Recommend
 
 Thumb up
 Hide
12 Posts

BoardGameGeek» Forums » Everything Else » OLD BGGBlogs (do not use)

Subject: Bayesian average? rss

Your Tags: Add tags
Popular Tags: [View All]
Romain Jacques
Canada
Gatineau
Québec
flag msg tools
Avatar
mbmbmbmbmb
The BGG rating is done with the Bayesian average. Could someone exlain what a bayesian average is?
 
 Thumb up
 tip
 Hide
  • [+] Dice rolls
Tim Benjamin
United States
Los Alamos
New Mexico
flag msg tools
badge
Avatar
mbmbmbmbmb
Pseudo-Bayesian
The current application of 'Bayesian statistics' is merely adding in of 30 'votes' with every value at approximately 5.9 to the real votes. With this you'll observe that the Bayesian Average is higher than the straight average when a game is rated below 5.9 and lowered for higher rated games. I think this is a useless mathematical manipulation.
 
 Thumb up
 tip
 Hide
  • [+] Dice rolls
David Boeren
United States
Marietta
Georgia
flag msg tools
Avatar
mbmbmbmbmb
Bayesian
Also, it has something to do with the number of ratings. If a game has 30 ratings which average to (let's say) 8, that's not as reliable as if it had 300 ratings which average to 8. So, the statistics play it on the safe side, and rate the 30-rating game lower, even though by a simple summed average they get the same exact rating.

Disclaimer: I am not an expert on statistics in general or in Bayesian statistics in particular
 
 Thumb up
 tip
 Hide
  • [+] Dice rolls
Tim Benjamin
United States
Los Alamos
New Mexico
flag msg tools
badge
Avatar
mbmbmbmbmb
Bayesian Calc
Bayesian Ave(BGG) =
((Real Votes x Straight Ave) + (30 x 5.9)) /(Real votes + 30).
 
 Thumb up
 tip
 Hide
  • [+] Dice rolls
Mark McEvoy
Canada
Mountain
Ontario
flag msg tools
badge
Avatar
mbmbmbmb
I think this is a useless mathematical manipulation.

I don't - do "Red Barricades - ASL Historical Module 1 ", "Whistling Death", "Downtown: Air War Over Hanoi, 1965-1972 " and "Code of Bushido - ASL Module 8 " truly represent the #'s 1-2-3-4 in board games? Because if the big list went by straight average (which allows a small sect of statistical aberration to cause a substantial impact on the list that comes far, far from reflecting the opinion of the majority), that would be BGG's top 4. Then, after Puerto Rico would be "Great Campaigns of the American Civil War ", "Yanks - ASL Module 3 " and "West of Alamein - ASL Module 5 "

Only the most deluded grognard believes that, if the entire votership of BGG were to play those seven titles, they would still hold their top 8 placings. Of course not - they're held high because, while the average of those who have played them is high, those who would be apt to vote them lower simply haven't played them (because they are not especially interested in their genre in general).

A non-bayesian average assumes that the mean now would remain the approximate mean given a larger sampling of the votership. I think that top 7 makes it quite clear that is not the case. Bayesian averaging isn't perfect - but with a big-list threashold as low as 30 votes, a mechnaism of that sort is a necessity for the big list to at all represent the entire votership of BGG.
 
 Thumb up
 tip
 Hide
  • [+] Dice rolls
Tim Benjamin
United States
Los Alamos
New Mexico
flag msg tools
badge
Avatar
mbmbmbmbmb
FORM
Mark,

If you look at several of my previous Geeklists you'll see that I don't advocate using just the straight average but, in fact, a modified ranking method (FORM) that uses the Average, Std Dev., and Number of votes. Give me your impressions.
 
 Thumb up
 tip
 Hide
  • [+] Dice rolls
Tim Benjamin
United States
Los Alamos
New Mexico
flag msg tools
badge
Avatar
mbmbmbmbmb
FORM Rankings
Mark,

Five of the seven examples you give are in the Bayesian TOP 100. I don't believe they should be ranked so high for just the reasons you've listed. The FORM rankings are much lower because they are such rarely played 'niche' games.

As of 20 Nov. 2004 I FORM rated 2255 games:

Puerto Rico: 1st
Downtown - Hanoi: 543rd
Whistling Death: 696th
Yanks: 741st
Great Campaigns of ACW: 788th
Code of Bushido: 932nd
West of Alamein: 940
Red Barricades: 999th
 
 Thumb up
 tip
 Hide
  • [+] Dice rolls
Luca Iennaco
Italy
flag msg tools
badge
Avatar
mbmb
Well...
I still remember that a user (sorry, I can't remember his name) made some interesting counter-arguments about FORM.
Every statistical system can be criticized in a way or another. The current BGG system is easy to understand (it simply adds those 30 "5.9" votes) and gives the desired result (no game can jump in the Top10 with only a few high ratings, usually likely for new games or "niche" games).

The best thing to do is not considering the ratings, but the COMMENTS (they're much more useful to understand if a game is going to satisfy you or not).

Have fun!
 
 Thumb up
 tip
 Hide
  • [+] Dice rolls
Mark McEvoy
Canada
Mountain
Ontario
flag msg tools
badge
Avatar
mbmbmbmb
I don't know enough about this FORM method, but the statement "I think this is a useless mathematical manipulation" led me to believe that you'd prefer *no* mathematical manipulation of the mean. Sorry.

Even if FORM is better, I wouldn't call pseudoBayesian 'useless'... 'sub-optimal' perhaps. But, IMHO, it is more useful for making the big list than a straight mean or median would be.
 
 Thumb up
 tip
 Hide
  • [+] Dice rolls
Romain Jacques
Canada
Gatineau
Québec
flag msg tools
Avatar
mbmbmbmbmb
Bayesian - FAQ
Thanks for your answers.

I think it should be added to the FAQ. The rating is an important feature of this site (at least for the newcomers) a short explanation should be usefull.

May I ask why 5.9 was chosen? Is it the average rating for a game in BGG?
 
 Thumb up
 tip
 Hide
  • [+] Dice rolls
Luca Iennaco
Italy
flag msg tools
badge
Avatar
mbmb
A choice
It's an arbitrary choice made by Aldie. It would work with 20 "4"s or 50 "6.5"s or... but Aldie selected 30 "5.9"s.
 
 Thumb up
 tip
 Hide
  • [+] Dice rolls
Mark McEvoy
Canada
Mountain
Ontario
flag msg tools
badge
Avatar
mbmbmbmb
Er, no... unless he's completely off his rocker, 5.9 was chosen beause 5.9 was the average of all game ratings here. Bayesian is intended to pull games of few ratings closer to the average - having the number be 4's or 6.5's or any number that doesn't represent the average, wouldn't accomplish that goal. If a 4 was used rather than 5.9, a game whose mean was 4.5 would actually be pulled _down_ by this pseudoBayesian calculation (when it should be pulled up).

Maybe the 30 was chosen somewhat arbitrarily, but it's no coincidencce that 30 is also the minimum number of ratings required before a game is considered for the big list (so when a game gets that one rating that puts it into the list, its Bayesian average is exactly halfway between its straight mean, and the systemwide average of 5.9).

But even if the 30 was tweaked, the 5.9 would be a constant.
 
 Thumb up
 tip
 Hide
  • [+] Dice rolls
Front Page | Welcome | Contact | Privacy Policy | Terms of Service | Advertise | Support BGG | Feeds RSS
Geekdo, BoardGameGeek, the Geekdo logo, and the BoardGameGeek logo are trademarks of BoardGameGeek, LLC.