Standing up for the 3 star rating

You didn't say that at all, but if that's what you later meant then that's fine.

I said exactly what I said. If you look at my original comment, you'll notice the future conditional "would be" was already there, I didn't edit it afterwards.

there is no median rating in a ½ step system, it falls between 2½ and 3, not 2 and 2½   To find the median you add the two extremes and divide by two, not subtract - ½+5 = 5½ / 2 = 2¾   In a normal distribution of ratings the average = the mean = the median = the mode   so, ½ + 1 + 1½ + 2 + 2½ + 3 + 3½ + 4 + 4½ + 5 = 27½; 27½/10 =2¾

2¾ = 2.75, which should be rounded to 2.5 had we a .5 rating system. A 2.75 rating would only be rounded up if the rating system did not admit .5 values. As 2.75 is more than 2.5, it would become 3, and that's actually what happens now.

Our rating guidelines say that 3-stars is "Good, but non-essential"

Exactly. Why are discussing about that ? It's written there and there's nothing we can do to change that. When I rate an album 3 stars on PA, I always bear in mind that 3 stars here mean "good", not "average" (note that I'm using "average" as a synonym for "mediocre", not "median". This is about English language, not mathematics).

If everything is good then good is average and average is good.   In a subjective system (which album rating is) to know whether "3" is good or average or mediocre what you need to know is the average rating of all the albums on this site.    M@x uses this value to compute the QWR value for chart position so by solving a simple simultaneous equation for the ratings of two albums it is possible to find this average.    I've done a quick back-calculation and the site average comes out at 4.165 , so a "3" is below that average rating.   For one of the albums I used to do this calculation (Vangough ~ Between the Madness):   Weighted average = 4.1111 QWR = 3.8914 Unweighted mean = 3.5833 Median = 3.5 Mode = 3   Which tells us that ratings on this site do not follow a normal (Poisson) distribution. But we can tell that from the little graph on the album page: Rating Number of votes Per centum   5 7 29.17% ***** 4 3 12.50% ** 3 11 45.83% ********* 2 3 12.50% ** 1 0 0.00%     All the "averages" say this is a 4-star album (3.89 and 3.58 would round up, 4.11 would round down), yet only 3 people out of 24 think that it is, more people (54%) think that it is 3-star or less album.   So... is Between the Madness a good album, an average album or a mediocre album?   Food for thought.

In think you're not getting the idea of "average" I exposed. We don't need to explain this in mathematical terms whatsoever, but, if you insist... Follow my thought: 1 - 2 - 3 - 4 - 5 are the rating options on PA. We have 5 numbers there, right ? Which one is in the middle ? 3. According to the dictionary, a median is "(Arithmetic, Statistics) the middle number in a given sequence of numbers, taken as the average of the two middle numbers when the sequence has an even number of numbers: 4 is the median of 1, 3, 4, 8, 9". Therefore, in this sequence of rating options, 3 is the median. The problem arrises because here, a 3-star rating does not mean the album is "average" or "mediocre", but "good, but not essential". I think there's nothing complicated about that...

I don't know Between the Madness, but, judging from the ratings, I conclude it is a very good or, at least, a good album to listen to, not an average one. Currently, we have 24 ratings for it. Nobody thinks it deserves 1 star; 13% rated 2 stars; 43% rated 3 stars; 13% rated 4 stars and 30% rated 5 stars. The percentage of people who rated it 4 and 5 stars (excellent or masterpiece) is exactly the same of those who rated it 3 stars (good). When you say "All the 'averages' say this is a 4-star album (3.89 and 3.58 would round up, 4.11 would round down), yet only 3 people out of 24 think that it is, more people (54%) think that it is 3-star or less album", you forget that, although only 3 people actually rated it 4 stars, 7 people rated it higher (5 stars) and 11 rated it lower (3 stars). It is basically the average (mathematically speaking) between the 3 stars ratings and the 5 stars ratings what makes the final rating result in 4. We would also have to consider the rating weight, which is different for pro-reviewers (admins, special collaborators et caterva), common members and non-members. If more experienced reviewers rated Between the Madness 4 or 5 stars, it doesn't matter if the majority of common members rated it 3 ou 2 stars because the ratings of the latter don't count as much. The "only 3 people out of 24" might be Prog Reviewers, just as much as the 7 out of 24 who rated it 5 stars...

But really, we don't even have to worry about these things. The system does this for us, so why bother with calculations ? All we have to do is judge wisely when reviewing an album. A .5 rating option would help us improve our "sense of justice", if you ask me... I'm in favour of it. 

claugroi wrote: I said exactly what I said. If you look at my original comment, you'll notice the future conditional "would be" was already there, I didn't edit it afterwards.

Erm... in the context you used it "would be" is not a future conditional since you used the subordinating conjunction "because"  linking to a dependant clause rather than a conditional conjunction such as "if" linking to a conditional clause.

So in your sentence: "The AVERAGE or MEDIOCRE rating would be 2.5 because our maximum is 5". The independent clause "the average... would be 2.5" is followed by the conjunction "because" which gives the dependent clause "our maximum is 5". "Would be" in this instance is past/present not future. 

You did not say "if we had a .5 rating." until a later and as a separate sentence.

But as I said, if that is what you later meant then that's fine.

claugroi wrote: 2¾ = 2.75, which should be rounded to 2.5 had we a .5 rating system. A 2.75 rating would only be rounded up if the rating system did not admit .5 values. As 2.75 is more than 2.5, it would become 3, and that's actually what happens now.

You are getting yourself confused. You made an error in your calculation and computed the median value as 2¼, I merely pointed out that it should have been 2¾. Rounding and ½-steps have nothing to do with it. 

claugroi wrote: Our rating guidelines say that 3-stars is "Good, but non-essential" Exactly. Why are discussing about that ? It's written there and there's nothing we can do to change that. When I rate an album 3 stars on PA, I always bear in mind that 3 stars here mean "good", not "average" (note that I'm using "average" as a synonym for "mediocre", not "median". This is about English language, not mathematics).

Hey, you started it with the "The AVERAGE or MEDIOCRE rating would be 2.5 " comment. I'm just playing with numbers because I like maths.

claugroi wrote: If everything is good then good is average and average is good. ::snip::  Food for thought. In think you're not getting the idea of "average" I exposed.

I'm sure I did, but please, continue...

claugroi wrote:  We don't need to explain this in mathematical terms whatsoever, but, if you insist... Follow my thought: 1 - 2 - 3 - 4 - 5 are the rating options on PA. We have 5 numbers there, right ? Which one is in the middle ? 3. According to the dictionary, a median is "(Arithmetic, Statistics) the middle number in a given sequence of numbers, taken as the average of the two middle numbers when the sequence has an even number of numbers: 4 is the median of 1, 3, 4, 8, 9". Therefore, in this sequence of rating options, 3 is the median. The problem arrises because here, a 3-star rating does not mean the album is "average" or "mediocre", but "good, but not essential". I think there's nothing complicated about that...

...and there is nothing complicated about that. Except for the psychological effect of having a middle number in any rating system that has a odd number of numbers. Even if we dispensed with numbers and used letters instead, the middle value will always be seen to represent the average value between excellent and abysmal or good and bad. No matter how often we stress that "3=good" we cannot over-come that psychological barrier that "middle=middling". Is anyone really confused by Starbucks' Tall, Grande and Venti? 

claugroi wrote: I don't know Between the Madness, but, judging from the ratings, I conclude it is a very good or, at least, a good album to listen to, not an average one. Currently, we have 24 ratings for it. Nobody thinks it deserves 1 star; 13% rated 2 stars; 43% rated 3 stars; 13% rated 4 stars and 30% rated 5 stars. The percentage of people who rated it 4 and 5 stars (excellent or masterpiece) is exactly the same of those who rated it 3 stars (good). When you say "All the 'averages' say this is a 4-star album (3.89 and 3.58 would round up, 4.11 would round down), yet only 3 people out of 24 think that it is, more people (54%) think that it is 3-star or less album", you forget that, although only 3 people actually rated it 4 stars, 7 people rated it higher (5 stars) and 11 rated it lower (3 stars). It is basically the average (mathematically speaking) between the 3 stars ratings and the 5 stars ratings what makes the final rating result in 4. We would also have to consider the rating weight, which is different for pro-reviewers (admins, special collaborators et caterva), common members and non-members. If more experienced reviewers rated Between the Madness 4 or 5 stars, it doesn't matter if the majority of common members rated it 3 ou 2 stars because the ratings of the latter don't count as much. The "only 3 people out of 24" might be Prog Reviewers, just as much as the 7 out of 24 who rated it 5 stars...

I presume you typed all that out to demonstrate to me that you understood what I wrote.

And btw. I forgot nothing.

And I purposely gave the unweighted average so we didn't have to consider the rating weight. Remember, the QWR (and subsequently the chart position) does not use the collaborator weighting.

claugroi wrote: But really, we don't even have to worry about these things. The system does this for us, so why bother with calculations ? All we have to do is judge wisely when reviewing an album. A .5 rating option would help us improve our "sense of justice", if you ask me... I'm in favour of it.