paper: Midwest Regional Strength of Schedule and RPI

[CJV648]

It is inspired by the RPI used to rank NCAA football/basketball teams that tries to correct for the differing schedules of teams. Their approach is to use a combination of own winning pct, opponents winning pct. and opponents' opponents' winning pct. FRC's alliance setup means that we should take into account the strength of alliance partners as well.

To implement this, the spreadsheet calculated a strength of match (SOM) for each team in each match. This is based on the won-loss record of alliance partners less the won loss record of alliance opponents normalized to zero for a nuetral strength match.

Technical considerations: The 1/6 in the cell arithmetic amounts to a dummy 50 pct winning term to replace the team's own record in calculating the SOM. Appropriate subtractions are made from each alliance's win-loss records to avoid bias based on the effect on the teams' records of the outcome of the match being studied.

A team's strength of schedule (SOS) is just their average SOM.

I got lazy with my RPI and just used a weighted sum of winning pct. and SOS