## Tuesday, January 7, 2014

### Manning, Roethlisberger, and Rivers -- comparing three QBs

Manning versus Roethlisberger and Rivers

Question:  Three very good quarterbacks, Eli Manning, Ben Roethlisberger, and Phillip Rivers were selected in the first round of the NFL draft in 2004.  Two of the quarterbacks, Manning and Roethisberger, have won two  Super Bowls each.

How do these quarterbacks compare based on aggregate and season QB rating statistics?

Do you believe this comparison of quarterbacks based on the NFL QB rating formula gives an accurate rating of the three quarterbacks?

Data and Methodology:  This paper compares final season QB ratings for the three quarterbacks over the 2004 to 2013 season.  The QB rating formula is a composite index that combines information from four statistics — completion percentage, yards per attempt, touchdowns, and interceptions.   I look at three statistics based on the complete season values of the three statistics — the mean, median and the standard deviation.   I also look at the QB rating system calculated over all passing attempts in a year.

Note the QB rating system is but one measure of QB performance.  It does not consider sacks or the ability to connect on third or fourth down.  Also, the season aggregate statistics discussed here will differ from statistics based on game-level outcomes.

Answer:  The season level QB rating outcomes (2004-2014) and the career to date QB rating observation for the three QBs are presented in the table below.

 Roethlisberger Manning Rivers 2013 92.0 69.4 105.8 2012 97.0 87.2 88.6 2011 89.1 95.1 88.7 2010 93.1 85.3 101.8 2009 100.5 93.1 102.3 2008 81.9 83.8 102.7 2007 101.8 77.9 83.0 2006 75.4 77.4 89.6 2005 99.4 73.5 50.4 2004 92.4 55.4 110.9 Mean 92.26 79.81 92.38 Median 92.75 80.85 95.7 STD 8.4 11.9 17.3 Career 92.6 81.2 96.0 P-Value for test that mean QB Rating for Manning is less than the Mean QB Rating for Rivers and Roethlisberger 0.0077 NA 0.0383

The QB rating outcomes on all four measures are considerably lower for Manning than for both Roethlisberger and Rivers.  This surpassed me a lot because I believe that Manning is the best of the three QBs especially when the game is on the line.  Best evidence of this opinion is Manning’s performance in two Super Bowls where he engineered fourth quarter comebacks against superior teams.

Roethlisberger has also won two Super Bowls and played well in both games.  However, I do not believe that Roethlisberger was as crucial to Pittsburgh’s victories as Manning was to New York’s victories.

Rivers has a slightly higher mean QB rating and career total rating than Roethlisberger.  Roethlisberger’s median QB rating is slightly higher than Roethlisberger.  These differences are  not statistically significant.

There was little difference between the mean and the median for the three players.  Hence the QB rating data is not skewed either left or right.  This makes sense because the four components of the QB rating system are bounded on both the top and the bottom.

Conclusions:  Manning was the first pick in the 2004 draft and the Giants traded up to make sure that they got the first pick.  The evidence presented here supports the applicability of the  Winner’s curse theory to the NFL draft.  Thaler and Massey are of the view that NFL teams overestimate their ability to pick good players and are therefore too willing to trade up to get a higher draft pick.

I suspect that despite the evidence presented here Manning is the best of the three quarterbacks. I don’t believe that either Roethlisberger or Rivers could have led the Giants to victory in the 2007 or 2011 Super Bowls against a superior and highly favored New England team.

For a discussion of issues related to the winner’s curse go see the reprint of my post on QB selection and the NFL draft.

Also perhaps see

How could Manning be better than two other QBs with superior NFL QB ratings?   Simply put, the QB rating system is imperfect.   One of the  imperfections with the QB rating system involves the omission of information on QB sacks.  Interested readers should see my post on this topic below.

I intend to do more posts teaching statistical testing with football examples.