questions and comments to info@pigskinrevolution.com
1. What is End Game Technologies, LLC ?
End Game Technologies, LLC was established in 2001 through the collaborative efforts of Frank Frigo and
Chuck Bower PhD. The goal from the onset has been to provide leading edge Game Theory tactics (proven
methods in other competitive games) to professional sports. ZEUS™ is their inaugural effort which literally
revolutionizes the way football is played. Please see Bios.
2. How does ZEUS™ work, and why are the model’s recommendations reliable?
ZEUS™ was built from the ground up through extensive research into NFL game logs, historical statistics
and the behavioral traits of coaches. The core model replicates, with amazing accuracy, the play-calling and
statistical outputs of typical NFL teams. ZEUS™ has the capability of being customized for the offensive and
defensive attributes of a subject team and its opponent. Then, with the capability of performing more than
1,000,000 game simulations in a matter of seconds, critical play choices can be assessed on their relative
merits. ZEUS™ takes the relative output of the simulation and performs a diligent analysis of statistical
significance and skill sensitivity (see F.A.Q. #4). There is simply not a more accurate way to assess a
critical play-calling decision in football.
Wikipedia provides a brief overview of ZEUS
3. Why are all plays assessed in terms of “Game Winning Chance” expectations rather than
actual results?
Every decision in a competitive sport should be based upon the optimization of Game Winning Chances
(“GWC”). However, coaches often lose sight of this goal by focusing on points rather than the statistical
expectation of winning. Points certainly matter in an NFL game, but not all points have the same value.
Consider a team trailing by 2 points on the last play of the game at their opponents 2 yard line: the extra 4
points that come with a touchdown in lieu of a field goal have no value whatsoever. The field goal is the
optimal GWC choice. In this simple example, if the team went for the TD and succeeded they would still be
charged with a large blunder even though it didn’t affect the outcome of the game. This is because the
chosen play will lose on average. ZEUS™ focuses on the methodology of optimal play-calling not the short
term results. Over the course of a long season, every small piece of GWC matters. A representation of
GWC "Equity Progression" for the 2004 AFC Championship Game as analyzed by ZEUS is shown here.
4. Does ZEUS™ take into account the relative strengths and weaknesses on offense and
defense?
Yes, while the core model is built upon the typical offensive and defensive attributes of NFL teams, the
subject team and its opponent can be customized with respect to their rank in passing, rushing, punting and
kicking. This is referred to as the "Base Custom Case". By making these pre-game adjustments, ZEUS™
can more accurately assess the relative merits of critical play choices.
ZEUS™ also performs a rigorous "Sensitivity" analysis to determine a "Confidence" factor for the model's
recommended play choice. This is a process whereby the model applies custom cases (extreme
combinations of offensive and defensive strengths and weaknesses) in an attempt to overturn its own
conclusion. The probability that the Base Custom Case can be overturned by an Extreme Case, results in
the assignment of a Confidence Factor (Low = 1, High = 10). A Confidence Factor of 10 represents
essentially irrefutable evidence for recommended play choice.
5. Aren’t field conditions, wind and emotional momentum important factors?
These factors certainly matter, and depending on the specific play-calling decision they may matter more or
less. Field conditions and wind often have neutralizing effects with respect to GWC early in the game
because both teams will likely face their fair share of adverse conditions. The higher the confidence level,
the less likely a ZEUS™ recommendation should be overturned by extraneous factors. As always, we
encourage the coaches discretion in such matters. Emotional momentum is a 2-way street and coaches
often focus on only the negative side of this equation. A critical 4th down success may inject the offensive
team with positive momentum just as a failure to convert may discourage them.
6. Where do the statistical assumptions come from?
Fortunately, very good statistical data is accessible from the NFL on a team-by-team basis. Using this data,
distribution curves were developed for the probabilistic outcomes of every possible play choice. Through
continued refinement, a core model was developed that very accurately replicates how typical NFL teams
perform against each other. After performing millions of simulations, a comparison of several key statistics
was conducted against actual NFL historical data. In categories such as average score differential, point
outputs, time of possession, rushing and passing yardage, kicking distances and field goal success rates,
the results of ZEUS™ were “spot on”. This provided the utmost confidence in the core model before allowing
it to be used to assess critical play calling. The remarkably close correlation between ZEUS analysis and
the best available NFL historical data is shown here.
7. What do you mean by Binary or Directional play choices?
Critical choices in football often center on two distinct, or directional play paths. A coach must decide to go
for the first down or punt on a ‘4th and short’. A coach must also assess the relative merits of a 1pt. or 2pt.
conversion. Such choices take distinctly different routes toward victory and each choice has its own set of
risk/reward considerations. These are often extremely complex decisions that cannot be accurately
evaluated in a real-time context without the use of technological assistance. A simplified example of a binary
P.A.T. decision is shown here.
8. Isn’t football inherently different than other game theory disciplines?
Surprisingly, games like Chess and Backgammon are tactically very similar to games like football and
baseball. While the “physical” nature of the game is very different, the “situational” nature is strikingly similar.
A football coach is constantly making decisions with respect to multiple variables (Score, Field Position,
Down, Yards to 1st, etc.). Each of these decisions should be based on providing his team with the highest
probability of winning the game (GWC). No decision, whether correct or incorrect provides guarantees….
only expected outcomes. The expected outcomes are affected by play choices, skill differentials and often
random elements. Sophisticated computer models and simulations were introduced in chess and
backgammon more than 20 years ago and much has been learned. To say that technology has
revolutionized these games would be an understatement. Just as the ZEUS™ model provides a
sophisticated “look-ahead” in football analysis, backgammon and chess models have been solving
previously unmanageable problems with great accuracy for 2 decades. There is absolutely no reason that
ZEUS™ can not have an equally revolutionary impact on professional sports such as football and baseball.
9. How meaningful is a single play error of 2 –3% GWC?
To put it in proper perspective, two errors per game (each with a 3% magnitude) would cost a typical NFL
team one full game per (regular) season. An analysis was performed on the ZEUS™ cumulative error rates
for a number of NFL teams during the 2003 season. On critical 4th down and P.A.T. decisions alone, the
cost of errors ranged between 0.6 and 1.25 games for the season. This is the approximate difference
between a 9-7 record and a 10-6 record. Playoff prospects often hinge on such differences.
10. What else can ZEUS™ do for an NFL team?
4th down play-calling and P.A.T. decisions are only a small part of the ZEUS™ value proposition to an NFL
organization. With respect to real-time decisions, ZEUS™ can also assess on-side vs. regular kickoffs,
penalty acceptance, timeouts and replay appeals. While 4th down and binary play-calling has been the
major focus of the application, a wealth of conceptual information is available regarding 1 –3 down decisions
and clock management.
A number of important individual and team statistics can also be compared and converted to GWC units.
Additionally, players can be measured in GWC impact across multiple positions. For example, the #1
ranked kicker in the NFL could be compared to the #32 ranked kicker specifically on their seasonal GWC
impact. This is especially important in calculating value (salary cost/expected win) ratios before the draft or
an important trade.
EndGame Technologies will be launching the ZEUS™ "Critical Call Index" in the near future. This ranking
system will objectively measure coaching performances in critical play-calling decisions.
11. What about College Football?
ZEUS is currently designed to accomodate NFL rules and the statistical range of NFL teams. However,
under its current design the model can provide a reasonably accurate assessment of many critical decisions
in the college game. With some modification, a very powerful product could be developed to assist the
college coach. Considering the recruiting challenges of 2nd and 3rd tier college programs, technology may
ultimately provide the key to competing at the highest level.
