Another Answers in Search of a Question Post: "We learn more by looking for the answer to a question and not finding it than we do from learning the answer itself." -- Lloyd Alexander.
John Hammond: You'll have to get used to Dr. Malcolm! He suffers from a deplorable excess of personality, especially for a mathematician.
Ian Malcolm: Chaotician, actually! Chaotician! John doesn't subscribe to Chaos, particularly what it has to say about his little science project!
Let's tackle the two opening paragraphs in reverse order. When asked to name one of the greatest football minds, who helped guide his team to three Super Bowl championships in the last ten years, how many of us would have automatically answered Bill Belichick? Probably, most of us. However, we would have also been wrong. The answer that we would have wanted is Ernie Adams. Few people outside of the NE organization are even aware that a man named Ernie Adams works for the Patriots. Few of the people inside the Patriots' organization know exactly what it is that he does. His job seems to be an enigma no matter how you look at it. Yet, he is a man that Tom Brady once described as knowing more about football than anyone he [Brady] has ever met. Boston Globe writer Bob Hohler described Adams as one "of the most influential and unrecognizable difference-makers in New England sports . . . yet is all but unknown beyond Gillette Stadium."
This little snippet of dialogue comes from the movie Jurassic Park. The character Ian Malcolm is a mathematician who specializes in that branch of mathematics known as Chaos theory. Chaos theory, as Malcolm eventually explains in the movie, deals with unpredictability in complex systems. There is much about this approach to analysis that is not explained in the movie however. We'll get to that shortly.
Scene shift: If I were to ask you to name one of the NFL's greatest football minds of the last twenty years (here's a hint: he helped guide his team to 3 Super Bowl Championships in the last 10 years), who would you name?
Scene shift: What on earth do either of those first two topics have to do with the Broncos?
The answers after the jump.
Adams carries the official title of Football Research Director. He has worked with Bill Belichick off and on since the days that they both played football for Phillips Academy Andover High School. Over the years, Adams has consistently demonstrated a love of knowledge which he has translated into a search for ways to make the Patriots a better team. No field of study is rejected as a possible source of inspiration. He puts in an unbelievable number of hours studying game films in order to prepare pregame planning notes for Belichick. He watches game film not only to see how an opposing team acts and reacts during a game -- looking for patterns and tendencies -- but also at how individual players move, act and react. He then determines why the player moved that way, which assists him in planning a counter-strategy for that player's actions. One of the ways he does this is by applying mathematical analysis to the sport of football.
A former high school friend of Adams, knowing of his love of mathematical analysis and its applicaton to football, mailed Adams a copy of a book called Chaos: The Making of a New Science (an out of print book on nonlinear mathematics) only to find out that Adams had already read it. That Adams does not look at the events in a football game as a series of random occurrences suggests that he has begun to apply at least some of the tenets of Chaos theory to the game of football. He has provided Belichick with detailed mathematical analysis on such subjects as: whether or not the Patriots have tried two point conversions too often, and whether or not NFL teams punt too often on fourth down -- can any of us recall a certain fourth down decision by Belichick last year? Any guesses as to why he chose to go ahead and go for it? The most intriguing aspect of Adam's story, at least in my opinion, is his use of Chaos theory as a part of his film analysis.
Now, I feel obligated to admit that I am neither a mathematician (I leave that up to my wife who teaches college mathematics), nor have I been formally trained as a statistician. My own training lies in the area of behavioral observation and the discernment of measurable behaviors. My fascination with Chaos theory has arisen from having watched the Jurassic Park movies multiple times. It has been furthered by a curiosity of whether or not it can be successfully used to improve my classroom and my students' behaviors. Finally, my interest has been deepened by Adams' story, the Patriot's multi-year successes, and my own desire to find additional ways to analyze measurable behaviors when it comes to the game of football in general, and to the Denver Broncos in particular.
Chaos theory, at a very basic level, has been described as an approach to looking at nonlinear systems -- systems that appear to be disordered, random, or at least unpredictable -- such as a football contest. That approach then tries to discover the underlying order in that system. An example of this is when Adams tries to discern why a given player moves the way he moves. Adams does not believe it to be random, but rather a result of specific factors. Chaos theory starts with the proposition that these systems are dependent upon initial conditions to the degree that even a very small change in the initial conditions can have a dramatic effect over time. In other words, very tiny changes can vastly change the outcome. In recent years, some scientists have begun the process of applying Chaos theory to the field of sports psychology. These scientists believe that a nonlinear approach to studying the behavior of athletes and the conditions in a sport can assist coaches to better determine how to prepare players to be successful. They base their work on three basic concepts:
(1)All complex behaviors follow simple laws that determine the behavior.
(2)All groups of behaviors, no matter how random or unpredictable they may appear, are -- in fact -- operating according to an orderly pattern, once all of the variables are understood.
(3)All groups of behaviors are incredibly sensitive to initial conditions, so that even the smallest of changes in those conditions will greatly affect the outcome.
So once again, what does this have to do with football and the Broncos? Let's take a look at a sports example, by comparing the linear, and the Chaos theory approaches to the Broncos.
The linear way of analyzing the Broncos would be to look at the Broncos as a complete team. Each individual player brings to the game his own, very specific skill sets. Those skill sets vary from position to position, and even slightly from player to player. Each of these skills can be assigned a value. By adding up all of the values for each player on a team, we could derive a total score for the team. Some fantasy football systems do this using yardage. One system I saw assigned skill position players points based on the yards they amassed. In this system, the fantasy team owner activates players on game day according to the criteria of wanting the players most likely to roll up lots of yards. Unfortunately, those who picked Eddie Royal for their teams under this system, based on his 2008 productivity, were sadly disappointed by his contributions in 2009.
Another linear system is the one that I designed to try to predict the winners each week in the 2009 NFL season. My system basically looked at Points For/Against, W-L Record, Conference/Division/Road/Home Records (as appropriate), and the current win/loss streak. Based on this linear system, I predicted that Denver would beat Baltimore 42-19 in week 8. Sadly, this was not the case as the Ravens gave the Broncos a sound thumping 30-7.
Still another example of applying linear thinking to the Broncos would be to look at the statistics for Robert Ayers in 2009. If we go to the player page for Ayers on nfl.com's website, we find that he had 14 tackles, 5 assists, no sacks, no interceptions, no forced fumbles and 2 passes defensed. Not a particularly impressive resume for the 18th overall pick of the 2009 draft. This had led some analysts to contend that Ayers is a "bust."
All three of these examples show that there are limitations to the linear method of analyzing behavior and performance in football. There were factors that were not accounted for in any of the three linear systems mentioned above. Fantasy systems struggle to be able to deal with variables like the play of the offensive line, or how one player can act as a decoy to open up another player. My points/record based prediction method failed to account for such things as motivation, and injuries. In fact, it was only correct about 50% of the time -- I could have achieved the same results by simply flipping a coin. The statistical review of Ayers -- as has been pointed out in other posts here at MHR -- fails to account for the times that his pressure from the outside forced the opposing to team to shift their blocking assignments, thus making it easier for Dumervil to get to the QB, or for the QB to hurry his throw. The play-by-play records as presented in the Gamebooks available from nfl.com are an example of a linear analysis of a game. Motivation is another variable that cannot be easily factored into a linear model. Conflicts between players and players or players and coaches do not fit into linear systems well. How many of us think that Tom Cable's alleged attack on an assistant coach did not have an affect on how well the coaching staff was able to prepare for the next game?
Consider these two drive examples from the Denver-Oakland game in week 15: this was a game that Denver was expected to win easily. The Broncos were 8-5, were playing at home, and had defeated the 4-9 Raiders 23-3 in Oakland. Linear thinking predicted a Denver win. This did not happen: leading 19-13, Denver took control of the ball with 3:59 left in the game:
1-10-DEN24 (3:59) K. Moreno up the middle for no gain (W. Joseph).
Timeout #2 by OAK at 3:52.
2-10-DEN24 (3:52) (Shotgun) K. Orton sacked at DEN15 for -9 yards (G. Ellis).
Timeout #3 by OAK at 3:46.
3-19-DEN15 (3:46) (Shotgun) K. Orton pass incomplete short left to L. Jordan.
4-19-DEN15 (3:41) M. Berger punts 59 yard to OAK26, Center-L. Paxton. J. Higgins to OAK38 for 12 yards (J. Barrett).
1-10-OAK38 (3:29) (Shotgun) J. Russell sacked at OAK25 for -13 yards (V. Holliday). FUMBLES (V. Holliday), recovered by OAK - C. Carlisle at OAK25. C. Carlisle to OAK25 for no gain (R. McBean).
2-23-OAK25 (2:44) (Shotgun) J. Russell pass incomplete deep middle to L. Murphy (A. Goodman).
PENALTY on DEN - A. Goodman, Defensive Pass Interference, 32 yards, enforced at OAK25 - No play.
1-10-DEN43 (2:38) (Shotgun) J. Russell pass incomplete short right to C. Schilens (R. Ayers).
2-10-DEN43 (2:31) (Shotgun) J. Russell pass incomplete short middle to L. Murphy (A. Smith) [D. Reid]. OAK-J. Russel was injured during the play.
3-10-DEN43 (2:26) (Shotgun) J. Losman pass incomplete short middle to L. Murphy (V. Holliday).
4-10-DEN43 (2:22) (Shotgun) J. Russell pass short middle to T. Stewart to DEN32 for 11 yards (W. Woodyard).
TWO MINUTE WARNING
1-10-DEN32) (2:00) (Shotgun) J. Russell pass short middle to T. Stewart to DEN23 for 9 yards (W. Woodyard).
2-1-DEN23 (1:18) (Shotgun) J. Russell pass short left to C. Schilens to DEN10 for 13 yards (A. Goodman).
Timeout #2 by DEN at 0:59
1-10-DEN10 (0:59) (Shotgun) J. Russell pass incomplete short right to J. Higgins (C. Bailey).
2-10-DEN10 (0:55) (Shotgun) J. Russell pass short right to C. Schilens to DEN6 for 4 yards (A. Smith)
PENALTY on DEN-W. Woodyard, Illegal Contact, 5 yards, enforced at DEN10 - No Play.
1-5-DEN5 (0:45) PENALTY on OAK-C. Green, False Start, 5 yards, enforced at DEN5.
1-10-DEN10 (0:45) (Shotgun) J. Russell pass incomplete short right to L. Murphy (D. Reid).
2-10-DEN10 (0:39) (Shotgun) J. Russell pass short middle to C. Schilens for 10 yards, TOUCHDOWN.
This presentation allows us to see what happened, and even why -- ill-time penalties, inability to keep the drive moving, etc. What it doesn't tell us, is how Oakland was able to pull off this upset.
The Chaos theory approach to this same problem -- predicting an outcome of a football game -- would take into account these additional, often overlooked or discount variables, such as: team chemistry, injury status of players, location of the game, weather, player moods, how individual skill sets are manifested, etc. Tendencies and trends would be noted -- such as, in an away game, in frigid weather, team A runs to the right tackle 65% of the time, out of a one back set, with player #82 lined up on the right side.
Including as many of these variables as possible better prepares a team to counter the opposition. In essence, Chaos theory stipulates that since even the smallest of changes in the initial conditions can cause radically different outcomes, the better your grasp of all of the variables affecting a situation, the more likely you are to discern an underlying pattern, the better you will be able to prepare for your opponent and the better you will be able to predict the outcome.
A Chaos approach to the Denver-Oakland game mentioned above, would look beyond the what and why, and attempt to discern how Oakland pulled off their upset. It would move beyond simply looking at the offensive plays vs the defensive plays. It would look deeper than the simply the play result. For example, on the first play listed:
Denver, 1-10-DEN24, Moreno had a run up the middle for no gain.
When the game film is looked at closely, one thing leaps out: The Broncos lined up in a two RB, two TE formation with Marshall wide right. Whereas the rest of the linemen set up in a 3-point stance with one foot back, Daniel Graham set himself in a 3-point stance, with his feet side-by-side, a shoulder width apart. All of the linemen including Graham, except Hochstein blocked their defenders to the left. Hochstein pulled and raced to the right side of the line. All of the linemen, except Graham pushed their targets off the line of scrimmage. Graham was stood up, and his target pushed the TE back against the line of scrimmage. The defender was further able to spin into the hole that was supposed to open up between Graham and Hochstein. From that flat-footed stance, Graham was unable to achieve leverage on the defender.
Further, when we look at Oakland's touchdown pass:
2-10-DEN10 (0:39) (Shotgun) J. Russell pass short middle to C. Schilens for 10 yards, TOUCHDOWN.
We see that Alphonso Smith had cheated up close to the line, directly in front of Schilens, and after the snap attempted to bump the TE to throw off the timing. Unfortunately, Smith had set himself flat footed, and did not move forward to initiate the contact. Schilens was able to force the smaller CB away from the line of scrimmage, and into another Oakland receiver who was sprinting straight up the field, as Smith and the other receiver bumped, Schilens made an abrupt cut to his left, and Smith was not able to clear from the contact with the other receiver in time to close and make a play.
It is these sorts of variables -- lining up flat footed to throw a block, or make a bump -- that a Chaos theory approach would attempt to identify, and thus allow the coaches to rectify. No factor would be too small to be considered.
Now, consider these factors: Can anyone tell me what Josh McDaniels' major in college was? If you answered "Mathematics," give yourself a pat on the back. McDaniels was a math major in college. He went on to become a fellow staff member with one Ernie Adams, a man who was well versed in the use of mathematical analysis. He was mentored by Bill Belichick (and possibly Adams), a man who had ties to the US Naval Academy and who -- along with Adams -- has been described as approaching football with a "war college" mentality that attempts to account for as many variables as possible, of examining as many options as possible in an attempt to provide a solution to each thing the opposing team might attempt. It really does not seem like all that much of a stretch that McDaniels would choose to apply that mathematical background, and the things he would have gleaned from Adams and Belichick to his own planning. Considered in this light, many of the things surrounding McDaniels' tenure in begin to make a weird sort of sense:
1)Why his interview with Bowlen reportedly lasted six hours.
Could it have been that McDaniels was providing Bowlen with a detailed analysis of the types of variables accounted for by a Chaos theory approach, along with the logical outcomes of those variables, and what changes would be need to break out of a pattern of 9-7, 7-9 and 8-8 seasons -- three years in which the Broncos lost 4 out of the last 6 games of each season?
2)McDaniels' attention to minute details.
I remember watching him giving instructions to players during a mini-camp. He wasn't talking about the play being run -- he was instructing the QBs how to position their hands for the snap, describing the tone, volume, and rhythm to be used in calling the cadence. He was seen directing a WR on how to position his body in order to make the necessary cut on a route. A more recent example can be found in McDaniels' analysis of Tim Tebow's throwing motion, and his contention that what was wrong with Tebow was not to be found in what Tim was doing with his left hand/arm during his windup and delivery, but rather what Tebow wasn't doing with the right side of his body.
3)McDaniels insistence on changing the culture of the locker room.
The building of a culture of team and confidence in which each player becomes dedicated to playing, not for himself, but for his teammates, is an essential part of what McDaniels is trying to do. This represents a change at the most basic level of the team and can have a tremendous impact on team chemistry, and thus on team success.
4)McDaniels' draft choices.
These may well have been made more to change some initial condition or variable which needed to be addressed, but which was not immediately discernible to the average fan or person looking in from the outside. He could well have been following neither the Best Player Available approach, nor the Fill a Need approach to the draft. He may have been aiming for a "change the initial conditions" approach. It is appearing more and more likely that McDaniels may have been targeting Tebow from the moment he was hired to be the Broncos' head coach.
If all of this is true, it will take more than a single season or three to show whether or not such an approach can pan out. If we look at the example set by Belichick, Adams and the Patriots, I would suggest that the answer is yes it can and will. It also makes me wonder if McDaniels' reputed claim that his Broncos are going to revolutionize the game of football, might not have as much to do with what goes on off the field as much as it does with what goes on on the field. The revolution may cover not just the offense, defense or special teams. It may start with how you build your locker room, how you talk about what you're doing, attention to everything from nutrition -- anyone recall how McDaniels retooled the cafeteria to address the issue of weight loss by the players during the 2008 season? -- to body positioning, to the pictures on the wall in the offices. The interesting thing about Chaos theory is that it focuses upon identifying as many variables as possible, determining how they interact, and from that identifying the underlying order that will have the greatest affect upon the outcome. The greater the number of initial variables successfully addressed, the greater the likelihood that a consistently successful and competitive team can be fielded.
My thanks to the following sources: