Discussion regarding the changes to M in beer lists

Was hoping to engaged in coversation here regarding the recent changes to M, and perhaps get further clarification.

My understanding on how the M is figured, is that it is calculated by finding the average number of ratings for all beers in the dataset (would top 250 not include ever single beer that is listed?)

Using simpler numbers (say for beers in a single state), there are 10,000 total ratings of 200 beers, that would give a value for M at 50?

Is this correct? I was hoping to get a better understanding of what the "dataset" actually is.

 

Would there be consideration to exclude beers with very few ratings (say, anything less than 10?)
My history dealing with statistics leads me to think that when you have beer ranging from just a couple of ratings, up to beers with 5,000+ ratings, using the Mean as an average isn't the best solution, as the extremes of both ends prevent an accurate "average".

Would using the Median average give a higher number (perhaps more accurate average) for the M?

 

Just like with all "top" lists (such as the new york beers), there is a formula that calculates that score.

For Top New York Beers:

How was this list calculated?

Lists are generated using a Bayesian estimate that pulls data from millions of BeerAdvocate user ratings and normalizes scores based on the number of ratings for each beer.

The general statistical formula is:
weighted rank (WR) = (v ÷ (v+m)) × R + (m ÷ (v+m)) × C
R = average (mean) rating for the beer = (Rating)
v = number of ratings for the beer = (votes)
m = minimum ratings required to be considered (currently 79)
= (the average number of ratings across the dataset)
C = the mean rating across the dataset (currently 3.7)

 

Some of the variables in the formula change:
M= minimum ratings required (this changes with each "top" list, as recently explained by Todd here:
http://www.beeradvocate.com/communi...mum-ratings-required-to-be-considered.222437/
C=the mean rating across that particular "top" list. For example, the mean rating for New york is 3.7. For another list, it could be higher or lower, thus changing the final calculated score based on the formula.