Instructing intelligent agents in team-based, multi-agent environments to respond to dynamic events is a lengthy and expensive undertaking. In this paper, we present a framework for modeling the decisions and behaviors of ball carriers in American Football using the Axis Football Simulator. While offensive strategies in football employ the use of prescribed plays with specific spatio-temporal goals, players must also be able to intelligently respond to the conditions created by their opponent. We utilize a two-part substate framework for ball carriers to advance downfield while avoiding defenders. Unlike existing football simulations that employ variations on professional football rules and regulations, our method is demonstrated in a realistic football simulation and produces results that are consistent with actual competitions.
When creating simulations or games with the intent to teach,
it is necessary to provide the user with an environment that
closely matches the real-world counterpart [
While there are several published works related to controlling players or overall team decisions — such as coaching responsibilities — in sports simulations, there does not yet exist a framework for managing the behaviors of players in American Football (football). The sports-based methodologies that do exist are either too generic or not applicable to football and are therefore unable to be utilized. Additionally, much of the published research pertaining to football exists in simulations that do not accurately reflect the rules, regulations, or conditions for professional football.
The goal of this paper is to present a framework for modeling the decisions and actions of an offensive ball carrier. The methods used in the framework will be implemented using the Axis Football Simulation (Axis) — a 3D American Football simulation created with Unity. Since the simulation can be used as a tool to train football coaches and players, the overall objective of the agents, under direction of various algorithms, is to collectively provide an environment that closely matches the decisions, actions, and capabilities of players in an actual football competition. Therefore, in an effort to maintain the validity of the simulation, behaviors that extend beyond normal human ability (e.g., processing information faster than possible, using data that an actual player would not have access to, and so forth) will be avoided. Additionally, Axis’ rules and regulations (e.g., field size, player capabilities, active participant numbers, and so forth) are intentionally designed to be consistent with actual football competitions.
While Axis is running, the user will always control a single character, leaving 21 other agents to be controlled by intelligent scripts. Agents can be categorized into one of a finite number of states based off of their current goal(s). Those goals are established by combining the prescribed instructions of the selected play and dynamic adjustments made in response to the changing conditions of the environment (i.e., the states and positions of the surrounding players and the location and possession of the ball). While on offense, an agent will fall into one of four goal-oriented states: RUNNING, THROWING, RECEIVING, or BLOCKING. On the defensive side, agents will also be grouped into one of four states: ZONE COVERAGE, MAN COVERAGE, BLITZING, or TACKLING. While this paper will focus only on the RUNNING framework, we believe the combination of the individual methodologies will produce behaviors that closely resemble the actions of professional football players at both the individual and team level.
The RUNNING state will function independently as a hierarchical state machine divided between positions of behind and in front of the imaginary line on the field where the play begins (i.e., line of scrimmage). When the player receives the ball behind the line of scrimmage, a series of raycasts will be performed in the surrounding area in order to determine the best place to run. If the runner crosses the line of scrimmage, they switch to a different substate that detects and avoids nearby defenders. We proposed that this two-part framework for controlling offensive ball carriers provides a realistic simulation of decisions and behaviors taken by actual players in football competitions.
In demonstrating proposed models or methodologies for a
particular set of agents in a sports environment, it is
necessary to have a simulation in which they can be applied. Rush
2008, a research extension of Rush 2005, simulates play in
an eight player variant of American football (football) [
Laviers et al. presented an approach for online
strategy recognition [
Laviers and Sukthankar later created a framework for
identifying key player agents in Rush 2008 [
Li et al. took a different approach and outlined a system
that analyzed preprocessed video footage of human
behavior in a college football game and used it to construct a
series of hierarchal skills[
The method Li et al. used for acquiring the constructed hierarchal skills was divided into three steps. First, the system observes the entire video-based perceptual sequence on actors achieving the intended goal and infers beliefs about each state. Next, the agent explains how the goal was achieved using existing knowledge. Finally, the algorithm constructs the needed skills along with any supporting knowledge, such as specialized start conditions, based on the explanation generated in the previous step. Those skills were tested using Rush 2008, and although the level of precision in ICARUS’ control was found to need improvement, the results suggested that their method was a viable and efficient approach to acquiring the complex and structured behaviors required for realistic agents in modern games.
While all of these studies produce improvements to
models or frameworks associated with football strategies, they
make no mention of the specific decisions that the individual
players use while the simulation is running. Additionally, as
shown in figure 1, a main problem exists that the
simulation in which their strategical improvements are found does
not accurately represent a football environment (e.g., Rush
2008 uses eight players instead of eleven). Removing three
players from each team has a drastic effect on not only the
strategic planning process, but also on the dynamic
spatiotemporal aspects of live play. As stated in a sports-based
game simulation research report, the development of a
program for playing a sports game presents a problem in that
the simulation of the game itself must be done in such a way
so that the physical interaction of the game is represented
accurately [
Gonzalez and Gross use this approach in their coaching
football simulation. The objective of the program — which
provides two basic decisions to make: what offensive play
to execute (if on offense), and what defensive formation to
use (if on defense) — is to make the best selection possible
based on the rules of the game, on a priori knowledge about
strategy, and on learning from the opponent’s play selection
[
Related research has also been conducted in the area of
complex multi-agent probabilistic actions where complex
means the actions contain many components that typically
occur in a partially ordered temporal relation and
probabilistic refers to the uncertain nature of both the model and
data. Essentially, the work surrounds the idea of
evaluating whether an observed set of actions constitutes a
particular dynamic event. Intille and Bobick presented a model
for representing and recognizing complex multi-agent
probabilistic actions in football [
While Intille and Bobick’s work can detect — with relative uncertainty — the goals and perhaps future actions of the offensive agents, doing so requires knowledge of the offense’s playbook (i.e., complete set of available plays the offense can run), something that is not only dynamic, but also secretive. Without the set of predefined temporal-action relationships, the defensive agents would be forced to build the dataset from observed plays during a game, and would then only be able to properly identify — again with uncertainty — plays that it has already observed. Additionally, as the number of plays the offense has the ability to run increases, the number of options the defensive agents must consider — and ultimately the complexity of the decision — also increases. Still, their work provides a building block that could serve as a framework for instructing individual defensive agents attempting to determine the offense’s intent.
Stracuzzi et al. build on that work by proposing an
application of transfer from observing raw video of college
football to control in a simulated environment. The goal is to
apply knowledge acquired in the context of one task to a
second task in the hopes of reducing the overhead
associated with training in the second task [
A last piece of related work focuses on the pursuit of
human-level artificial intelligence and its application to
interactive computer games. Laird and van Lent describe
human-level AI as being able to seamlessly integrate all
the human-level capabilities: real-time response, robustness,
autonomous intelligent interaction with their environment,
planning, communication with natural language,
commonsense reasoning, and learning [
In American Football (football), the goal of the ball carrier is to advance as far down field as possible — with the ultimate goal of reaching the end zone. Our system places the ball carrier in a hierarchal RUNNING state, which happens whenever an offensive player receives the ball (e.g., handoff, completed pass, or recovered fumble), the quarterback crosses the line of scrimmage with the ball, or a defensive player gains possession of the ball (i.e., a turnover). It is important to note that while designed running plays have prescribed paths that runners are instructed to follow, it is impossible to predict the defensive player’s actions. Therefore, in order to maintain acceptable levels of intelligence, actual paths — and ultimately holes — must be determined dynamically. When an offensive player receives the ball behind the line of scrimmage, they determine the best hole through which to run by factoring the size of the available holes with the player’s proximity to those holes. Holes themselves are determined by decomposing a rectangular area of the field surrounding the blockers at the line of scrimmage. As shown in figure 3, the raycasts are spaced at a static interval slightly smaller than the approximate shoulder width of an average player. We will discuss the effectiveness of various raycast spacing strategies in subsequent sections.
The methodology for advancing down field under the RUNNING state is divided into two substates: HOLE SELECTION and AVOIDANCE. As shown in figure 2, the substate is determined by the position of the player in relation to the line of scrimmage. If an offensive player receives the ball behind the line of scrimmage, they enter the HOLE SELECTION substate. All other conditions — including the player crossing the line of scrimmage while in the HOLE SELECTION substate — will result in the player entering the AVOIDANCE substate. While the focus of this paper is on the running aspect of the simiulation, it is also important to note that a player who catches a pass will immediately enter the AVOIDANCE substate regardless of their position in relation to the line of scrimmage.
The goal of the HOLE SELECTION substate is to find the best hole (i.e., gap between players) through which to run.
Once the raycasts are executed, the area is decomposed into a single dimension Boolean structure reflecting whether or not the casts collided with any player. The structure is then transformed to reflect the number of consecutive empty positions at each hole. The player’s position is normalized along the width of the decomposition area to determine the index of the structure closest to the player. The system then generates a value for each hole within five positions to the left and right of the player’s index. The value is calculated by taking the size of a hole and subtracting from it the distance in positions from the player. The largest resulting value is chosen as the hole through which to run, and the player selects the midpoint of that hole at the line of scrimmage as the goal position. The entire algorithm for the process can be seen in algorithm 1. Once the runner reaches the goal position, it transitions to the AVOIDANCE substate.
Three important notes are worth mentioning with respect to the methodology used during the HOLE SELECTION substate. First, when the initial raycasts are made to decompose the area around the line of scrimmage, collisions with either offensive or defensive players will flag that position as non-empty. Logical arguments can be made that only defenAlgorithm 1 Runner Hole Selection 1: function FINDHOLE(decSize; spacing; vision) 2: startP os runnerP os:x (spacing decSize=2) holes[ ] new [decSize] for i 0 to decSize 1 do castLoc startP os + (i spacing) if Raycast(castLoc) then
holes[i] 0 else holes[i]
1 for i 0 to decSize 1 do if holes[i] = 1 then j 1 while j +1 < decSize and holes[j +1] 6= 0 do
j j + 1 v j i + 1 for j i to i + v do
holes[j] v i v + i index (player:x startP os) = spacing) + 1 start max (index vision; 0) end min (index + vision; decSize) bestP os 0; bestV al 1 for i start to end do v (vision abs(index i)) + holes[i] if i > bestV al then bestV ale v bestP os i if bestP os < index then
return startP os + (bestP os spacing) ((holes[bestP os]=2) spacing) else
return startP os + (bestP os ((holes[bestP os]=2) spacing) spacing) + sive players pose a threat to the runner, and that offensive players should be ignored during decomposition. When attempting to determine the best approach to selecting a hole for the runner, we ran tests with casts that both collided with and ignored offensive players. However, ignoring offensive players provides information to the runner beyond what they have the ability to observe. Because the runner is behind the offensive linemen at the time that the raycasts are made, the line of sight to potential defenders directly in front of those linemen will be obscured. Therefore, it is unrealistic to expect the runner to be able to accurately see the positions of those players. Additionally, ignoring offensive player collisions with the raycasts caused the runner to unnecessarily collide with a lot of their blockers, reducing their ability to advance downfield.
The second important distinction relates to the lateral distance with which the runner is able to view when determining which hole to select. The average human has a peripheral vision extending 120 degrees, so holes beyond five positions from the runner were beyond their perceived vision and were ruled out as unrealistic choices. On the other hand, reducing the lateral visibility distance to four or fewer positions caused the runner to miss holes of a larger size that were perceived to be in their field of view. Ultimately, extending five raycast positions was found to produce results that were the most consistent with the perceived vision limits of the runner.
Finally, it is also important to note that the decomposition and hole selection occurs only once at the time of the handoff. Our initial approach utilized a continuous check (i.e., the runner would decompose and select the best hole at each game step), but this produced erratic behavior from the runner that was inconsistent with actual player behaviors. Furthermore, we believe that continuously decomposing the environment using our algorithm extends beyond normal human processing and reaction abilities and places unnecessary stress on the simulation.
The goal of the AVOIDANCE substate is to advance as far downfield as possible while avoiding defending players. The runner employs the use of a 120 degree field-of-view reaction radius for the basis of its running direction. The bounds of the cone-shaped radius are determined by the dot product of the runner’s normalized forward vector and the normalized vector to potential tacklers. Defenders outside of the cone — including those that are behind the runner — will be ignored under the premise that the runner would not be able to see them. If the runner’s reaction radius yields no threats, the player is instructed to run straight forward towards the end zone at their current lateral position on the field.
If there are defenders inside the radius, one of two scenarios can occur. First, if there is only one defender or all of the defenders are on only one side of the runner, the runner will attempt to avoid the threat by taking an angle away from the closest defender. This is shown in figure 4. Second, if there are threats on both the left and right side of the runner, the player concludes that collision is unavoidable and attempts to gain as much yardage as possible prior to being tackled. This, like when there are no threats, is achieved by running straight forward along the runner’s current lateral position.
For the two substates of RUNNING, a series of tests were run to determine the specific values that yielded the highest results for each of the individual methodologies. For all of the tests, a series of 100 plays were run with all other factors (defensive play calls, agent behavior, and so forth) remaining constant.
The first set of tests was designed to determine the most accurate and efficient way to decompose the area where the ball carrier is attempting to run. Decomposition refers to the structuring, at the variable level, of the physical objects present in the simulation. Our goal was to identify the specific locations of the players — and ultimately the spaces between them — while minimizing the processing requirements on the simulation. a high amount of diminishing returns in the accuracy of the raycasts when performed at intervals smaller than the approximate shoulder width of the players (four units).
Our first goal was to determine the maximum lateral spacing between each raycast that would produce an appropriate environmental representation. Figure 5 shows the accuracy of a variety of raycast quantities within the same decomposition area in determining the existence of a player at that position. Each of the raycast spacing distances was tested by executing 100 plays and the accuracy of the raycasts in identifying the actual location of the players was recorded. For the purpose of testing, an arbitrary unit spacing value was defined with the value of a single unit approximating one-fourth the width of an in-game player. The results show
Once the appropriate raycast spacing was determined, the
next goal was to specify the lateral bounds of the
decomposition area — specifically regarding the horizontal distance
that the raycasts were extended toward the sideline. Because
part of the decision for selecting the hole is based upon its
size, increasing the width of the decomposition area places
extra emphasis on running outside of the tackle box (i.e., the
area between the far left and right offensive tackles) since
that area is not typically occupied by defenders at the time
of a handoff and the larger perceived hole will be more
attractive to the runner. That is not to say that one-sided holes
will be ignored or under-emphasized. Indeed, figure 6 shows
an environment state that presents an outside run as a
desirable path option. Finally, because the intent of the algorithm
is to produce behavior that closely resembles the decisions
and actions of professional players, our goal was to closely
match the number of inside (i.e., between the tackles) and
outside paths that were ultimately taken with data compiled
from the National Football League (NFL). According to Pro
Football Focus, the ratio of inside to outside runs in the
2013-2014 NFL season was 55:45 [
In this paper, we presented a framework for the decisions and actions of ball carriers in American football using the Axis Football Simulator. We divided the overall task of advancing downfield into two substates: HOLE SELECTION and AVOIDANCE, each with individual goals. During HOLE SELECTION, the runner attempts to find the best space between nearby players through which to run. Our tests conclude that a decomposition area of 31 raycasts, spaced at four units (roughly the width of a player) around the line of scrimmage, produces the most accurate results in identifying the location of players while minimizing the frequency of raycasts. Additionally, our tests proved the consistency of inside to outside runs that resulted from that decomposition methodology as it relates to National Football League data collected from the 2013-2014 season.
In the AVOIDANCE substate, the ball carrier attempts to avoid nearby threats by running at angles away from defenders. Our tests conclude that the best angle at which to avoid threats on a single side of the runner is 80 degrees. Overall, this framework provides specific and flexible methods for instructing ball carriers in games and simulations that utilize or implement the rules, regulations, and restrictions of American Football.
For future work, in terms of providing a comprehensive framework for controlling all players in a football simulation, our work relating to ball carriers is only one piece of a much larger puzzle. While the Axis Football Simulation provides a set of instructions for all player positions that is consistent with actual football competitions, we believe that they can be iteratively improved to provide a more realistic simulation.