Based on The Anatomy of a Game.
The current scoring rules weren't decided on all at once. They evolved over the years.
At the outset, football was played according to whatever rules the two teams agreed to. The first rules meeting was in 1876. Before this, there was no standard ruleset for the sport of football.
Initially, it was the students at Rutgers, Princeton, Yale, and Harvard who created rules that varied from a strictly kicking game to a game that allowed running the ball.
The first ruleset, created in Princeton in 1871, included these rules related to scoring:
- Games are played to to 4 of 7 goals (best of 7)
- No player shall toss or carry the ball
- Goalposts were 25 feet apart (kicking the ball through the goal posts was the only way to score)
Harvard drafted their own ruleset in 1872, based off of the Princeton/Rutgers rules. Theirs was closer to rugby, due to their Canadian connection with McGill University. Theirs allowed running and throwing:
- No player may run with the ball unless pursued by an opponent, and only then so long as pursued
- No player may pass or throw the ball unless pursued by an opponent
- Scoring was still only by kicking through the goalposts
Yale created a ruleset very similar to Princeton's, prohibiting picking up, throwing, or carrying the ball.
In 1873, Princeton, Rutgers, and Yale met to organize a standard ruleset. The outcome was a set of 12 rules. Out of those, these related to scoring:
- Games are to 6 goals. Goals are scored by the ball passing between the goal posts.
- No player shall throw or carry the ball.
In 1876, Princeton, Yale, Columbia, and Harvard met to further unify the rulesets (Harvard had not attended the previous meeting due to their commitment to a running/Rugby style of game). The outcome was 61 rules. Here is how they related to scoring:
- The rules defined punts, placekicks, and dropkicks
- Goalposts now were based on top of a crossbar 10 feet from the ground
- Goals are scored by any kick other than a punt that goes through the goalposts
- Matches are decided on a majority of touchdowns (touchdowns had a different meaning than today)
- A goal equals 4 touchdowns
- A touchdown is when a player on the ball on the ground in touch or in goal so that the ball is dead
- Players may run. If a player runs with the ball across the goal line and touches it down, it is called a run in.
- Backward throws were allowed.
- After a touchdown, the ball is brought out for an attempt at a goal (just like the extra point today)
- In these rules, the safety was not explicitly stated but it was called a touch-in-goal. A team that has touched down the ball in their own goal were to immediately kick it away. These did not count against the team.
In 1881, the safety was officially included in the rules, and counted against the team, but only in a tie-break situation:
- In case of a tie, [play more]. If the game still remains a tie, the side which makes four or more safeties less than their opponent shall win the game.
In 1882, safeties became part of the scoring, and the tie-break advantage switched from kicks to touchdowns:
- Four touchdowns takes precedence over a goal from the field (which is worth four touchdowns)
- Two safeties equals one touchdown
This was all part of an overall strategy to increase the pace of the game and eliminate stalling that occurred under the previous rules. Downs were also added at this time.
In early 1883, scores were first attached to the various ways of scoring:
- Safety: 1 point
- Touchdown: 2 points
- Goal after touchdown: 4 points
- Goal from the field: 5 points
Later in 1883, scores were further amended:
- Safety: 2 points
- Touchdown: 4 points
- Goal after touchdown: 4 points
- Goal from the field: 5 points
In 1887, scores became:
- Safety: 2 points
- Touchdown: 5 points
- Goal after touchdown: 1 point
- Goal from the field: 5 points
In 1904 and 1909, the goal from the field was reduced to 4, and then 3 points.
In 1912, touchdowns became worth 6 points.
That is the history. It was never a decision involving the current scoring system versus something dramatically different. They were all incremental changes, being made to encourage certain types of play.