Classical Football 101

Welcome to classical football 101.

This class will cover classical football from a historical perspective, starting with 17th century english village contests.

We will then cover the development of association football and rugby football, through to the emergence of the modern conceptualization of the game in the late 19th century, with particular emphasis on the role of the grid, the introduction of the "forward pass" and the role of equipment improvement in improving the game in the early 20th century.

We will cover the early Ivy League, in detail, and the post-World War II rise of "professional football", ending with the beginning of the modern game and the introduction of the "Super Bowl".

The class will consist primarily of lectures, focusing on the "east coast system".
There is no formal text, but I will be producing a "play book", which will be available for sale at a modest price from the University Book Store.
I will, of course, also post a summary of the basic concepts on the class website, and provide pointers to the MIT on-line series "Introduction to Modern Football", although that goes into considerably more depth than we will. You won't need to know all those trick plays for an introductory class, and I'm not all that sure about their exercise regime. Too intense, we'll take a more classical approach.

I assume most of you played High School Football, but if you didn't, no worries, you are all quite fit, otherwise you wouldn't be here, and I'm sure you'll soon catch on.
Although at least a full year of High School Football would be useful, ideally we expect two years of High School Football, not that it is a formal prerequisite.

I gather the Physical Education department has changed its curriculum and rather than starting off with the traditional strength and speed training is doing a more modern approach, starting with "analytic meditation" and "the topology of yoga", but their sophomore series on applied physical methods is really rather good, and will serve you well for "Modern Football 201/202" next year, and I'll introduce any physical education techniques you actually need in class: just remember "lift with the knees", eh? Heh.

There is an associated mandatory practicum, and I am happy to say the department has given us four part time coaching assistants. Now, they are all quite busy as they are in pre-season training camp for the Steelers, but they know a lot, and they were students just last year, and they will be running once-a-week 40 minute "exercise classes", you will be assigned to sections. Remember there are 35 of you per section, so you're really on your own there.
The coaching assistants also run the practicums, each section will meet every other week for a hour and a half. Since this is a historically based class we will do the first four weeks old style - no pads, and then we will do four weeks of scrimmage with original early 20th century gear, the Presidents Office very generously got us a full set of leather helmets! Just like those used at Notre Dame. That will be a lot of fun. The President is a firm believer in a traditional approach providing a historical perspective.

There are three in-class mid-terms, you can drop one, they'll consist mostly of class material, some rapid push-ups and chin-lifts (hint!) and of course theoretical questions. I'll give examples in class: like
"it is 3rd and long, you're on the 37 yard line and you're down 4 with 46 seconds to go" do you a) punt, b) kick a field goal, c) run a full back up the middle or c) split three left and go long?

Ok, there will be a final: the final is 30% of your final grade, and 30% from the mid-terms the rest is lab and homeworks. The final will consist mostly of 40 yard sprints and bench presses. I know we don't cover sprints until the final two weeks, but that way the technique will be fresh in your legs at the final. You should have done strength training in you concurrent Physical Education classes. (What? I'm not responsible for PhysEd changing the order of their curriculum, I mean, come on, it is just bench presses). We do "curve" the final grade, so it is not how fast you run, it is how fast you run compared to your teammates...
No we're not going to do "throwing" and "catching" in this class, that comes in Football 201. Well 202 really, 201 focuses on the hand-off and kicks.
Option runs? Well, aren't we ambitious. Option pitches and sweeps are 4xx level optional classes, for majors only. If you last that long. First two years we do "up the middle and cloud of dust", you need to learn the basics before you start throwing. As I said, this class takes a historical approach to teaching football. Basics first.

Now, we are going to run an informal "football careers" seminar in paralllel. This is always a veeery popular seminar, we'll have free soda and pizza.
You have to realise that only a small percentage of you will make the pros.
Many of you won't even get post-graduate coaching assistantships or be called to camp.
But, you will all be very fit, and be able to talk very authoritatively to your buds, oops and "girlfriends" - sorry ladies, heh - about the game, over beer and stuff. Heh. Don't tell the President I said "beer". Wink-wink.

We will cover alternative careers, there are lots of options. Well paid. Socially respectable: bodyguards, used car salesmen, marketing managers, government service, sports announcers, and, of course, coaching.
And, may I say that there is always a demand for high school coaches, we're not just training people to be college or professional coaches. A high school football coach plays a very important role, they are respected members of the community and are critical in spotting and developing new talent and keeping the sport alive among our youth.
The better AAAA districts don't pay badly either, and the season is short. Ok, the smaller district might have you coach baseball as well, or even soccer, but a job is a job, and its not like you'll have to teach math!

Any questions?

Ok, so - most footballers agree that football, as we know it, started in the village of Woolsthorpe in England, when some lads, exiled from their schools in the Home Counties during the Great Plague, started a weekly game of "kick the bladder".
This is of course apocryphal, but may contain an essential truth, there are some records of a series of games between Woolsthorpe and Colsterworth in the summer of 1666, where, according to local legend a local lad, Isaac, rumoured to have been a rower at Cambridge, became legendary for his ruthless plunges to the Colsterworth touch line, "smashing through their Hookers like a giant rampaging against a team of dwarves", as a local scribe recorded.
It would appear though, that this is more the first formal historical record of a more ancient and well established Northern English game. Possibly records of earlier games were destroyed by the Puritans, since games were traditionally played on sunday, after, or even instead of, going to church. Players also reportedly wore colourful uniforms identifying the village of their origin, which would have offended the sensibilities of the Puritans.
In either case, Pepys' diaries of the Wolsthorpe games gives us the first known historical record of actual games, with scores, players and by inference the rules. Pepys of course assumed the reader would be familiar with the rules, another indication the Games had a more ancient origin. It is from Pepys that we have the legend of Coach Wren, and the hints of the "Invisible College" Association from which developed the later Football Associations.

Now, let us consider the standard Northern English pitch in 1666. Assume, for simplicity, a spherical ball...


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You could have Paterno guest lecture about his days coaching the Woolsthorpe PlagueDogs to the title in 1675....

Rutgers - The Birthplace of Intercollegiate Football

Rutgers University and its neighbor, Princeton, played the first game of intercollegiate football on Nov. 6, 1869, on a plot of ground where the present-day Rutgers gymnasium now stands in New Brunswick, N.J. Rutgers won that first game, 6-4.

The game, which bore little resemblance to its modern-day counterpart, was played with two teams of 25 men each under rugby-like rules, but like modern football, it was "replete with surprise, strategy, prodigies of determination, and physical prowess," to use the words of one of the Rutgers players.

William Leggett

William J. Leggett, captain of the Rutgers team who later became a distinguished clergyman of the Dutch Reformed Church, suggested that rules for the contest be adopted from those of the London Football Association. Leggett's proposal was accepted by Captain William Gunmere of Princeton, who later became Chief Justice of the Supreme Court of New Jersey.

At 3 p.m. on that memorable afternoon, the 50 combatants and about 100 spectators gathered on the field. Most of the assemblage sat on a low wooden fence and watched the athletes doff hats, coats and vests and use suspenders as belts. To distinguish themselves from the bareheaded visitors, 50 Rutgers students, including players, donned scarlet-colored scarfs which they converted into turbans....

I think that must win some sort of award for one of the silliest things you have written to date.

By Brad Holden (not verified) on 21 Apr 2008 #permalink

Very nice...and I would expect the class to be taught in the finest, most modern facilities available.

So, is there a class dedicated to Canadian football?
Likely would not be a well attended lecture ...

By Pat Durrell (not verified) on 21 Apr 2008 #permalink

Pardon the snark, but I think there is more to learn from football than countless hours staring into space, let alone traveling through it!

By onkel bob (not verified) on 21 Apr 2008 #permalink

Of course.
This is why, for non-footballers, we offer:

"Balls and Stars: The Universe of Football 001"

It covers a lot of material. The history of football, rules of the games, a football video game, and a mandatory one night pick-up game.
Very popular to satisfy certain quantitative general education qualifications.
Doesn't actually teach you how to play football, but gives you a real good feel for what the college players go through, taught, some of the time, by a real pro who has seen it all.

Preliminary Notes on Football Physics (or, by duality, Phootball Fysics)
Professor Jonathan Vos Post

Bill Shankly, the former manager of Liverpool football club, once said: "Football is not about life or death. It is more important than that."

"Physics is the branch of science that deals with the physical world. The branch of physics that is most relevant to football is mechanics, the study of motion and its causes [and momentum, mass, drag, and the mysterious Wave-Particle duality].... Football provides some great examples of the basic concepts of physics -- it's present in the flight of the ball, the motion of the players and the force of the tackles. In this article, we'll look at how physics applies to the game of football." [Freudenrich].

Regarding tackles: "The average football sack can produce a bone-shattering 1600 lbs of force.... [as deduced from the] Head Impact Telemetry System, which employs sensors and wireless transmitters in helmets. 'We see 100-g impacts all the time," says Stefan Duma, director of the university's Center for Injury Biomechanics, 'and several over 150 g's.'" [Higgins 2007].

Let us not sweep under the astroturf the connection between inertia and mass: "A football moving through the air has inertia--the universal tendency of objects in motion to remain in motion (and objects at rest to remain at rest). If not for gravity and air resistance, it would simply sail away in a straight line and never come down." [Willett 2001]. Of course, modern fans know that there are no straight lines in Football -- only geodesics.

"Many fans will remember the free kick taken by the Brazilian Roberto Carlos in a tournament in France [summer 1997]. The ball was placed about 30 m from his opponents' goal and slightly to the right. Carlos hit the ball so far to the right that it initially cleared the wall of defenders by at least a metre and made a ball-boy, who stood metres from the goal, duck his head. Then, almost magically, the ball curved to the left and entered the top right-hand corner of the goal - to the amazement of players, the goalkeeper and the media alike.... Apparently, Carlos practised this kick all the time on the training ground. He intuitively knew how to curve the ball by hitting it at a particular velocity and with a particular spin. He probably did not, however, know the physics behind it all." [Physicsworld 1998].

"The first explanation of the lateral deflection of a spinning object was credited by Lord Rayleigh to work done by the German physicist Gustav Magnus in 1852. Magnus had actually been trying to determine why spinning shells and bullets deflect to one side, but his explanation applies equally well to balls. Indeed, the fundamental mechanism of a curving ball in football is almost the same as in other sports such as baseball, golf, cricket and tennis." [op cit, see also Mehta]. The analysis of spin, and spinors is beyond the scope of this Note.

As to tackles, heading, and "boot to the head" dynamics: "The New England Patriots have been using a retainer like mouth guard designed specifically to reduce concussion. In fact they have had only two in the last two seasons. Both players were using a non-jaw-positioning mouth guard. The Colts have had over twenty in the same time span." [the video archive of the Patriots is unavailable for further study, due toe Heisenberg effect of too-close an observation of signals in the game arguably affecting the game and even the meta-game].

But why tackles? "The tackler's goal is to rob the runner of his momentum. The first way to do that is to hit the runner directly. If he's moving fast enough and weighs enough, he'll win the ensuing transfer of momentum, absorbing the runner's momentum and passing on enough momentum of his own to knock the runner down. The second way to get rid of the runner's momentum is to transfer it to the ground by knocking the runner's feet out from under him. The third method is to knock the runner out of bounds. This is often the easiest choice because, while a runner with a great deal of momentum is hard to stop, he's easy to steer. A push redirects his momentum toward the sidelines. The runner has to push at the ground to correct his trajectory. If he's close to the sidelines, he probably doesn't have time--and ends up transferring his momentum to a photographer, cheerleader or TV camera." [Willett 2001]. Again, the interaction of Football star with TV camera was analyzed by Heisenberg. Nor, by "star", do we mean to exclude Black Holes and other non-Classical bodies.

"After a hard day of calculations about oscillating bodies, it's nice to watch some oscillating bodies" [Feynman 1973]

"A long bomb is thrown both up into the air and very hard to maximize the distance it travels. A short bullet pass is thrown almost horizontally, because gravity has little time to work on it." {insert slides here of the Bullet Galaxy, with accompanying caption on dark matter and gravity}

However, the elementary treatment conceals some interesting speculations in modern Unified Sports Theory.

First, "Assume, for simplicity, a spherical ball..." -- this neglects the supersymmetry between the two basis shapes.

As wikipedia summarizes:

A football is a ball used to play one of the various sports known as football. In the distant past, crude balls such as an inflated pig bladder were used, now high-tech balls are designed by teams of engineers to exacting specifications. Each code of football uses a different ball, though they all belong to one of two different basic shapes:

1. a sphere: used in Association football (soccer) and Gaelic football;
2. a prolate spheroid ('oval-shaped'):
* either with rounded ends: used in Rugby football and Australian rules football,
* or with more pointed ends: used in American football and Canadian football [As for who invented football, it's believed to be Walter Camp. Canadians love to claim they invented American Football].

The precise shape and construction of footballs is typically specified as part of the rules and regulations.

As we know [Hobill 1991], the "mixmaster" model of the football cosmos assumes oscillation between oblate and prolate, with the spherical merely a local maximum of volume. The Bianchi IX Mixmaster cosmology is treated as a non-linear dynamical system and the entire spectrum of Lyapunov exponents is calculated from a numerical integration of the full Einstein equations. The behaviour of the solutions is studied for times close to the initial and final singularities as well as for times near the point of maximum expansion. It is demonstrated that the methods of numerical integration must be chosen carefully if a vacuum spacetime is to be simulated in a self-consistent manner. In addition it is shown that previous results pointing to chaotic behaviour are due to inaccurate numerical methods and/or the introduction of non-vacuum behaviour. We return to expansion later (inflation) and the non-vacuum (pressure).

"When you throw [or, by supersummetry, kick] a football across the yard [meter] to your friend, you are using physics. You make adjustments for all the factors, such as distance, wind and the weight of the ball. The farther away your friend is, the harder you have to throw the ball, or the steeper the angle of your throw [kick]. This adjustment is done in your head, and it's physics -- you just don't call it that because it comes so naturally." [Freudenrich].

Second, this 3-dimensional model misses the point, in terms of point-set Topology. Higher dimensional Football begs the question: what is the dimension?

Third, Most modern footballs (soccerballs) are stitched from 32 panels of waterproofed leather or plastic: 12 regular pentagons and 20 regular hexagons. The 32-panel configuration is the spherical polyhedron corresponding to the truncated icosahedron; it is spherical because the faces bulge due to the pressure of the air inside. The first 32-panel ball was marketed by Select in the 1950s in Denmark. This configuration became common throughout Continental Europe in the 1960s, and was publicised worldwide by the Adidas Telstar, the official ball of the 1970 World Cup.

The question whether the cosmos has dodecahedral (or, dually, icosahedral) symmetry is still open, pending higher resolution measurements.

Older balls were usually stitched from 18 oblong non-waterproof leather panels, similar to the design of modern volleyballs and Gaelic footballs, and laced to allow access to the internal air bladder. This configuration is still common.

In American or Canadian (Rugby-derived_ Football, Four panels or pieces of leather or plastic are required for each football. After a series of quality control inspections for weight and blemishes, workers begin the actual manufacturing process.

Two of the panels are perforated along adjoining edges, so that they can be laced together. One of these lacing panels receives an additional perforation and reinforcements in its center, to hold the inflation valve.

Inflation is the dominant theory of the origin of Football, in which the game expanded faster than the speed of light, thus accounting for the flatness of the football field (or pitch), which is formally treated by Conformal Field Theory.

Each panel is attached to an interior lining. The four panels are then stitched together in an "inside-out" manner. The edges with the lacing holes, however, are not stitched together. The ball is then turned right side out by pushing the panels through the lacing hole. This does not work for non-orientable manifolds, such as Klein Bottles, which, to be sure, make magnificent trophies, if it were not for champagne leakage through quantum tunnelling.

A polyurethane or rubber lining called a bladder is then inserted through the lacing hole.

Polyvinyl chloride or leather laces are inserted through the perforations, to provide a grip for holding, hiking and passing the football.

This leads to the question: How many laces are on a football? Answer Four, unless you're counting the stitching around the laces. Should we count that or not? Another source of so far fruitless debate, although there are some promising developments in fractal stitches (which involved Knot Theory beyond the scope of this Note).

Before play, the ball is inflated to an air pressure of 12.5-13.5 psi (86-93 kPa) (although this measurement depends on inflation assumptions, and a definition of "air" as opposed to, for example, primordial hydrogen/helium mixtures, or aether). The ball weighs 14-15 ounces (397-425 g) (with a caveat as to missing matter and dark football).

If the lace of a football is too prominent, it interferes with the natural release of the ball off the fingertips. If the ball's lace is too minimal, it does not provide an anchor for the ring finger (and the small finger if so applied). The Baden lace has been designed with precisely the optimal thickness, height and spacing. Additionally, as competitors use slick composite material for their laces, Baden's exclusive textured material provides the best grip under wet conditions.

The issue of stitching leads us to the next point. Compared to the three-dimensional ball moving as a function of time (in Minkowski space or ant-deSitter space), the two-dimensional field (or pitch), the laces are one-dimensional.

However, the String Theory of Football has, despite some beautiful mathematics (out of scope in these Notes) failed to make any testable predictions. Although the endless arguments about which was really the best team in any given season have given rise to the Landscape model of the many Worlds, Many Games hypothesis. Out of 10^500 possible seasons, it is considered likely that your team will win... next year. Of course, that is based on the highly controversial Anthropic Football Argument.

"So, what to do? The answer comes from a wartime collaboration between economist Oskar Morgenstern and mathematician John von Neumann. They produced a 'theory of games,' which mathematically analyzed situations of strategic interaction --that is, any situation where participants have to take into account the other side's responses. A free throw in basketball is not a strategic interaction, but a soccer penalty is.... But rather than aiming to help footballers or gamblers, von Neumann and Morgenstern believed that game theory could illuminate anything from pay negotiations to waging war.... Ignacio Palacios-Huerta, an economist at Brown University, found that individual strikers and keepers were, in fact, master strategists. Out of 42 top players whom Palacios-Huerta studied, only three departed from game theory's recommendations -- in retrospect, they succeeded more often on one side than the other and would have been better altering the balance between their strategies. Professionals such as the French superstar Zinedine Zidane and Italy's goalkeeper Gianluigi Buffon are apparently superb economists: Their strategies are absolutely unpredictable, and, as the theory demands, they are equally successful no matter what they do." [Harford 2006].

And since it all comes down to Economics, even in putatively Amateur venues, I've got to get back to work now. There's a Football Pool at work, and I've got to make an optimum prediction. "Never in the face of human conflict has so much been owed by so many to so few." These geniuses do not just think with their feet. Or meters. Or Angstroms.

Almost all theorists and experimentalists agree on one thing. Football is more than a game. The same year that John Forbes Nash, Jr., was born, 1928, John von Neumann showed that in simple games like checkers or football, where one player's gain is the other's loss.

And if I stop this Note right here, we have a win-win situation known as a Nash Equilibrium. Goooooooooal! Or touchdown. Whatever.


Anon, Baden Sports - Football.

C. B. Daish, The Physics of Ball Games , London: The English University Press, 1972.

Richard Feynman, Random Observations at a Pasadena Strip Club, 1973.

Craig Freudenrich, Ph.D., "How the Physics of Football Works", Howstuffworks.

S. J. Haake (ed), The Engineering of Sport, Rotterdam: A A Balkema, 1996.

Tim Harford, "World Cup Game Theory: What economics tells us about penalty kicks",
Slate, Posted Saturday, June 24, 2006.

Matt Higgins, "Football Physics: The Anatomy of a Hit -- Researchers are using new tools to study the science of a football fundamental: the tackle", Popular [Classical] Mechanics, February 2007.

D Hobill, D Bernstein, M Welge and D Simkins, The Mixmaster cosmology as a dynamical system, 1991 Class. Quantum Grav. 8 1155-1171 .

R. D. Mehta, Aerodynamics of sports balls, Ann. Rev. Fluid Mech. 17 151-189, 1985.

Mehtamathematics, and the Metagame, The physics of football, 1 June 1998.

Wikipedia, Football (ball).

Edward Willett, "The Physics of Football", Regina (Saskatchewan) Leader Post and Red Deer (Alberta) Advocate, Posted May 18, 2001.

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