pianistamediano
Forum Master
My expectations is that at festivals the larger number probably means more number of good dancers. If a % of good dancers is say 10% then that percent of a larger number of attendees should be bigger. Downside is very crowded rondas. I use that as an opportunity to either find good dancers or dance with good ones. Going as a total solo stranger I have also observed that many people are either attending with friends or there are many who know each other from elsewhere (other festivals or cities over the years).
The problem with festivals (and any other event with a sufficient number or beyond a critical mass of attendees) is that, reasonably assuming normally distributed skill and experience, you get a wider variety of dancers. More good dancers? Sure, depending on which event you go to. But I find that the majority of followers at a big festival are not worth dancing with, mostly due to inadequate skill, feeling and compatibility issues. So I too observe and rely on my instincts developed from years of watching dancers on the pista to decide which few followers I want to dance with.
Consider this hypothetical scenario: Three events, one with 150 dancers, another with 350 dancers, and one more with, say, 1000 dancers (which I took from the BTE Facebook page). Suppose that each dancer is assigned a rating of 0 to 10, depending on how perfect a partner they'd be for you. Say you're looking at a 'group' (could be standing close together) of 5 opposite-role dancers. Smaller events tend to be better balanced in terms of roles, but for the sake of simplicity I'll assume that they're the same.
This is then sampling from a finite population without replacement; the corresponding variance of the mean of a sample is then (N - n) / (N - 1) * σ^2 / n, where σ is the population variance, which we assume to be the same for each event, n is the number of dancers in the 'group' we are looking at, and N is the total number of opposite-role dancers at an event, which is just half of the total number of all dancers.
We then get corresponding variances (with multiplier σ^2) 14/74 < 34/174 < 99/499, in ascending order of total number of dancers.
In general, solving the simple inequality of (N_1 - n) / (N_1 - 1) * σ^2 / n > (N_2 - n) / (N_2 - 1) * σ^2 / n, N_1 > N_2 > 1 gives us n > 1, which means that the variance in mean rating of any random sample of dancers at an event is higher with a higher number of participants.
So while the mean rating of the sample is simply expected to be the population mean, and therefore the average rating would be the same regardless of the total number of attendees, cabeceo-ing any one dancer in that sample group is expected to lead to more extreme results.
If we now modify our initial assumptions and now assume that the mean rating of dancers decreases with an increasing number of attendees, which I consider realistic if the smaller event's organisers are actually selective about who they allow to attend, then a random sample of dancers from the smaller event is expected to have a higher mean rating and a lower variability of rating compared to that from the larger event.
Of course, there's always the issue of whether you'll be invited, or if your invitation will be accepted...
