The following might be controversial.
I propose a logical division of Olympic sports into two groups. It is very difficult to define a sport; I suppose I might use the
SportAccord definition, but the exact definition is beyond the scope of this entry.
Consider the set of competitive athletic activities, especially those that are in the Olympics. The activities can be divided into two classes depending on whether subjective evaluation directly influences the comparative metric. Enforcing rules is subjective (e.g. referees in team sports), but only indirectly influences the comparative metric like the score or whether someone is disqualified. Most sports have some officiating to enforce rules, and the spectrum of rule violations ranges from the almost unambiguous - like false starts or stepping out of your lane in track - to the arguable, like whether a foul occurred as in soccer or pass interference in American football. However, while subjective rule enforcements can change the state of the activity (which can in turn affect the score, e.g. if a goal or touchdown is rescinded, or race result if DQ), they do not directly affect the result metric. A referee cannot add 10 points to the score of a football team because it is his judgment that they deserve it.
In contrast, many sports have subjective judging - for example, gymnastics, figure skating, ski jumping. In these activities, judges directly influence the score. Many of these activities have hallmarks like the term "style points," the presence of non-functional ornamentation, music accompanying the activity, and strange hand gestures that are not functional.
This partition of the set of athletic activities isn't as perfect as I would like because of some ambiguity on officiating and can probably be contested. I would describe many of the subjectively scored activities as [athletic] "performances." Certainly figure skating, gymnastics and others are incredibly demanding athletic activities which require years of disciplined training, focus, etc. But objectively scored activities like basically all races and most team competitions are much purer and less ambiguous to me. Either you won the race or you didn't (if you followed the rules). They also are much less prone to "controversies" like the recent one out of the
Sochi figure skating competition. Even objectively scored (or indirectly-subjectively influenced) activities are not without complaint, as any search of "NFL referees" will reveal.
Subjectivity is inherently undesirable because it increases the uncertainty of the competition
given the set of events from the activity. The latter case can be somewhat rectified by simplifying rules and adding technology - false start sensors, instant replay - to try to get the call right. The subjectively scored case can sort of be rectified by defining deductions, penalties, additions - i.e. using well-prescribed formulas for scores.