the actual formula used...

The formula in the paper is more than a bit unnecessarily complex. The evidence points to the following explanation provided by Bert 690 in the slashdot discussion for this story:

OK, after a bit more thinking, you were indeed very close. It appears the actual formula is:

points(0 stars)=1
points(1 stars)=3
points(2 stars)=4
points(3 stars)=5
points(4 stars)=6
points(5 stars)=7

probability(X stars) = points(X stars) / 26

This yields the following probabilities, listed along side the observed values from the article along with 95% confidence intervals.

p(5 star)=.2692 [.270 +- .0038]
p(4 star)=.2308 [.230 +- .0036]
p(3 star)=.1923 [.189 +- .0033]
p(2 star)=.1538 [.154 +- .0031]
p(1 star)=.1154 [.118 +- .0027]
p(0 star)=.0385 [.039 +- .0016]

As you can see each computed probability falls within the 95% confidence interval, so there’s a good chance this is the correct forumla.

Boy do I have too much time on my hands today.

RE: the actual formula used... by Anonymous

This seems to be correct. This way of calculation the odds offers a way how to program the random play, too.

Just define an array and, for example, put a five rated song seven times into the array, an four rated song 6 times and so on. Then run a usal random function over the amount of entries and your done. Quite easy.

RE: the actual formula used... by Anonymous

Pretty interesting, but dear god, get a hobby =)