emmitt smith

emmitt smith

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Emmitt Smith & His Annual Rushing Yards
     Emmit Smith announced his retirement February 3, 2005. It was a very emotional moment for Smith, who has played running back in the NFL for fifteen years (thirteen of those years for the Dallas Cowboys). As Smith announced his retirement tears began to flow down his face stating “It’s been a tremendous ride.” Over his career in the NFL, Smith has racked up many impressive statistics and awards. Smith has played on three Super Bowl championship teams (including an MVP award in 1993). Smith is currently the NFL’s all time leading rusher with 18,355 yards.
     For my derivative project I chose to graph Emmitt Smith’s annual rushing yard total. Emmitt was drafted out of University Florida in 1990 and began his career as an NFL Great. As you can see on the graph, Smith began his career slowly, amassing only 937 rushing yards his rookie year. However, his second year Smith improved to 1563 rushing yards. In his third season, Smith again improved to 1713 rushing yards. The decrease in production Smith’s fourth and fifth year (1486 and 1494 respectively) in the NFL can be partially credited to the fact Smith did not compete in all sixteen regular season games due to injuries. Smith redeemed himself the following year with a career high 1773 rushing yards. Over the next six years Smith’s age slowly caught up to him as he ranged from 1021 to 1397 yards. Finally, after his thirteenth year as a Dallas Cowboy, Smith was traded to the Arizona Cardinals. In his first year with the Arizona Cardinals (2003), Smith was injured and played as a backup for the majority of the year. This is illustrated through his career low 256 rushing yards. However, in Smith’s final year in the NFL, he rushed for 937 rushing yards, bouncing back from a disappointing year. Strangely, Smith ended his last season with the same rushing total as his rookie season. I plotted these points in a graph in an excel document and created a line of best fit. This line was a cubic equation (f(x) = 1.4228x3 - 8533.3x2 + 2E+07x - 1E+10).
     To calculate the first derivative, I found the average rate of change of Emmitt Smith’s annual rushing yards from the two years surrounding the year I was deriving. Smith’s yards per year had an increasing slope in the years 1990, ’91, ’94, ’97, ’98, and 2004.

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However, Smith’s yard per year had a decreasing slope in the years 1992, ’93, ’95, ’96, ’99, 2000, ’01, ’02 and ’03. The graph of the first derivative illustrates a “U” like trend so I created a quadratic line of best fit. This is fitting because the original equation from Emmitt Smith’s annual rushing yards was cubic (the derivative of a cubic equation is a quadratic equation). This equation was f'(x) = 12.009x2 - 47978x + 5E+07.
     To calculate the second derivative, I found the average rate of change from the first derivative of the years from the two years surrounding the year I was deriving (for the second time). Smith’s yards per year was increasing at an increasing rate or decreasing at a decreasing rate in the years 1993, ’96, ’97, 2002, ’03, and ’04. Smiths yard per year was increasing at a decreasing rate or decreasing at an increasing rate in the years 1990, ’91, ’92, ’94, ’95, ’98, ’99, 2000, and ’01. The graph of the second derivative illustrates a mostly increasing trend. I used a linear equation because the derivative of a quadratic equation is linear (and the graph of the first derivative was quadratic). This equation was f"(x) = 44.4x – 88648.
     Emmitt Smith once said, “For me, winning isn't something that happens suddenly on the field when the whistle blows and the crowds roar. Winning is something that builds physically and mentally every day that you train and every night that you dream.” Smith proved his ability to be a winner by producing consistently high amounts of rushing yardages throughout his career in the NFL. Smith will always be remembered for his time as a player, a leader, a record-setter, and a great focus for an end of the year calculus project.
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