Math in the News: 8/15/11
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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. For more media resources go to http://www.media4math.com.
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Math in the News: 8/15/11
- 1. 8/15/11
- 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.