In this issue we look at the new NFL Collective Bargaining Agreement. In particular, we look at the minimum salary data tables provided to see how much a player can earn under the new agreement.
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2. 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.
3. NFL by the Numbers The first column counts the number of Completed Seasons. A value of zero is for a rookie.
4. NFL by the Numbers The other columns show the minimum salary (in thousands of dollars) for years 2011 to 2014.
5. NFL by the Numbers Let’s look at the graph of the salary data for Completed Seasons versus the minimum salary for 2011.
6. NFL by the Numbers This is an example of a discrete function, where the values along x and y change in whole number amounts.
7. NFL by the Numbers This is also an example of a step function, which is much easier to see by connecting the points.
8. 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.
9. NFL by the Numbers Here is a graph of the salary data. Note that it is a linear function.
10. NFL by the Numbers This is the equation for the function.
11. NFL by the Numbers We can generate a data table using this function.
12. NFL by the Numbers Over a ten-year period, the player will earn nearly $8 million dollars.
13. 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.
14. NFL by the Numbers Here is a graph of the data. Do you see that it is a nonlinear graph?
15. NFL by the Numbers A quadratic regression shows the equation that fits the data.
16. 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.
17. 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.
18. NFL by the Numbers Furthermore, the new agreement includes an expanded pension program, with the teams contributing for the first time in league history.