Question: Often comparisons based on medians differ
from comparisons based on means. We
illustrate this difference with QB data from the 2014 season for the two Super
Bowl quarterbacks – Peyton Manning and Russell Wilson.
How do the median and mean QB statistics over the 2014
regular season differ for Peyton Manning and Russell Wilson?
What can we learn from the comparison of Manning and Wilson
QB statistics?
How do comparisons based on medians differ from comparison
based on means?
Data: We look at medians and means of 9 QB statistics
 attempts, completion percentage, yards per game, yards per attempt, TDs,
Interceptions, Sacks, Sack Yards, and overall QB rating.
The game means and game medians of these statistics are
presented below.
Median


Manning

Wilson

Difference Manning
Wilson


Attempts

41.5

26.0

15.5

Completion Percentage

66.4

66.0

0.5

Yards per Game

342.0

208.0

134.0

Yards Per Attempt

8.1

8.1

0.0

TDs

4.0

1.5

2.5

Interceptions

0.0

0.5

0.5

Sacks

1.0

2.0

1.0

Sack Yards

4.5

16.5

12.0

QB Rating

110.5

100.3

10.2

Mean


Manning

Wilson

Difference Manning
Wilson


Attempts

41.2

25.4

15.8

Completion Percentage

69.1

62.6

6.5

Yards per Game

342.3

209.8

132.5

Yards Per Attempt

8.4

8.3

0.1

TDs

3.4

1.6

1.8

Interceptions

0.6

0.6

0.1

Sacks

1.1

2.8

1.6

Sack Yards

7.5

17.0

9.5

QB Rating

113.7

100.0

13.6

My observations:
·
Manning threw the ball a lot more than Wilson.
·
Manning and Wilson have quite similar statistics
for median completion percentage, yards per attempt, and interceptions.
·
The larger yards per game, total yardage and TDs
for Manning was the result of the larger number of passing attempts rather than
difference in completion percentage or yards per attempt. Ditto for TDs.
·
Manning has the higher QB rating for the two
quarterbacks. The major reason for the
difference in the QB rating was TDs.
Seattle may be making their TDs on the ground.
·
The difference in the median game QB rating is
considerably smaller than the difference in the mean QB rating.
·
Manning has the lower sack percentage and the
lower sack yards. I have not included
data on yards rushing, which would presumably be higher for Wilson.
Concluding thoughts:
The difference in QBs
may not be that important in the Super Bowl.
Manning has the higher QB rating because of his TD total, which is in
part attributable to the fact that he passes a lot. This difference is not important if Seattle
can punch it in on the ground at the end of a drive.
The difference in the two quarterbacks based on median QB
rating is considerably smaller than the difference in mean QB ratings.
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