One of the game elements that's often misunderstood is the place of highscores. Ever since 1959 has game theory been rejected as the sole explanator for behavior contingent to points gained after an action.
The problem can be detected easily using a model of limited effects, as used in communication science.
"Who says What to Whom through Which channel with What effect?"
Behavioral psychologists mostly use very simple models that allow them to expect behavior after a certain stimulus. But these models will always fail to predict reactions of first introduction to a stimulus like a game and learning behavior thereafter, because our environment is complex and we don't do everything just for arousal (what use would such a big brain be). Still our social worlds are grey, so even behaviouristic prediction models can predict a percentage of the outcome of actions.
Awarding points to players is one such problem. Mostly points are rewarded after success in a game (task contingent), or after taking a gamble (risk contingent). I will only talk about the task contingent point rewards here. These points add as a player progresses in the game. Some players see these points as rewards for their action and are driven by it to play more and more. A lot of games reward players early on to stimulate playing and make these points harder to get later in the game. Other players see these points as a proof of personal skill and use them to measure their own competence (maybe due to a lack of other feedback). While the first kind of player is theorized to be mostly aroused by the points and gaining points, the second kind of player is not aroused by the points but finds fulfilment in rising above the challenge to their skill. Even though you might think that both these types of players would end up equally skilled, the first type of player uses a lot of shortcuts and other tricks to increase their points without improving skill. The intrinsically motivated player is more likely to attain a higher skill level, and somehow also enjoyment. [Note to self; this enjoyment might be higher because reaffirmation of skill refers back to oneself and might be more fun because of that]
But how do you point your player in a certain direction? Well for a large part you are powerless as game designer, you can't manipulate the tendencies of people to be motivated by intrinsic or extrinsic factors and you can only try to invoke their interest with a cool demo or trailer. Still there is an important difference between the two kinds of players. Players that relate points to intrinsic motivation see them as informational. This informational character can be emphasized. You can couple points with automated vocal praising to stimulate intrinsic motivation, with quotes like "you're great", "multi-kill", "wow!" Points can also be divided into categories that are related to specific actions in a skill menu and it's also possible to simply award more points to skill related actions like in Skyrim. Anyway, the points have to be related to specific actions while gaining them with clear feedback to stimulate intrinsic motivation. Pinball machines for examples seem to give you points for everything but mostly do not convey specifics, like bumber x is 10 points ans bumber y is 100 points. However some will still remain motivated by the points themselve, humans are not machines. Luckily so, else we wouln't experience the joy of games.
White, R. W. (1959). Motivation reconsidered: the concept of competence. Psychological review, 66(5), 297.