>If you want an unbiased ratings curve, how many 9s or 10s should there be?
We can use the Binomial distribution to calculate how many albums should be in each group 0-10. The Binomial is similar to the Normal distribution in shape, but describes discreet probabilities, which is suitable for integer album ratings. This makes the probability of getting a 10/10 equal to the probability of tossing 10 fair coins and getting heads (or tails) on all of them. The equation for binomial probability is:
P(X=k) = (n choose k) * p^k * (1 - p)^(n - k)
where k is the rating we're interested in,
n is the number of rating categories (here 11)
p is the bias (unbiased is 0.5, larger is skewed up, lower skewed down)
So for ratings 0-10 we have the following probabilities:
0: 0.0009765625, 1: 0.0097656250, 2: 0.0439453125, 3: 0.1171875000, 4: 0.2050781250, 5: 0.2460937500, 6: 0.2050781250, 7: 0.1171875000, 8: 0.0439453125, 9: 0.0097656250, 10: 0.0009765625
So if you have 1000 ratings, you should have 0-1 10/10, and 9-10 9/10s.
ok I'm done