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[FiM] States Point Cutoff Projection
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! 1. 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. 2. 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. Anyway, using the same fudging constant of 7, we guess the rank fraction needed this year will be (1607)/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) 
#2




Re: [FiM] States Point Cutoff Projection
I did more work on this today to do an actual regression to put a more rigorous result on this rather than "eyeballing it", and potentially make something that could be used more generically to predict cutoffs.
I collected all of the district data from the past two years, using the same methodology as I did just for FiM above, and they all seemed pretty close. A little more variation since I think smaller districts just will have more variation from the usual distribution. I used an "inverse logistic" fit, which is something I'm pretty sure I made up for the most part, but the graph kind of had a logistic look to it, but inverse. I tried power fits, exponential fits, but they didn't match it all that well. Specifically, I used the parameters defined in the inverse of the 4parameter logistic curve, described here: https://www.myassays.com/fourparame...egression.html. This gave a fairly strong fit, with coefficients of roughly a=1.0048,b=0.4216,c=51.413,d=0.0793 as in the link above. Using FiM's numbers of 160 qualifiers over 451 teams, and a guessed fudging or 7 for Chairman's autoqualifiers, this gives a fraction of slots approximately 0.339, and I get 62.54, which rounds to the 63 points I eyeballed, and got from my other method in the first post. The actually useful part of this method though, is not only do I now have an equation that could be used in the future, but we can give experimental bounds on the accuracy of this number. By also graphing the residues of my fit, we can see that in the range of about 0.15 to 0.55, which contains most districts and definitely FiM, the residues almost never exceed 5, and the outliers as far as I can tell are often very small districts like Indiana and North Carolina which will naturally have more variation from the usual distribution because of their small numbers. I attached my spreadsheet (which contains a lot of my 'scratch work' for lack of a better word) with the graph of all points as a paper: https://www.chiefdelphi.com/media/papers/3360 
#3




Re: [FiM] States Point Cutoff Projection
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