The QB Rating System and Its Four Components

The graphs above illustrate how each of the four components of the QB Rating System actually relate to the QB Rating.  

The first component (shown in the first graph, in blue), relating to Completions per Attempt (or, Completion Rate), has a correlation coefficient of 0.956 with the QB Rating system.  I've actually taken the calculation of the completion rate in the QB Rating System itself (remember, it's scaled to be a number between 0 and 2.375).  This doesn't change the correlation since it is a linear transformation of the Completion Rate.  If Don Smith (the creator of the QB Rating System) had simply decided that a quarterback was going to be rated by his pass completion rate, and not tried to adjust for league averages and include other components, we wouldn't be having this debate.  Besides, the Completion Rate has an elegance about it in that it can never be greater than 100% (nor less than 0%).

The second component (shown in the second graph, in green), relating to Yards per Attempt, has a correlation coefficient of 0.492 with the QB Rating system.  Besides, the calculation itself has historically hovered around the intended average of 1.000.  This in and of itself is interesting.  Since Yards per Attempt = Yard per Completion * Completions per Attempt, and we have seen from the first illustration that Completions per Attempt has been steadily increasing over time, then Yards per Completion must be proportionally decreasing over time.  This should come as no surprise, as NFL offenses have adopted the West Coast Offense to varying degrees since its introduction to the game in the late seventies/early eighties by Bill Walsh of the San Francisco 49ers.  The West Coast Offense is known for its highly precise, short passes.

The third component (shown in the third graph, in dark blue), relating to Touchdown Rate, or, touchdowns per attempt, has a negative correlation with the QB Rating system over time.  The correlation is significant, at -0.521.  I found this to be remarkably surprising.  The calculation itself has remained tightly averaged around 0.800 since the merger of the AFL and the NFL in 1970.  

The last component (shown in the fourth graph, in purple), relating to Interception Rate, or interceptions per attempt, has an astounding 0.965 correlation coefficient with the QB Rating calculation (technically, the interception rate itself is negatively correlated with the QB Rating system, whereas the transformed calculation, with a minimum of 0 and a maximum of 2.375 has a positive calculation).  I certainly expected the first component, completions per attempt, to be highly positively correlated with the QB Rating system.  Although I expected this component to be also positively correlated, I did not expect that it would be more positively correlated with the QB Rating system.  I suppose we could all have saved ourselves a lot of headaches over the years if we simply designed the QB Rating System as 1 - Interceptions/Attempts.