What does the graph show
The blue bars show heaps' actual passing efficiency for each game this season. Heaps' performance (in term of passing efficiency) is compared to a matched sample (the red bars). The sample is constructed using non-glory years BYU quarterbacks playing in their sophmore years: Walsh (1993), Feterik (1997), Beck (2004), and Hall (2007). The sample is constructed by computing the average passing effficiency for games played by those quarterbacks that had a similar computer model ranking as the team the BYU/Heaps played against this season (I could sharpen this part up a bit but it is hard to do at this point season ... the model rankings for 2011 are pretty noisy at this point). I also adjust efficiency for home field advantage (note for what every reason, after adjusting for opponent quality the matched sample of quarterbacks actually has higher efficiency on the road).
The computer model rankings are computed each year using a regression based margin of victory model (very similar to the Sagarin predictor model). I make two adjustments; first I throw out all games played by BYU in the model. This avoids a bias relative to whether BYU won or lost the game. Second, I only rank Division 1-A teams; this keeps the number of teams ranked relatively constant.
It is worth noting what this doesn't do. It doesn't control for the supporting cast of the team. If the matched sample have far superior supporting casts then inferences are likely to be suspect.
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