Math in the News: Issue 51

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In this issue of Math in the News we look at Peyton Manning's new contract with the Denver Broncos. Was this a good deal or not?

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Math in the News: Issue 51

  1. 1. Year 1 Payment ($ millions) 1 18 2 20 3 20 4 19 5 19Peyton Manning’s ContractManning’s $96 million contract is spread out over five years, with paymentsshown in the table. Each year is not guaranteed, so Denver might not payout the full amount.
  2. 2. Peyton Manning’s ContractThis graph of the data shows how pivotal years 2 and 3 are. Clearly, ifManning performs well in the first year, the next two years offer relativelyhigh payments, with the amounts decreasing in the out years.
  3. 3. The average career length for a quarterback is under 6 years, but Peyton Manning has already played 14 years.Peyton Manning’s ContractAlthough Manning has already played 14 years, he is also in a specialcategory of quarterbacks and can be compared to some of the bestquarterbacks in NFL history.
  4. 4. • Joe Montana • Steve Young • Dan Marino • Terry Bradshaw • John Elway • Kurt Warner • Johnny Unitas • Roger Staubach • Brett Favre • Jim Kelly • Bart Starr • Bart StarrPeyton Manning’s ContractThis, while not an exhaustive list, includes some of the best quarterbacksin NFL history. We can compare their career stats to Manning’s to see if hefits in this group.
  5. 5. Years Games Passing Passes QB Played Played TDs Yards Completed Joe Montana 15 192 273 40,551 3409 Dan Marino 17 242 420 61,361 4967 John Elway 16 234 300 51,475 4213 Johnny Unitas 18 211 290 40,239 2830 Brett Favre 20 302 508 71,838 6300 Steve Young 15 169 232 33,124 2667 Terry Bradshaw 14 168 212 27,989 2025 Kurt Warner 12 125 208 32,344 2666 Roger Staubach 11 131 153 22,700 1685 Jim Kelly 11 160 237 35,467 2874 Bart Starr 16 196 152 24,718 1808Peyton Manning’s ContractThis table shows the career stats for this list of quarterbacks.Source: http://www.pro-football-reference.com/
  6. 6. Years Games Passing Passes QB Played Played TDs Yards Completed Peyton Manning 14 208 399 54,828 4682Peyton Manning’s ContractHere are Manning’s stats. Let’s compare.
  7. 7. Peyton Manning’s ContractThis represents the number of years played for all quarterbacks. The redbar is for Peyton Manning.
  8. 8. Peyton Manning’s ContractThis graph is for the number of games played.
  9. 9. Peyton Manning’s ContractThis graph is for the number of touchdowns.
  10. 10. Peyton Manning’s ContractThis graph is for the total number of passing yards.
  11. 11. Peyton Manning’s ContractThis graph is for the number of completed passes.
  12. 12. Peyton Manning’s statistics are comparable to those of a quarterback at the end of his career. How do we know he can play for more years?Peyton Manning’s ContractOf all the statistics, there is one that suggests that Manning is still viablefor a few more years, and why Denver likely struck the deal with Manning.
  13. 13. Peyton Manning’s ContractThis box and whisker plot shows the length of the careers for the list ofquarterbacks shown earlier. The median number of years is 15. Manninghas played 14 years, one less than the median.
  14. 14. Peyton Manning’s ContractWhile it’s unlikely that Manning will play another five years, even if he did, itwould still place him within the range of career lengths, but a little closer toan outlier.
  15. 15. Peyton Manning’s ContractHow do you think Peyton Manning will do as a quarterback for Denver?

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