Weighted vs. Unweighted ratings?

 Goat Talk (@goattalkC) caught me again.  He left a cryptic reply to my class three boy's ratings of "Summit over Greenwood?"

Well, Goat Talk, you aren't the first person to point out a discrepancy in my ratings.  In fact, I bet that I get a dozen or so comments about some team that beat another team but Gramps has the losing team ahead of the winning team in Gramps Braggin' Rights ratings.

Yep.  It happens and sometimes Gramps is wrong and sometimes, well, statistics are just statistics.

I went back and looked at both school's basketball schedules and did an analysis of my ratings, both unweighted and weighted.

Both schools are private.  Summit Christian Academy over in Lee's Summit, MO, and Greenwood HS in Springfield MO.  Summit Christian Academy has 1200 students, K-12, and Greenwood Laboratory School, established in 1908 on the campus of Missouri State University, has a proud tradition of offering outstanding K-12 college preparatory education. Greenwood has 386 students. 

I posted the ratings based on unweighted ratings, ie. I did not put more emphasis on the head-to-head game they played.  The unweighted ratings for the two teams, put SCA slightly above Greenwood, most likely due to a couple of blow-out games.  Both teams played about an equal strength of schedule.  

If I had looked a little closer, Greenwood is undefeated and Summit Christian Academy is 6-2, but then I am rating 90 teams in class three and 550 teams in all six classes of boys (and 530 girls teams).  Sometimes I need guys like Goat Talk to point out my errors of omission.

That is where weighted ratings come into play.  Weighting means that I add the game results more than once into the rating average for each team.  Since SCA was slightly better than Greenwood unweighted, I added the SCA-Greenwood result (Greenwood by seven) several additional times into each team's rating formula until I get Greenwood rated above SCA.  That looks like this:

So, if you check the class three boys' ratings again, Goat Talk, you will see Greenwood above SCA because of their seven-point win.

Sometimes, even Goat Talk is right.