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01 Apr 2005

A Revolution in NFL Analysis

Guest Column by Dr. William Kilgore

(Yes, now it can be revealed, this is an April Fools' column. I know, I know, you are disappointed that it isn't real. It sprung from the fertile mind of Mr. Michael Tanier.)

For decades, football analysts, statisticians, and handicappers have searched for the one statistic that best determines success or failure in the NFL: the figure that, when calculated, can determine Sunday's winners on Friday afternoon or a Super Bowl champion in mid-August. Such a statistic represents the Grand Unification Theory, the Rosetta Stone, the Holy Grail, or even the Kama Sutra of sports statistical research.

Football-metricians (the profession needs its own title, like baseball's "sabrmetricians"; terms like statistician seem somehow too prosaic and limiting for such noble and satiating work) have grappled for years with fundamental questions. Does replacement level exist? How much of a running back's performance is determined by the offensive line? Is it possible to set up the pass by running the ball? Such basic questions often proved impenetrable to study: efforts to isolate player performance from team performance or yardage from context tended to evaporate into quantum foam when subjected to mathematical scrutiny. More than one brave soul sacrificed decades before the altar of football statistics, only to find that he labored in vain.

Here at Football Outsiders, readers have enjoyed the work of Aaron Schatz, who has creaked open the door of football insight with quaint numerical models like DVOA and DPAR. Now, it's time to knock the door off its hinges. The time has come for a seismic shift in the way the sport of football is analyzed. It turns out that DVOA and DPAR were just calculated rumblings that presaged the arrival of the Numerical Barometer of Selected Quantitative Uniform Indicators of Dependence, hereafter known as NumB SQUID.

An Infallible Method

NumB SQUID is the most tested statistical model in all of football, and it has won over skeptics throughout the football world. Mathematicians from Southern Mississippi University, East Carolina University, and other Conference USA schools have thoroughly vetted the stat and it's underlying mathematical model. It has been duly patented (US6004596), and will soon be written up formally in the prestigious Australian Journal of American Sports Statistics.

As part of the rigorous testing, raw data from the last 39 seasons of the NFL were entered into NumB SQUID. A full simulation for each season was done to determine the Super Bowl champion. The method was 100% accurate in picking champions. Amazingly, the method even predicted Super Bowl III and IV results accurately, even though careless interns neglected to enter any AFL data. The NumB SQUID model correctly postulated the existence of Joe Namath, Weeb Eubank, and Hank Stram from whole cloth.

As a failsafe, data from the last 120 college football seasons were entered, and the system was asked to produce conference champions and bowl winners. Here, there were some discrepancies. NumB SQUID predicted that Villanova would beat Auburn 9-7 in the 1937 Bacardi Bowl; in fact, the game was a 7-7 tie. Two separate Raisin Bowl mistakes occurred: the system had Colorado State beating Occidental in 1948 and projected Baylor into the bowl in place of Texas Tech in 1950. But these are quibbles: NumB SQUID correctly predicted records, championships, and Heisman winners year in and year out.

A Preemptive Note About Criticism

The NumB SQUID system has its detractors, and FO readers are free to scoff at it after reading through the following explanation. However, it's important to make the following concessions: it is not appropriate to criticize the method, it's rationale, it's approach, or any specific calculations. It is also inappropriate to criticize the system's designer, my football or mathematical credentials, or my long association with certain controversial political organizations.

Why? First, mere laymen aren't competent enough to lob such criticism. Second, the system has proven itself to be so airtight that any discrepancies between NumB SQUID results and reality are clearly errors in reality, not in the system. Poor or inscrutable results must be attributed to such forces as Alpha Waves, the Butterfly Effect, Heisenberg's Uncertainty Principle, or the ever-present hand of the Illuminati.

Calculating NumB-SQUID: Rationales

The NumB-SQUID method is built upon the most unassailable statistic in all of football: the quarterback rating formula. Take that figure, make some critical adjustments, factor in some other key data (punts inside the 20, passes defensed, two-point conversion rate, and some minor figures), and perform a quantitative distribution regression analysis, then divide by six, and you have NumB-SQUID.

A note about rounding: some readers may try to do the math along with the author from this point forward. It is essential to round all decimals to five significant digits, with one exception. For pi, the biblical value of three is used (I Kings 7:23-26).

Step One: Converting Initial Values

All preliminary statistics must be converted into irrational numbers using a technique called the Four-Step Correlation Overlay Regression Equation. 4-SCORE is a method I developed seven years ago to link together statistics that, to the untrained eye, have no relationship whatsoever.

4-SCORE is easy to compute:

Step 1: Make the team's passer efficiency rating negative, then take the fourth root of it.

Step 2: Change "i" in the resulting complex number to a more football-relevant vowel: "e" (2.718).

Step 3: Multiply this number by the mean of a team's punts inside the 20 and passes defensed (either the arithmetic or geometric mean will do).

Step 4: Quod erat demonstradum, you are finished.

4-SCORE is the numerator of a quotient called the Double Parabolic Asymmetry Constant, or 2-PAC. The name "double parabolic" comes from the two quadratic equations used in the formula, as follows:

2-PAC = S-tI l2 + αlIve2

The variables are as follows:

  • S = the number of safeties the team allowed in the given year
  • tI = the initial starting time of kickoff for the team's opener
  • l = the reciprocal of the team's opposing third down percentage
  • α = average starting field position
  • lI = the team's third down percentage on 3rd-and-1
  • v = the sum of the team's rushing touchdowns and defensive hurries.

The letter e is a constant, of course.

Confused? Try a concrete example. Run the numbers on the 1978 St. Louis Cardinals. Did you get a Four-SCORE of 56.7113 and a 2-PAC of 11.713? Very good. Now we can move on.

Step Two: Finalizing and Interpreting Calculations

Once Four-SCORE is divided by 2-PAC, you get a number called the Selected Quantitative Uniform Indicators of Dependence Provisional Quotient, or SQUID Pro Quo. We have just a few more adjustments to make:

1) If the SQUID PRO QUO is greater than one, make it a number between 0 and 1 by subtracting away the integer value.

2) Raise the resulting number to the 54th power.

3) Add the team's actual winning percentage for the given season.

4) Make meta-adjustments to account for park effects, weather effects, playoff performances, random factors, and calculation errors.

These meta-adjustments are currently proprietary information, but not for long. My team and I are currently in negotiations to release an encyclopedia in the summer called Total NumB-SQUID. The encyclopedia will include NumB-SQUID values for every player and team in the modern era, as well as informative articles on football by Bruce Coslet, Martin Gardner, and the Indigo Girls. The book will also use modern methods to tackle issues including Mike Martz's clock management style and the controversial release of Troy Brown.


As you can see, NumB-SQUID is brilliantly conceived, easy to calculate, and extremely useful. Its merits are unassailable: it's the only football statistic ever to win the $1,000,000 grand prize from the James Randi Educational Foundation. Given a few minutes with an Excel spreadsheet, and you can crank out NumB-SQUID for hundreds of players and teams -- even your son's high school team!

Does that mean that DVOA and DPAR are dead? Are FO's writers inept and narrow of intellect, it's readers shamefully uninformed? Has Aaron's hard work been in vain: a long, depressing trudge down a dead end filled a bear traps?

Of course it does, they are, and his has. Schatz, as it turns out, was Salieri to my Mozart, Wally Pipp to my Lou Gehrig, Alberti to my Da Vinci, John the Baptist to my Jesus. As Bob Dylan once said, the times they are a' changin'. He also said you don't need a weather vein to know which way the wind blows. And, something is happening here and you don't know what it is, do you, Mr. Jones?

But I digress. The time has come to join the NumB-SQUID revolution. Make NumB-SQUID a part of your football life. Demand that it be included in fantasy magazines and newspaper leaderboards. Petition FOX and ESPN to make it part of their telecasts (forget CBS; they haven't had an innovative idea since Father Mulcahy performed the tracheotomy with the Tom Nix penknife and the tube from a ballpoint pen). And purchase Total NumB-SQUID not once, but twice, as a show of solidarity, or possibly fealty.

Football fans unite! You have nothing to lose but your chains.

Dr. Kilgore is a professor of elementary education, Kirlian photography, and silk screening at University of Maryland-Glenn Burnie. His interests include football, HAM radios, and older women. Surely, you can't be serious? I am serious, and don't call me Shirley.

Posted by: Guest on 01 Apr 2005

2 comments, Last at 07 Dec 2005, 9:02pm by L. Goodman


by Terry Smith (not verified) :: Fri, 07/29/2005 - 2:21pm

I actually looked the patent up. It's for a crustless, sealed sandwich.

by L. Goodman (not verified) :: Wed, 12/07/2005 - 9:02pm

Does anyone know what the beta is for these quarterback ratings?