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When early computers and video game consoles first entered the market, they were designed with limited functions. One major function that has been present since the beginning is performing simple calculations. With numbers being calculated, video game designers had a way of rewarding gamers by incorporating a point system; a way to keep score for early adopters to brag about their skills. From a simple scoring system like that seen in Pong to an RPG-like experience system, a way of rewarding gamers has evolved drastically since the creation of video games.
Many of the earlier video games introduced with consoles were based on pre-existing games people had created throughout history when technology wasn’t advanced enough for computers to keep score. Titles such as Pong, Baseball, Basketball, and Soccer were all based on previously existing sports that already had their own way of keeping score. While these titles have a similar design where two sides are competing to score in intervals of one, except for basketball where points are rewarded two or three at a time, other games were developed where hundreds or points would be accumulated contributing to a total score.

Asteroids is one such game, where points are gained for every asteroid destroyed. The goal with this game is to get as many points using only the limited amount of lives. Once all lives have been used up, the game is over and the total score is the only way of determining a difference in experience between gamers. This concept of a high score has been carried over to other genres such as puzzle games like Tetris and side-scrolling shooters like Gradius.
With the introduction of save data, video games started allowing characters to be controlled that would develop through gaining experience points. Experience points are gained by defeating enemies encountered throughout the game. By gaining enough experience points, characters level up which increases basic stats such as Attack, Defense and Speed. Instead of the game ending when the character gets defeated, progress can be continued with all the stats previously gained.
While early side-scrolling shooters focused on high scores, more modern first-person shooters have been incorporating an RPG experience system. Borderlands and Fallout 3 are examples of first-person shooters where gaining experience points is vital to progressing in the game. Without building a strong character, gamers will have a hard time defeating enemies of higher levels, no matter how much they have upgraded their weapons.

Since the creation of video games, performing basic calculations has always been a function that doesn’t seem likely to die anytime soon. Considering the kinds of calculations used to keep score in modern games, it is obvious that ways of keeping score have evolved. Whether evolution is believed by gamers, there is no denying that evolution exists within video games.
I agree that we have had new ways of keeping score, and I never really thought that experience points were score. But that's very interesting.
Achievements and trophies are a new way of scoring too. What they do is take the non-quantifiable experiential activities in video games and puts a score on them. Kind of like RPGs, but there is not that feedback loop of "scoring high -- improve performance -- score higher". Although it would be interesting to see if achievements do take on a Perks system. Would having a specific "Xbox Level" or "PlayStation Level" get you more out of a game as soon as it comes out of the box? We might be headed that way.