First, we will take note of two histograms ("percent frequency histograms" more

Size: px

Start display at page:

Download "First, we will take note of two histograms ("percent frequency histograms" more"

Laurence Morris
5 years ago
Views:

1 III. Understanding the Differences (if any) Results and Interpretations A. The Graphs First, we will take note of two histograms ("percent frequency histograms" more specifically) for the "Hall of Famers" group that places all of the data points into categories and creates bars that indicate their percent frequency. Career yards and touchdowns are displayed below and each histogram presents a normal distribution of the data points we are using in this experiment. Evidently, around 40% of Hall of Fame quarterbacks threw between 20,000 and 30,000 yards over their careers. Here, again, we find a fairly normal (bell shaped) distribution for touchdowns thrown through their years in the pros. The median is between 150 and 200 touchdowns with about 30% of Hall of Fame quarterbacks falling under this category. We will now do the same for the "Non Hall of Famers" group.

2 Again, we have bell shaped distributions in these two histograms as well. It is curious, however, that 45% of the non Hall of Famers fall under the same median category for touchdown passes as the Hall of Fame group. Almost 50% of the non Hall of Famers threw between 20,000 and 30,000 yards over their careers; furthermore, the distribution tells us that the non Hall of Famers performed admirably in these two categories compared to "the immortal" Hall of Famers. Clearly, we are dealing with good and large samples. Both groups enjoy variables that are normally distributed (allowing us to use z scores) and we can use their means as the preferred measure of central tendency since neither sample is skewed. Each histogram shows the percentage of measurements that fall under each category on the x axis for both groups. We will take a closer look at their means and other related statistics in part B of this section. Next, we have two pie charts showing the percentage of players in each group who won and did not win a title.

3 So, what do we have here? Roughly 3/4 of Hall of Fame quarterbacks won a championship title and about 3/4 of the non Hall of Famers failed to succeed on the grandest stage. This qualitative variable may bear some significance in our multiple regression analysis. When we place this statistic next to career touchdowns and yards thrown, it could be inferred that championships play a key role in Hall of Fame selection since both groups match up fairly evenly in the other two categories. The

4 regression will tell us with certainty whether or not this variable is important. Let us now take a look at two scatter plots taken from two simple regressions I created: one shows the relationship between career yards (independent variable) and Hall of Fame induction (dependent variable) and the other illustrates the relationship between career touchdowns (independent variable) and Hall of Fame status (dependent variable.) Hall of Famers are denoted on these plots as "1" and non Hall of Famers are "0." Both scatter plots give a better understanding of the relationship between yards and touchdowns with Hall of Fame status than the histograms above. Hall of Fame quarterbacks seem to be more spread about the spectrum of yards and touchdown categories in both plots than non Hall of Famers and could indicate that those variables are not necessarily essential to Hall of Fame selection. Also, we gain a better sense of which numbers in the Hall of Fame plot are outliers since both points 0 and 1 have at least one outlier at either low or high ends. Thus, we may infer that other variables

5 bear more significance than these two categories of stats that are so popular in arguments over who does and does not belong in the Hall. In the next section, we will dive straight into the statistical analysis. You will find the other two graphs that could be included here (scatter plot and residual plot) in the "statistics" section because they apply directly to some of the models included in the following chapter of this experiment; in fact, to keep them separate would only disorganize the flow of this investigation.

6 APPENDIX (Data Set) Quarterbacks HOF Status Title Winner Career Yards Career TDs Career Comp. % Earl Morrall*^ , Vinny Testaverde , Jim Harbaugh , Ken Stabler*^ , Jim Plunkett*^ , Daryle Lamonica*^ , Rich Gannon* , Don Meredith* , Craig Morton* , Danny White , Drew Bledsoe* , Phil Simms*^ , Joe Theismann*^ , Roman Gabriel , John Hadl*^ , Boomer Esiason* , Randall Cunningham , John Brodie , Ken Anderson* , Jim Everett , Dave Krieg , Archie Manning , Charlie Conerly*^ , Jim Hart , Steve Bartkowski , Steve Deberg , Neil O'Donnell* , Bernie Kosar , Jack Kemp , Norm Snead , Billy Wade*^ , Tommy Kramer , Joe Kapp* 0 0 5, Arnie Herber! 1 1 8, Sammy Baugh!^ , Benny Friedman! Sid Luckman! , Earl "Dutch" Clark! 1 1 1, Clarence "Ace" Parker! 1 0 4, Len Dawson*^ , Bob Griese*^ , Roger Staubach*^ , Y.A. Tittle*^ , Bob Waterfield*^ , Sonny Jurgensen*^ , Steve Young*^ ,

7 Troy Aikman*^ , Johnny Unitas*^ , Joe Namath*^ , Dan Fouts , George Blanda*^ , Otto Graham*^ , Bobby Layne*^ , Bart Starr*^ , Norm Van Brocklin*^ , Jim Kelly* , Dan Marino* , Joe Montana*^ , Terry Bradshaw*^ , Fran Tarkenton* , Warren Moon , John Elway*^ , Kurt Warner? , * = Played in at least one NFL or AFL Championship Game/Super Bowl ^ = Won at least one NFL or AFL Championship Game/Super Bowl? = Will most likely be inducted to the HOF since recent retirement! = "Pre-Modern Era" QB (played through years ranging from the league's birth to 1953)

Speak to a football fan long enough and the conversation will cease to cover simple questions

Speak to a football fan long enough and the conversation will cease to cover simple questions The Hall of Fame vs. Non Hall of Fame Quarterback Challenge: Making a Statistical Case for the Enshrinement of 33 of the Greatest Who Ever Played the Game (or, "Is There a Statistical Difference Between