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NFL Sunday critical field goals  OT (math)
Posted By: Chuck Bower
Date: Wednesday, 25 January 2012, at 3:28 p.m.
In Response To: NFL Sunday critical field goals  OT (answers) (Jason Lee)
What are you cubically fitting, and why?
Plot success rate (made/attempted) as a function of distance for all FG attempts over a six year period. Fit r = a + b*D^3 (r is success rate, D is FG distance, a and b are constants determined by LSQ fitting). Note I WEIGHTED by variance where variance was determined by binomial method on a pointbypoint basis.
Why cubic? It looked much better than linear and quadratic.
Uncertainty for a given point was computed as dr = sqrt[da^2 + (db*D^3)^2] where da and db are the LSQ fit uncertainties on a and b.

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