8/15/11

NFL by the Numbers

• One of the

biggest changes

to the new

Collective

Bargaining

Agreement is

with the minimum

salary structure.

This table

summarizes the

salary scale.

NFL by the Numbers

• The first column

counts the

number of

Completed

Seasons. A value

of zero is for a

rookie.

NFL by the Numbers

• The other

columns show

the minimum

salary (in

thousands of

dollars) for years

2011 to 2014.

NFL by the Numbers

• Let’s look at the

graph of the

salary data for

Completed

Seasons versus

the minimum

salary for 2011.

NFL by the Numbers

• This is an

example of a

discrete function,

where the values

along x and y

change in whole

number amounts.

NFL by the Numbers

• This is also an

example of a

step function,

which is much

easier to see by

connecting the

points.

NFL by the Numbers

• Let’s follow the

potential salary for

a player over the

first four years.

The player starts

in 2011 as a

rookie. The

highlighted

salaries are what

he earns in the

first four years.

NFL by the Numbers

• Here is a graph of

the salary data.

Note that it is a

linear function.

NFL by the Numbers

• This is the

equation for the

function.

NFL by the Numbers

• We can generate a

data table using

this function.

NFL by the Numbers

• Over a ten-year

period, the player

will earn nearly $8

million dollars.

NFL by the Numbers

• But what if a

player doesn’t last

10 years? This

table shows the

cumulative salary

for career lengths

up to 10 years.

NFL by the Numbers

• Here is a graph of

the data. Do you

see that it is a

nonlinear graph?

NFL by the Numbers

• A quadratic

regression shows

the equation that

fits the data.

NFL by the Numbers

• In order to get the

most salary

possible, it is in a

player’s best

interest to prolong

their career as

much as possible.

NFL by the Numbers

• To that end, the

new Collective

Bargaining

Agreement

includes some

procedures to

minimize player

injury, which

indirectly prolongs

a player’s career.

NFL by the Numbers

• Furthermore, the

new agreement

includes an

expanded pension

program, with the

teams contributing

for the first time in

league history.