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Take a Good Look, using Mathematics
"Wells' career short, but robust"
Forty-six years ago a young man greeted me in the hallway of the Nabrit Science Building at Texas Southern University, Houston, Texas. He was on his way to Mrs. Corinne Newell's mathematics class and I was taking a break, walking down the hallway. That moment began an adventure in collaboration and I am taking a good look at the people and experiences of the past.
The man, an elementary education major, who spoke to me in the hallway at Texas Southern is Warren Wells. He became a professional football player, a wide receiver, while I became a mathematics professor. After re-encountering him in February 2007, I began to search for some way to measure the impact of his career. Unfortunately, I did not archive statistics on the NFL or on his career. On May 18, 2008, however, a sports enthusiast and researcher published a quantitative analysis of thirty-three of the NFL wide receivers, starting with Don Hutson (January 31, 1913 -- June 24, 1997). Wells, a veteran who is now 65 years old, was included. I scanned the data and saw that Wells ranked No. 1 in two categories, and it looks like he has held that rank for about 38 years.
I decided to compare Warren Wells with Jerry Rice by analyzing the plot of the data for the two wide receivers. Letting the leftmost, lower corner of the chart be (0,0), I let the vertical axis represent ranking and the horizontal axis categories (spaced at 5 point intervals). So, if Rice, an NFL wide receiver, ranked 5 in the fifth subcategory, there was a point in his data set of (5, 5). Data points were plotted and a line graph was drawn for both Rice and Wells. The next step was to turn the problem over to my calculus class and ask the students to calculate the area under each of the line graphs. One of my students who received his law degree from Harvard University saw a few flaws in our approach. I encouraged him to improve our initial approach. The students then realized that the incrementation of the x axis was arbitrary, and the size of the intervals of the x axis did not matter as long as the same partitioning was used for each player, and that the length of each interval on the x axis was the same (uniform).
The students got excited because they were using calculus to analyze historic NFL data, and they were totally surprised that the mathematics professor was talking about great wide receivers. The students began to take a good look at the NFL data, using mathematics.
What were the results of the study? Well, the students concluded that overall Rice ranked higher than Wells, although Wells ranked higher in two subcategories. His rank is No. 1 in "Yards/Reception" and in Rushing "Yards/Attempt". He has held the top rank for 38 years, which is longer than Rice's career of 20 years. Using calculus, the total area under Rice's curve was found to be greater than the area under Wells' curve. The difference in the areas was not that large. Also, although Rice's overall average rank is greater than Well's, Rice is ranked No. 1 in only one category, "TDs/Game."
In the three categories for "Rushing" Wells, Don Hutson and Rice each rank No. 1 in one category. Hutson, the first NFL wide receiver, dominates "Yards/Game" while Rice dominates "TDs/Game" and Wells dominates "Yards/Attempt". The alumnus from Texas Southern University has career statistics that are shining bright in 2008.
My students and I encourage you to take a good look at the data on http://www.behindthesteelcurtain.com/2008/5/18/520032/quantitative-analysis-of-t and decide whose career statistics stands out over a long time period. You may be surprised at your results. Here is a short report based on student input:
Calculus students analyzed a quantitative analysis comparing the career statistics of Rice and Wells. They created a model for each player by graphing a piecewise defined function connecting ranks and then used integration to find the area under the piecewise linear curves. The students asked, "Why hasn't Wells been considered as a nominee to the Hall of Fame since he ranks No. 1 in two of the seven categories in the quantitative study?" They noted that the statistics indicate that Wells has ranked No. 1 in two categories for about 38 years. Source: WolfpackSteelersFan on May 18, 2008 7:42 PM EDT