Why is the player in the middle of I-formation called the fullback?

Question

From the names of the positions, I would assume that in an I-formation the order (from front to back) would be quarterback, halfback, then fullback.

This Image of the I-Form shows the fullback in between the quarterback and the running back, and the text from wikipedia says

Typically, fullbacks are larger in size than halfbacks and in most offensive schemes their duties are split between power running and blocking for both the quarterback and the other running back.

So I can see why this kind of player would line up where he does, as it enables him to block for the other running back. But why is he called the fullback?

Answer 1

Here's an attempt to layout the history of the position, and the time periods in which it changed. All of this information can be found here, although it's buried with all of the history of every other position as well. This question requires a good understanding of nomenclature, and I would encourage you to read the entire article in the link, especially the sections labelled "Age of Confusion" and "Making Sense of it All." As the article states:

The trend away from geometric naming of the offensive positions has led to considerable confusion

So here are the bullet points that help identify the evolution of the fullback position. The origin of the fullback was in 19th century rugby. Originally these positions were named "tends," but the evolution of the game created some new positions with new names.

As the game became more sophisticated, backs positioned at different depths (i.e. distances behind the forwards) were further differentiated into half back, three quarters (the fraction 3/4) back, and full back... It was the Irish nomenclature of quarter back, half back, and full back that came to North America for use in what was to become the dominant native form of football. The terms became hyphenated and eventually unhyphenated single words, "quarterback" (QB), "halfback" (HB), and "fullback" (FB).

In the early days of American football (around the beginning of the 20th century), the role of the fullback was altered. Instead of the position just indicating a position behind the line of scrimmage, it began to also identify the role and physical nature of the position.

Over time, the typically fast back who played fullback, on offense and defense, was replaced by a heavier one who presented a greater threat to run with the ball more or less straight ahead, and to tackle his opponent trying to do the same. For this purpose, the player tended to be placed closer to the line than previously—often as far forward as the halfbacks (the offensive backs then forming a letter T, sometimes called a "straight T", later to distinguish it from slight variants wherein other backs did not form a line perpendicular to that from the quarterback) or even farther forward. But the position kept being called "fullback".

In the 1960s, many non-professional teams lost the distinction between a halfback and fullback. The NFL maintained the nomenclature of halfback and fullback:

...the distinction between fullback and halfback was erased, each replaced by "running back" (RB). That term became popular during the 1960s as well, although even into the 1970s, some playing the pro set kept the HB-FB distinction... The distinction referred to the build of the players, the fullback being a stronger runner more or less straight ahead, and the halfback faster to attack the defense's flanks. However, on many teams there was no strong distinction between those backs, and since their major role was running with the ball, "running back" was most descriptive without maintaining a spurious geometric connotation that'd become outmoded by their lining up in different depth relationships.

This trend has continued on. The present day explanation of fullbacks:

[T]o this day many teams maintain the offense's fullback-halfback distinction... [S]ome formations have placed the heavy back even more starkly forward, to function as a blocker for the running backs.

There are a number of current NFL teams that do not have a full-time fullback in their starting lineup. The three with no fullback listed:

• New England Patriots
• Indianapolis Colts
• Detroit Lions

The four that have a hybrid fullback:

• Kansas City Chiefs (Peyton Hillis is listed as a RB/FB)
• Denver Broncos (Chris Gronkowski is listed as FB/TE)
• Chicago Bears (Evan Rodriguez is listed as a FB/TE)
• Seattle Seahawks (Michael Robinson listed as RB/FB)

In some instances, teams will line up a defensive lineman as a fullback:

In selected plays, some teams will have a defensive lineman report as an eligible receiver to line up as a fullback. Examples of such players who have been frequently used as situational fullbacks include Haloti Ngata, Vince Wilfork, and Isaac Sopoaga.

Answer 2

It all goes back to the beginning of the game.

Way back when, the Quarterback would be a quarter of a yard away from the line of scrimmage, the halfback would be half a yard away, and the fullback a full yard away.

Hence the name, Fullback.

Answer 3

Perhaps a better way of putting this question would be, "Why did football teams put the fullback in the middle of the (relatively new) I formation in contrast to his traditional role?"

The three types of "backs" (the offensive players behind the line of scrimmage) are the quarterback, half back, and fullback.

Besides their "traditional" positioning, one quarter, one half, and one full yard behind the line, the quarterback is the most versatile, insofar as he can either pass or run with the ball.

The job of the two "halfbacks" is to use speed to run to either side of the line, sometimes past the end (end run), sometimes behind the tackle (off tackle).The job of a fullback is to run through the center of the opposing line (if the quarterback determines that his threatened pass maneuvers have caused the opponents to weaken their defense). But he was held back in "reserve" because this was typically the least favored offensive option.

Starting about 50 years ago, one of the halfbacks would become a "flanker" who would outflank one of his ends on the line of scrimmage to become a "wide receiver" This created a so-called "strong" side, with the extra pass receiver. Defenses adapted to this change by "shifting" an extra man on the strong side.

The I formation was the standard counter to this new defense. The idea was to use the non-flanking halfback to run to the weak side (the opposite side to the wide receiver). To create a further numerical imbalance, the fullback would be used as a blocker for the halfback, instead of as a runner up the middle. That's why the fullback was inserted between the quarterback and the halfback in the I-formation.

Of course there were variations of this, if the defense "compensated" by moving a man back to the "weak" side. The fullback could be deployed to the strong side as a blocker for a "pitchout" to the halfback, or given the ball to run through the center, depending on how the quarterback "sized up" the defense. The i-formation was adopted because it gave the most flexibility to the offense.