In the wake of the state meet, I ran the numbers on my algorithm to see how well it performed. The spreadsheets with the actual vs predicted places for boys, girls, and teams are linked below:
Here's the short version:
My predictions were a median 11 places off for boy's individual results. Out of 160 total places, that's an error of 6.875%. The girl's individual results were a median 12 places or 7.5% off. Median was used as a measure of center for the individual data because the long tail of the distribution (a couple of really bad predictions--sorry, Thomas Breuckman: I think your name may have been written "Tom" in some results lists) skewed the data.
For the team results, my predictions were a mean 1.25 places off for the girls and a mean 1.625 places off for the boys. That's an error of about 7.8% and 10.15% respectively. The boy's rankings were especially effected by Grand Rapids losing Sam Stertz.
All told, I'm very pleased with the algorithm's accuracy. Given all the random variation involved in ski racing, I truly think 7-10% is approaching the minimum error that can be expected. There are certainly ways to improve the algorithm, however.
Lessons learned: People who didn't race very much during the season, especially the Northern schools, were often grievously underranked. This was the largest source of error, leading to the biggest failures of the algorithm: Aidan Ripp and Garrett Beckrich outperformed their rankings by huge margins. (I was aware of this going into the State Meet). In the future, the northern sections will be weighted 4.5-5x (as compared to the average section, which is weighted 3x). This should help the star northerners gain their fair share of points before State. Next year, this year's data (with some regression to the mean applied) will be used to establish a starting database. This should lead to greater accuracy throughout the year, but results will be especially improved at the beginning of the season.