Rolling, Variable Phase Order
Raters: 327
Avg rater optimism: 0.26 ratings points
Rank change: #875 => #1285
 
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9. Board Game: Warhammer Quest [Average Rating:7.42 Overall Rank:802]
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(1995) Fantasy, Adventure, Tile Placement, Co-operative Play, Role Playing
Raters: 419
Avg rater optimism: 0.13 ratings points
Rank change: #229 => #334
 
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10. Board Game: The Settlers of Canaan [Average Rating:6.76 Overall Rank:2349]
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(2002) Civilization, Ancient, Set Collection, Trading, Hand Management
Raters: 453
Avg rater optimism: 0.15 ratings points
Rank change: #262 => #379
 
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11. Board Game: RoboRally [Average Rating:7.09 Overall Rank:400]
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The next ten biggest relative movers:

Stratego: Star Wars
(2002) Fighting, Fantasy, Science Fiction, Secret Unit Deployment
Raters: 112
Avg rater optimism: 0.42 ratings points
Rank change: #1600 => #2313

Star Munchkin
(2002) Card Game, Humor, Science Fiction, Hand Management
Raters: 564
Avg rater optimism: 0.21 ratings points
Rank change: #851 => #1215

RoboRally
(1994) Racing, Science Fiction, Simultaneous Action Selection
Raters: 3646
Avg rater optimism: 0.00 ratings points
Rank change: #66 => #94

Dungeoneer: Den of the Wererats
(2004) Card Game, Dice, Fantasy, Exploration, Adventure, Action Point Allowance System, Tile Placement, Modular Board, Variable Player Powers, Hand Management, Dice Rolling
Raters: 174
Avg rater optimism: 0.23 ratings points
Rank change: #671 => #948

Risk: Godstorm
(2004) Dice, Fighting, Mythology, Area-Impulse
Raters: 437
Avg rater optimism: 0.18 ratings points
Rank change: #688 => #966

Carcassonne: The City
(2004) City Building, Medieval, Tile Placement
Raters: 1051
Avg rater optimism: -0.01 ratings points
Rank change: #62 => #87

Dragon Strike
(1993) Fighting, Fantasy, Exploration, Adventure, Variable Player Powers, Role Playing
Raters: 147
Avg rater optimism: 0.33 ratings points
Rank change: #1631 => #2282

Dungeons & Dragons: The Fantasy Adventure Board Game
(2002) Fighting, Miniatures, Fantasy, Exploration, Adventure, Horror, Modular Board, Variable Player Powers, Co-operative Play, Role Playing, Dice Rolling
Raters: 260
Avg rater optimism: 0.20 ratings points
Rank change: #698 => #975

Heroscape Master Set: Rise of the Valkyrie
(2004) Miniatures, Fantasy, Science Fiction, Adventure, Modular Board, Hex-and-Counter, Dice Rolling
Raters: 2204
Avg rater optimism: 0.08 ratings points
Rank change: #118 => #164

Risk: Star Wars – The Clone Wars Edition
(2005) Wargame, Movies/TV/Radio theme, Dice Rolling
Raters: 327
Avg rater optimism: 0.21 ratings points
Rank change: #815 => #1131


So when it comes down to it, the ratings are not being massively shaken up by any coincidences of optimism.
 
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12. Board Game: Twilight Struggle [Average Rating:8.31 Overall Rank:7]
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THE TOP TEN...
... are still all in the top ten! But, technically, along with the biggest rank drop the two biggest relative rank climbers of all games, Twilight Struggle and Die Macher, are here because the absolute rank numbers are so low.

Puerto Rico
(2002) Economic, City Building, Variable Phase Order
Raters: 8055
Avg rater optimism: 0.02 ratings points
Rank change: #1 => #1

Tigris & Euphrates
(1997) Civilization, Tile Placement
Raters: 4905
Avg rater optimism: -0.06 ratings points
Rank change: #2 => #2

Power Grid
(2004) Economic, Auction/Bidding
Raters: 4187
Avg rater optimism: -0.08 ratings points
Rank change: #3 => #3

Caylus
(2005) Economic, City Building, Medieval
Raters: 3524
Avg rater optimism: -0.08 ratings points
Rank change: #4 => #4

Twilight Struggle
(2005) Wargame, Political, Campaign/Battle Card Driven
Raters: 1020
Avg rater optimism: -0.20 ratings points
Rank change: #8 => #5

Die Macher
(1986) Economic, Political, Auction/Bidding
Raters: 1098
Avg rater optimism: -0.19 ratings points
Rank change: #9 => #6

El Grande
(1995) Political, Auction/Bidding, Area Movement
Raters: 3770
Avg rater optimism: -0.07 ratings points
Rank change: #6 => #7

Age of Steam
(2002) Transportation, Trains, Tile Placement, Pick-up and Deliver, Commodity Speculation
Raters: 1928
Avg rater optimism: -0.18 ratings points
Rank change: #10 => #8

The Princes of Florence
(2000) City Building, Renaissance, Auction/Bidding
Raters: 3439
Avg rater optimism: -0.09 ratings points
Rank change: #7 => #9

BattleLore
(2006)
Raters: 1387
Avg rater optimism: -0.01 ratings points
Rank change: #5 => #10
 
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13. Board Game: Friedrich [Average Rating:7.55 Overall Rank:601]
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BUT WHAT ABOUT THE OTHER END OF THE SPECTRUM?
Are there any games being dragged down by Marvin-esque raters seeing the bad side of everything?

Outside the top ten, here is the biggest relative improver after adjusting for pessimism.

(2004) Wargame, Hand Management
Raters: 481
Avg rater optimism: -0.26 ratings points
Rank change: #67 => #45
 
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14. Board Game: Struggle of Empires [Average Rating:7.49 Overall Rank:429]
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(2004) Wargame, Civilization, Political
Raters: 945
Avg rater optimism: -0.22 ratings points
Rank change: #34 => #23
 
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15. Board Game: Santiago [Average Rating:7.12 Overall Rank:632]
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(2003) Negotiation, Farming, Tile Placement, Auction/Bidding
Raters: 1146
Avg rater optimism: -0.19 ratings points
Rank change: #77 => #53
 
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16. Board Game: Bonaparte at Marengo [Average Rating:7.39 Overall Rank:1524]
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(2005) Wargame, Napoleonic, Action Point Allowance System, Secret Unit Deployment, Area Movement
Raters: 407
Avg rater optimism: -0.24 ratings points
Rank change: #59 => #42
 
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17. Board Game: The Scepter of Zavandor [Average Rating:6.99 Overall Rank:1073]
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(2004) Fantasy, Auction/Bidding, Variable Player Powers
Raters: 586
Avg rater optimism: -0.25 ratings points
Rank change: #120 => #86
 
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18. Board Game: Indonesia [Average Rating:7.85 Overall Rank:202]
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(2005) Transportation, Economic, Industry / Manufacturing
Raters: 290
Avg rater optimism: -0.28 ratings points
Rank change: #114 => #82
 
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19. Board Game: Tichu [Average Rating:7.58 Overall Rank:147]
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(1991) Card Game, Trick-taking, Partnerships
Raters: 1168
Avg rater optimism: -0.18 ratings points
Rank change: #36 => #26
 
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20. Board Game: Roads & Boats [Average Rating:7.75 Overall Rank:335]
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(1999) Transportation, Civilization, Economic, Tile Placement, Pick-up and Deliver, Modular Board
Raters: 467
Avg rater optimism: -0.22 ratings points
Rank change: #40 => #29
 
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21. Board Game: Hammer of the Scots [Average Rating:7.56 Overall Rank:383]
Joe Grundy
Australia
Sydney
NSW
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(2002) Wargame, Medieval, Secret Unit Deployment, Simultaneous Action Selection, Area-Impulse, Area Movement
Raters: 999
Avg rater optimism: -0.18 ratings points
Rank change: #26 => #19
 
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22. Board Game: Medici [Average Rating:7.14 Overall Rank:504]
Joe Grundy
Australia
Sydney
NSW
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(1995) Renaissance, Set Collection, Auction/Bidding
Raters: 1444
Avg rater optimism: -0.18 ratings points
Rank change: #97 => #71
 
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23. Board Game: Crokinole [Average Rating:7.83 Overall Rank:72]
Joe Grundy
Australia
Sydney
NSW
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The next ten biggest relative movers:

Crokinole
(2000) Action/Dexterity, Partnerships
Raters: 784
Avg rater optimism: -0.18 ratings points
Rank change: #38 => #28

Princes of the Renaissance
(2003) Economic, Negotiation, Medieval, Renaissance, Auction/Bidding, Variable Player Powers, Dice Rolling
Raters: 753
Avg rater optimism: -0.19 ratings points
Rank change: #76 => #56

Bridge
(1925) Card Game, Trick-taking, Auction/Bidding, Partnerships
Raters: 604
Avg rater optimism: -0.21 ratings points
Rank change: #103 => #76

Logistico
(2003) Transportation, Abstract Strategy, Economic, Trains, Nautical, Industry / Manufacturing, Action Point Allowance System, Pick-up and Deliver, Area Movement, Simulation
Raters: 242
Avg rater optimism: -0.23 ratings points
Rank change: #916 => #683

Imperial
(2006) Economic, Fighting, Area Movement
Raters: 473
Avg rater optimism: -0.20 ratings points
Rank change: #52 => #39

Volldampf
(2001) Trains, Pick-up and Deliver
Raters: 305
Avg rater optimism: -0.26 ratings points
Rank change: #287 => #216

Street Illegal
(2002) Card Game, Racing, Sports, Bluffing, Modular Board, Simultaneous Action Selection, Hand Management
Raters: 145
Avg rater optimism: -0.27 ratings points
Rank change: #1947 => #1469

Keythedral
(2002) City Building, Medieval, Auction/Bidding
Raters: 1023
Avg rater optimism: -0.17 ratings points
Rank change: #90 => #68

Fresh Fish
(1997) Transportation, Tile Placement
Raters: 475
Avg rater optimism: -0.26 ratings points
Rank change: #421 => #320

Europa 1945-2030
(1998) Negotiation, Political, Voting
Raters: 201
Avg rater optimism: -0.23 ratings points
Rank change: #1798 => #1373
 
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