The term "football" referred to a variety of games prior to the 19th century. Some of these, like soccer, were kicking games where you weren't allowed to touch the ball with your hands or run with it. Others were running games, where you were allowed to use your hands. Rugby was one of these running games, and what we Americans call soccer was one of the kicking games.
An apocryphal story of Rugby's origin states that in 1823, a player named William Webb Ellis, frustrated in the midst of a game of football being played at Rugby College, picked up the ball and ran with it. In the interest of enforcing the rules, the other players tackled him. The image I've included at right is a statue of William Webb Ellis located at the junction of Lawrence Sherrif Street and Dunchurch Road next to the Rugby school and across the street from the Webb Ellis museum (from RugbyFootballHistory.com).
Some thus point to William Webb Ellis as the originator of the sport of Rugby, but seeing as there's no documented evidence of Webb Ellis ever performing that feat, the story has remained merely apocryphal. However, that hasn't stopped rugby aficionados from around the world hailing William Webb Ellis as the founder of the sport. Heck, the international committee that governs rugby named the rugby world cup title the "William Webb Ellis Trophy."
Why, you might be wondering, am I talking about rugby when this post is supposed to be about American football?
Well here's the problem -- American football as we know it today didn't properly exist until Walter Camp came around in the 1880s. Prior to that, elite Northeast colleges like Rutgers, Yale, and Harvard all played variations on either soccer or rugby ("kicking games" or "running games"). Rugby codified its rules in 1845, and cross the Atlantic to Canada, where it would eventually evolve into Canadian football. Canadian football had its own influence on American football, specifically through the Harvard-McGill game of 1874.
At that match, the Harvard players saw the squad from McGill University throwing the ball to each other during warmups. Harvard called a brief conference and they and McGill decided to play one running game and one kicking game. The Harvard team enjoyed the running game so much that they incorporated the system into their day-to-day playbook.
It's Harvard, in fact, that we have to thank for American football in its current form. Prior to the Harvard-McGill game of 1874, four prominent schools in the Northeast -- Columbia, Yale, Princeton, and Rutgers -- codified the first set of "football" rules in the United States. This game forbade running with the ball or touching the ball with your hands. That game became soccer.
Harvard didn't like this, or that the rules forbade aggressive physical contact on the field. The obstinacy of the Harvard Crimson led to first the game against McGill, and then the Harvard-Yale game of 1875, in which players were allowed to carry the ball. Those two games -- Harvard vs. McGill and Harvard vs. Yale -- set American football off and, well, running.
Even though interest in collegiate football spread across the Northeast and the rest of the United States, there was still a major problem. The rules changed from game to game, depending on the teams and what they agreed to. Some teams played with 15 men on the field, while others put 11 players on the field. This variation in rules across all the various teams lead to the founding of the Intercollegiate Football Association in 1876. The aim of the association was to codify the rules and make them consistent across all colleges with football teams.
Walter Camp (photo below from WalterCamp.org), a former Yale player, was in attendance at those meetings. Between 1880 and 1883, Camp introduced a laundry list of innovations as coach of the Yale football team. From HistoryofFootball.net:
"Between 1880 and 1883 this coach of the Yale football team came up with several major adjustments to the game: an eleven player team, a smaller field, and the scrimmage –a player handing the ball backward to begin the play. An even more important alteration, if the offensive team failed to gain five yards after three downs they were forced to surrender the ball. Camp also established the norm of a seven-man line, a quarterback, two halfbacks, and a fullback. Thanks to Walter Camp, football as we know it finally took shape."It's because of those innovations that Walter Camp is known as the Father of American Football. Without his influence, and that of Amos Alonzo Stagg, the Father of American Football coaching, we wouldn't now have the game we have today. Stagg himself also offered several innovations to the game.
"Stagg created a plethora of football firsts including the huddle, putting numbers on uniforms, the T formation, the punt formation and the end around. His is also credited with dreaming up famous “trick” plays like the hidden ball and the Statue of Liberty. Stagg invented several pieces of equipment still used in sports today including blocking sleds, tackling dummies and the batting cage for baseball." (SportsKnowHow.com)At last, on November 12, 1892, Yale All-American guard William Heffelinger became the first professional football player when a Pittsburgh football club paid him $500 to play against another team. Football clubs had sprouted all over the country by this time, and these clubs would eventually (through several intermediary steps) create the National Football League.
Answers.com) in the common players' uniform of the early 20th Century. As you can see, there was very, very little in the way of protection. American Football has always been an aggressive sport, and dozens of men died on field between the 1890s and 1905, when President Teddy Roosevelt ordered the fledgling football associations extant at the time to either make the game safer or he would outlaw it.
New rules required seven men to be on the line of scrimmage, which ended a common play known as the Flying Wedge. In the years after Roosevelt's decree, more players also opted to wear protective pads and helmets, thus further reducing injuries.
In 1920, at last, 11 football clubs banded together to create the American Football Association. The group elected famed player Jim Thorpe as its president, and sold franchises for $100 to anyone who wanted one. Two years later, with 18 professional teams in existence, the AFA changed its named to the National Football League. And the rest, as the cliche goes, is history.
You may perhaps be asking what this has to do with Steampunk. One of the things I've noticed a lot in fiction is that writers tend to ignore certain aspects of culture; sport is chief among these. Granted, we can't always work sports into our novels like J.K. Rowling did with Quidditch in the Harry Potter books; however, there's nothing that says a writer can't have a character mention a sport in passing. Like, for example, overhearing a conversation in a bar. That could work very much in the writer's favor for adding flavor to the world.
And also: imagine how cool a Steampunk variant of American Football might be. Clockwork robots rushing downfield with the ball tucked in their mechanical arms while engineers control them from high above the stadium, the roar of the crowd staring through their far-seeing glasses to slow down the action. Oh the possibilities to play with this are endless.
Besides that, if you write a story set in Boston in 1875, it would behoove you to mention the Harvard-McGill game as something of a crowd pleaser (which it very much was). Those are just my thoughts, however. You are, as always, welcome to your own.