I have been asked to do point projections for FiM again, seeing as no one else has done so. My previous prediction for last year here guessed 72 points, with an actual of 73.
I used two primary methods to get separate answers, which happened to agree!
By taking all the results up through Week 4, we can take the teams that have played at least once, and estimate the points of the teams that have played just once by adding their score from their first event again. We can proportion the number of slots by the number of teams this accounts for. However, we can also fudge the number of slots for Chairman’s Teams before this proportion. My (admittedly arbitrary) rule of thumb is between 1/4 and 1/3 of the DCA winners will not have qualified otherwise, so for this year’s 23 events, I fudged by 7. We then find the points of the accounted for slots, which happened to be ~145 slots, and we find the points are 63 points.
I mapped the distribution of Points as a function of Rank Ratio (that is, rank/number of teams) for 2015 and 2016. It gave a distribution that seemed fairly similar for both years, which loosely implies that the distribution stays relatively constant. http://i.imgur.com/67RCCaS.png
Anyway, using the same fudging constant of 7, we guess the rank fraction needed this year will be (160-7)/451 or about 0.339. Ideally one would do a regression of some type of curve, but just eyeballing it gives around 63 points as well.
Future Ideas: Besides applying a more rigorous regression to the distribution, it would be interesting to add in districts other than FiM in order to make a robust model to predict any district. Theoretically, one can already do that with this distribution, but I have a sneaking suspicion that the distribution changes based on # of teams enough so that the distribution for FiM with 400+ teams is different enough from a much smaller district with 50 teams.
Conclusion: More work could be done, but a hasty 63 points is my guess for now. (Which is nice in my opinion, since it backs up from the nasty inflation of cutoffs in recent years)