What Makes a Great Quarterback

1
What Makes a Great Quarterback?

• Dylan Riekeman

2
Well Im glad you asked

• In 1971 Don Smith came up with a method to rate
  quarterbacks based on their performance
• Smith was an executive at the Pro Football Hall
  of Fame who was known as a statistical whiz

3
The Passer Rating

• Smith combined four statistical categories
• Percentage of Completions (per attempt)
• Percentage of Interceptions (per attempt)
• Percentage of Touchdowns (per attempt)
• Average Yards gained (per attempt)
• The categories are rated in such a way that an
  outstanding performance would score two points
  and an average performance would score one point

4
The Passer Rating

• ((COMP/ATT) 100) - (30/20)
• ((YDS/ATT) - 3) (1/4)
• (TD/ATT) 20
• 2.375 - (INT/ATT) 25

5
What seem to be some problem?

• The 2.375 maximum is very arbitrary number
• The rating leaves out some statistics that are
  important to quarterbacks
• The scale from 0-158.3 is not very intuitive for
  comparing quarterbacks
• The passer rating has little to do with a
  quarterback actually winning a football game
• There is no rationale that says that the four
  categories should be given the same weight

6
We have problems! What are the answers?

• Inclusion of more statistical categories
• Removal of the 2.375 maximum
• A scale that is easier to understand, and

7
Drum roll please

• A way to weight each of the statistical
  categories
• That is, the statistic that is most important to
  a quarterback winning football games is the
  statistic that will be weighted the most on the
  scale.

8
The Setup

• Statistics on quarterbacks from the last 20 years
  were imported into an Excel Spreadsheet
• Quarterbacks who had started less than 12 games
  in a given year were removed
• If a quarterback had started fewer than 16 games
  his statistics were projected to what they would
  have been if the quarterback had started the
  entire season

9
The Setup

• Five categories were selected to be used in the
  new quarterback rating
• Yards (in a season)
• Touchdowns (in a season)
• Interceptions (in a season)
• Completion percentage (in a season)
• Sacks (in a season)

10
The Setup

• A 0-10 scale was created for each category where
  a record setting score would result in a 10, an
  average score would result in about a five and a
  performance of no value would result in a 0. A
  line was then found using two points, the min and
  the max

11
And the setup is finally over
12
So what category is most important?

• For each year, three quarterbacks, one who won 12
  or 13 games one who won 8 or 9 games and one
  who won 4 or 5 games, were selected
• A linear optimization problem was then set up
  using Mathematica

13
So what does a linear programming problem look
like?

• X1chair
• X2table
• Maximize 5 X1 3 X2 (Profit)
• Subject to2 X1 X2 ? 40 labor constraintX1
  2 X2 ?50 material constraintand both X1, X2 are
  non-negative

14
So what category is most important?

• Weights were found for each category such that
  the statistics for the quarterback who won 12 or
  13 games were maximized and
• The total for the quarterback who won 12 or 13
  games was greater than the total for the
  quarterback who won 8 or 9 games, and the total
  for the quarterback who won 8 or 9 games was
  greater than the total for the quarterback who
  won 4 or 5 games for each of the 20 years
• And the five weights added up to 1

15
So what category is most important?
16
All that work for five numbers?!?!

• a.395814 (completion percentage)
• b.146419 (yards in a season)
• c.177534 (touchdowns in a season)
• d.151336 (interceptions in a season)
• e.129898 (sacks in a season)

17
The final rating system
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What else can this rating system show us?

• The highest rated quarterback over the past 20
  years is Steve Young, followed closely by Peyton
  Manning
• From 1987-2005, 41 quarterbacks were taken in the
  first round of the NFL draft
• Of those 41 quarterbacks, only 9 had career
  averages above 52.8 (the average of all the
  quarterbacks)

19
What else could be done?

• See if other categories would merit inclusion in
  the rating
• Find a way to weight certain times in a football
  game as more important than others
• Examine if the method could be applied to other
  sports

20
Thank you very much!

• Dr. Riggs who helped me with the research and
  helped make this presentation possible
• Dr. Lunsford for making sure I got this project
  done on time
• Any redistribution or rebroadcast of this
  project or any pictures descriptions or accounts
  of this project without the express written
  consent of Dylan James Riekeman is strictly
  prohibited

21
Bibliography

• Abrahamson, David L and Sparks Rebecca L. A
  Mathematical Model to Predict Award Winners.
  Math Horizons, April 2005 (5-13).
• The ESPN Pro Football Encyclopedia, Second
  Editon. Edited by Palmer, Pete Pulis, Ken
  Lahman, Sean Tod, Maher Silverman, Matthew
  Karhl, Christina and Gillette, Gary. Sterling
  Publishing Company, New York, NY. 2007 (1-18).
• Kolman, Bernard. Introductory Linear Algebra with
  Applications. Macmillan Publishing Co, New York,
  New York. 1976 (237-283).
• Sposito, V.A. Linear and Nonlinear Programming.
  Iowa State University Press Ames, Iowa. 1975.
  (3-16).
• www.nfl.com
• www.espn.com
• www.armchairquarterback.com