1
NFL Game Simulator
Oliver Reimer, Matthew Crites, & Brian Jones
University of North Carolina Wilmington
Abstract
Our goal was to accurately simulate a National
Football League game, given a number of meaningful
statistics. To find how important each stat was to the
result of a game we multiplied each stat by a weight.
This implies an optimization problem; which
combination of weights would give the best win
percentage of NFL game simulations. We used a
genetic algorithm to optimize these weights. The
weights our algorithm gave us came close to 70%
accuracy in predicting a past NFL season. Our
algorithm consistently favored high weights for
fumbles recovered, and interceptions, while
consistently gave low weights to first downs allowed.
However there is still room for improvement to our
algorithm; more stats can be considered and different
ways of evaluating the cost of our stats can be
considered. We used a relatively simple algorithm,
and a small subset of statistics in an NFL game; this
leads us to believe more ground can be covered, and
better algorithms can be created to forecast the
winner of an NFL game.
Key Words: Genetic Algorithm, National Football
League, Optimization, Simulation, Weights
1. Introduction
This project began as an amalgamation of our
collective interest in football, statistics, and
algorithms that potentially could be used to predict a
National Football League game. Coming into the
project we knew there were many, factors that could
play into an NFL game. Many of those factors are
difficult to classify numerically. It is difficult to
quantitatively represent every aspect of an NFL
game. Our goal was to take the crucial factors of an
NFL game and factor them into an algorithm that
would, as accurately as possible, predict an NFL
game.
For any algorithm to forecast a future event,
background knowledge is needed. The background
knowledge was based on statistics. Obtaining stats is
not difficult for professional sports; they are
meticulously recorded and for the most part are
obtainable online. Our primary focus was to figure
out which stats are the most important and how they
affected an NFL game. We approached this as an
optimization problem, where each stat was assigned a
modifier. Our goal was to optimize each modifier so
that a given combination of weighted stats would
select a winner between two NFL teams. Our chosen
weapon of optimization was a genetic algorithm.
2. Formal Problem Statement
Given two teams denoted as 𝑇𝑒𝑎𝑚𝐻 and 𝑇𝑒𝑎𝑚𝐴
determine the winner of a NFL game. This is done
through statistical analysis using common NFL
statistics and assigning them a specific weight.
Because each statistic is weighted differently, those
with heavier weights indicate that they have a larger
impact in the outcome of a game than those with
lighter weights.
To test the algorithms, the statistics from the
previous 16 regular season games for all teams were
used. The statistics used for offense and defense were
as detailed in Table 1. All stats were based on pergame averages of the team over the past 16 regular
season games.
Offensive Statistics
Passing Yards
Rushing Yards
Points
Fumbles Lost
First Downs
Interceptions
Defensive Statistic
Passing Yards Allowed
Rushing Yards Allowed
Points Allowed
Fumbles Recovered
First Downs Allowed
Interceptions
Table 1
This allowed a controlled environment where game
outcomes were already known, making algorithm
validation more accurate.
3. Background Information
Our project was conceived through our collective
interest in sports, and how a computer might be able
to predict the outcome of a game. We were able to
find a number of methods previously used to some
degree of efficacy. Our research started with Jack
David Bundell’s use of a linear regression model. He
states, “As well as using data such as the two teams’
previous results, novel features such as Stadium size
and the distance the away team had to travel were
incorporated” [3]. This gave us insight into how
much of a factor a small number of stats could be.
Blundell in his research used linear regression models
to predict the outcome of a game. Interestingly, he
found that choosing a winner with a bias towards
home teams was generally more accurate than basing
2
a victor off of previous matchups between the teams.
This gave us the notion that home field advantage
should be taken into account when predicting the
outcome of a game. We also gleaned information
from the algorithm used by Ed, from Ed’s tech cave.
Ed hypothesized that:
Prediction relies on estimating two numerical
characteristics per team, an Offensive Strength
Factor (Fo(t)) and a Defensive Strength Factor
(Fd(t)). The model assumes that the score (S)
achieved by a team 'A' when playing against team 'B'
is given by S(A) = M * (Fo(A)/Fd(B)) [2].
We were able to take this model and adapt it to
our genetic approach which rewarded us with very
similar results as Ed; we found this encouraging. We
wondered how our algorithm stacked up against other
methods of predicting a game, such as going off
intuition or plain old guessing. The following website
helped us with this how our algorithm stacked up to
other forecasting styles, some computerized, some
not. The staff of Betting Expert did some algorithm
work predicting the results of soccer games. The
algorithms predicting the outcome of soccer games
were pretty consistent with the betting odds. This
gave us hope that with more advanced analytics, and
more stats examined we can get closer and closer to
an effective football forecasting algorithm [1].
We were not able to find any public research
claiming greater than 80% accuracy in forecasting a
game. Our research indicates that using basic stats
can give a high degree of accuracy; we feel that
utilizing more advanced stats and analytics can only
improve the percentage of correct predictions.
4. The Method
To determine the winner of a game we used the
equations:
𝑬𝑯 =
𝑶𝑯
𝑫𝑨
𝑬𝑨 =
𝑶𝑨
𝑫𝑯
Where 𝑂𝐻 is home offensive rating divided by away
defensive 𝐷𝐴 rating making the home team’s edge
𝐸𝐻 . Likewise the away offensive rating, shown above
as 𝑂𝐴 , divided by the home defensive rating, 𝐷𝐻 , will
render the away team’s edge 𝐸𝐴 . When the home
team’s edge is greater than the away team’s edge, the
home team is the predicted winner. If the away
team’s edge is greater than the away team is the
predicted winner.
Defensive and offensive ratings are determined by
normalizing and summing their prospective statistics:
Normalized offensive statistics =
Normalized defensive statistics =
𝒕𝒆𝒂𝒎 𝒂𝒗𝒆𝒓𝒂𝒈𝒆
𝒍𝒆𝒂𝒈𝒖𝒆 𝒂𝒗𝒆𝒓𝒂𝒈𝒆
𝒍𝒆𝒂𝒈𝒖𝒆 𝒂𝒗𝒆𝒓𝒂𝒈𝒆
𝒕𝒆𝒂𝒎 𝒂𝒗𝒆𝒓𝒂𝒈𝒆
For example, if a team had 1,000 rushing yards and
the league average rushing yards was 2,000, then that
team would be given a rushing yard rating of
1,000/2,000 = 0.5. However, if the teams rushing
yards allowed is 1,000 and the league average
rushing yards allowed is 2,000, then that team would
be given a rushing yard rating of 2,000/1,000 = 2.0. It
is important to have the league average in the
numerator since a team always wants to be under the
league average in terms of defensive statistics.
5. The Genetic Algorithm
Genetic algorithms are excellent for solving
optimization problems. These algorithms can be
compared to the biological evolution of a population.
At the start, a set of solutions is compiled into an
original starting population. Each solution is rated by
its effectiveness in solving the problem. Attributes
from the better rated solutions are combined to form
new solutions. After many iterations, or generations,
of this process, an optimal or near optimal solution is
found; however, the gene pool can easily stagnate if
initialized with poor solutions. To prevent this stand
still in the population, mutations are introduced.
These random changes in the solution set keep the
population ever-changing. Algorithms of this nature
are often easy to implement, but produce great
solutions to optimization problems.
Being tasked with optimizing weights, a genetic
approach was a perfect solution to the problem. First,
a population of solutions must be prepared. The
number of parent solutions can vary. In our
simulations, the starting pool of solutions consists of
12 solutions. Each solution was a set of randomly
generated weight values. The weight values ranged
from 0.0 to 1.0 exclusive. The random set of
solutions was then ranked based on fitness criteria.
There were four different fitness ratings used which
will be explained in more detail below.
After each solution was rated, the higher rated
solutions were merged and the lower rated solutions
were replaced. Given n solutions, each solution
ranked n/2 to n would not be present in the next
generation of solutions. The solutions were merged
by taking the average of the weight vectors. For
example given the sets of weights x and y:
X
Y
0.3
0.5
0.6
0.4
0.4
0.6
0.9
0.7
0.1
0.3
3
merging set x with set y will produce a set z:
Z
0.4
0.5
0.5
0.8
0.2
The initial population of solutions was bred to form
the first generation. This process was repeated for a
set number of generations. Our simulation used five
generations. At the conclusion of the fifth generation,
the set of weights with the highest fitness rating was
kept and used in the simulation of the game.
6. The Rating System
Two different methods were used to rate the solutions
which the genetic algorithm produced: edge
magnitude and simulation. Edge magnitude is simply
the absolute value of the difference of each team's
edge in a particular matchup:
| 𝐸𝐻 - 𝐸𝐴 |
This method was designed to look at how evenly
matched two teams appeared statistically. A lower
edge magnitude implies that one team did not have a
huge edge over the other. Whereas a higher edge
magnitude indicates that one team had the clear
advantage in the matchup.
The simulation method differed from the edge
magnitude method because it took into account
results from the previous season. The set of weights
needing rating was used to simulate each one of the
257 games of the 2014 NFL season. Since the
outcome of these games is already known, the results
could be classified as accurate or inaccurate. The
percentage of these games the set of weights
predicted accurately was the rating the solution was
assigned.
For each of these two methods, the ratings were
sorted both in ascending and descending order. The
order in which the solution pool was sorted allowed
the simulator to breed for different solutions. For
example, by order the solutions by edge magnitude in
descending order, the simulator, in theory, was
searching for a set of weights which produced a
simulation with a lopsided result (a high edge
magnitude). Sorting the pool by edge magnitude in
ascending order would search for weights that
produced a close result (a low edge magnitude).
7. The Perfect Weights
At the conclusion of five generations of the
genetic process, one solution was given. This solution
is near optimal but is not always perfect. To ensure
the simulator runs with the most accuracy, the genetic
approach was expanded. For each condition, (edge
magnitude and simulation both ascending and
descending) the genetic algorithm was executed 1
million times. The average of each solution out of all
1 million trials was calculated. This average set was
coined the perfect weight for each condition. The
perfect weights that were determined are outlined in
Table 2. The variables SIMD, ASC, DES, and SIMA
relate to the fitness rating conditions simulation
descending, edge magnitude ascending, edge
magnitude descending, and simulation ascending,
respectively.
OFFENSIVE
PPG
FLPG
FDPG
PASS_YPG INTPG
RUSH_YPG
SIMD
0.586039
0.387547
0.530422 0.547612
0.590935 0.496791
ASC
0.4899
0.45325
0.490675 0.477683
0.513831 0.506735
DES
0.532413
0.464036
0.538195 0.534158
0.470165 0.536802
SIMA
0.501823
0.507713
0.505403 0.505435
0.506435 0.497627
DEFENSIVE
PAPG
FRPG
FDAPG
PASS_YAPG INTPG_D RUSH_YAPG
SIMD
0.603601
0.286293
0.57432
0.59289
ASC
0.59359
0.383621
0.583781 0.573764
0.43375
DES
0.322485
0.711595
0.353089 0.383612
0.594453 0.358635
SIMA
0.363092
0.637764
0.352727 0.354634
0.727386 0.361065
0.327986 0.539183
0.580627
Table 2
8. Results
Our genetic algorithm was a success in the fact
that we are able to correctly predict NFL games with
a reasonably high level of accuracy - around 70%.
How the accuracy of the results of the simulation
were heavily dependent on the fitness rating method
used in by the genetic algorithm. A detail account of
the results of the simulation is present in Table 3.
Simulation Descending
Edge Magnitude Ascending
Edge Magnitude Descending
Simulation Ascending
48.8%
50.4%
70.7%
70.7%
Table 3
The edge magnitude descending and simulation
ascending conditions produced the best simulation
results. These results differed from the hypothesized
results. The edge magnitude descending condition
was intended to mimic a lopsided match-up between
two teams. While a skill gap exists between certain
teams, the gap is normally small. All players in the
league are professionals and blowouts are rare
occurrences. This condition was hypothesized to
represent the antithesis of the reality of the league;
however, it produced the best results.
4
The simulation ascending condition was designed
to select weights which produced poor results in our
simulation tests. Because the results were sorted in
ascending order, the solutions with the lowest
percentage of correctly picked games were kept and
used. Given that in development these weights
performed poorly, the final results were expected to
be poor; however, like the edge magnitude
descending condition, great results were achieved.
Our algorithm deemed the stats highlighted in
yellow (in Table 2) as the most important (higher
weights), and the stats highlighted in red (in Table 2)
as the least important. These stats were selected
because in the two best conditions (edge magnitude
descending and simulation ascending) The weights
had a great variance from the mean weight. It was
encouraging to find the weights match up with what
we thought some of the most important stats are. For
instance, we hypothesized that first downs allowed
per game (FDAPG), shouldn’t be weighted very high.
We based the hypothesis upon the bend-but-not break
defensive philosophy in football; this makes sense
because first downs do not score points. Using
similar logic, fumbles recovered and interceptions
were given high rankings because these stats create
more possessions for a team. The more possessions a
team has throughout the course of a game, the more
opportunities they will have to score.
9. Future Work
Future work will consist of being able to add
statistics to the algorithm. It could be argued that
other statistics are equally important in dictating a
winning team. This leads into being able to use
individual player statistics rather than just team
statistics. Considering individual players can
considerably change a defense or offense rating
depending on particular matchups. An example of
this would be if the leading NFL rusher is not playing
due to an injury and his team is playing against an
average rated rush defense. If the leading rusher was
playing you could predict that the possibility of
touchdowns would be greater which would give a
higher edge value for that team. Taking weather into
consideration would be part of our future work as
well. Some teams have home field advantage due to
the climate in which they practice. A team from the
north will be acclimated for cold weather giving them
the edge over a visiting team from the south.
However this is reversed when the northern team as
to go to the south to play being the northern team will
be more prone to dehydration and fatigue. This effect
is even more evident when a team accustom to
playing indoors is forced to play outside in freezing
weather or other sub-optimal conditions.
10. References
[1]http://www.bettingexpert.com/blog/how-to-builda-football-game-prediction-model
[2]http://www.edscave.com/football_algorithm/footb
allalgorithm.htm
[3]http://www.engineering.leeds.ac.uk/eengineering/documents/JackBlundell.pdf
[4]http://www.pro-football-reference.com