Friday, November 30, 2012

NFL Salaries (part 2) - Is Average really Average?



In my last blog entry, I discussed average NFL salaries.  I had initially hoped to talk about median salaries but, with my limited internet searching skills, was not able to find enough information about the history of median NFL salaries.

When analyzing data, why do we often focus on the median instead of the average (mean)?

The fact is that the average (mean) is not always so average (typical).  If we want to get a good picture of what a typical NFL player makes, we should analyze median salaries. 


Indianapolis Colts – 2012 Salaries

Rk
Player
Salary
1
Dwight Freeney
$19,035,000
2
Antoine Bethea
$6,225,000
3
Robert Mathis
$5,750,000
4
Andrew Luck
$4,015,000
5
Reggie Wayne
$3,500,000
6
Adam Vinatieri
$3,200,000
7
Antonio Johnson
$2,000,000
8
Samson Satele
$1,866,667
9
Anthony Castonzo
$1,818,431
10
Cory Redding
$1,716,667
11
Jerry Hughes
$1,691,250
12
Winston Justice
$1,500,000
13
Austin Collie
$1,417,388
14
Donald Brown
$1,385,000
15
Pat McAfee
$1,322,500
16
Drew Stanton
$1,225,000
17
Pat Angerer
$1,132,500
18
Tom Zbikowski
$1,033,333
19
Coby Fleener
$971,000
20
Vontae Davis
$957,500
21
Fili Moala
$873,000
22
Trai Essex
$825,000
23
Mewelde Moore
$825,000
24
Jerraud Powers
$784,625
25
Darius Butler
$770,000
26
Mike McGlynn
$700,000
27
Moise Fokou
$627,438
28
Drake Nevis
$622,278
29
Donnie Avery
$615,000
30
Justin King
$615,000
31
Delone Carter
$571,301
32
Dwayne Allen
$565,826
33
Ricardo Mathews
$551,628
34
Kavell Conner
$551,309
35
Josh Gordy
$540,000
36
Jeff Linkenbach
$540,000
37
Seth Olsen
$540,000
38
Matt Overton
$540,000
39
T.Y. Hilton
$521,750
40
Sergio Brown
$490,000
41
Cassius Vaughn
$490,000
42
Joe Lefeged
$467,667
43
Kris Adams
$465,000
44
Mario Addison
$465,000
45
Martin Tevaseu
$465,000
46
Joe Reitz
$455,000
47
Vick Ballard
$426,140
48
LaVon Brazill
$409,670
49
Chandler Harnish
$401,474
50
Mario Harvey
$390,000
51
Justin Hickman
$390,000
52
Dominique Jones
$390,000
53
Nathan Palmer
$390,000
54
Bradley Sowell
$390,000
55
Jerrell Freeman
$375,000
Source: Fox Sports*
As an example, let’s look at the salaries for the 2012 Indianapolis Colts.
This team is somewhat of an anomaly because they have the highest-paid player in the league (Dwight Freeney) and the lowest total team payroll in the league.  This makes the Colts an exaggerated microcosm of the NFL – a league in which most players earn a high salary, but a few players earn an insanely high salary.


So, how much money does the typical player on the Colts earn?


If we use average salary (rounded to the nearest dollar) the answer is $1,469,115 – but is this really typical?  43 players, representing78 percent of the team, make less than this amount.


The average salary is artificially inflated by the top-earning players on the list.  If we take the top three salaries (Freeney, Bathea, and Mathis) off of the list and recalculate the average, it becomes $957,526 (again, rounded to the nearest dollar).  Removing three players caused the average salary to decrease by about 35%.


It seems more reasonable to use median salary and state that the typical player on this team earns $622,278.  This amount is not artificially inflated by the top earners on the list.  If we remove the top three salaries, the median becomes $615,000.  This number is about 1% lower than the original median.


If the example of the Colts does not convince you that median is the better way to go, consider this example:


A group of one hundred people decide to look in their wallets to see how much money each person is carrying.  Ninety-nine of the people are carrying $1 and one person is carrying $1,000,000.  The average amount of money per person is $10,000.99 ($1,000,099 ÷ 100).  Does this mean that the typical person in this group is carrying over ten thousand dollars in his/her wallet?  Of course not.


In situations like these, median gives the best approximation of the typical case – the average is not really very average.

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