It’s not terribly difficult to define a query that results in numbers being assigned to hockey players.  Goals scored, hits taken, and save percentage can be calculated from the play-by-play data I’ve been working with lately.  The idea of enforcement can likewise be used to give each player in the league a number conveying the degree to which he brings enforcement to the game.

However, qualities like goals scored and enforcement seem to be in a different category than physical quantities like mass and volume.  I would think the most apparent difference would be that an object has the mass that it has regardless of what you or I believe.  Thus, when we measure the mass of an object, there’s a real value that we try to get as close to as possible with our measurement.

The goals scored by a player is only slightly less substantial than that player’s mass: after all, according to the rules of a game there were in fact goals that occurred, and the goals scored is simply a tally of these events.  Compared to a notion like enforcement, the acceptability of goals scored sits pretty well, particularly when three different definitions of enforcement seem equally good.

Brian Ellis, in his book Basic Concepts of Measurement, points out that what’s needed to kick things off is a crude order of things according to the quantity such that

  • sufficiently knowledgeable people will more or less agree
  • no formal measurement is used

For example, most people can sort a group of rocks by mass by picking them up two at a time, one in each hand.  When two rocks are close together in mass, even expert rock balancers come up with different results, but the ordered groups are by large similar.

Now imagine there’s a bunch of hockey experts in a room, individually asked to write down the top 20 enforcers from this past season.  There’d be differences in the lists, but I’d expect there to be more similarity than difference.  This is just like Time’s top 100 list of influential people, AMC’s list of top 100 films, and People’s list of the 100 most beautiful people.  In each of these cases, there’s something substantial that we’re talking about, regardless of whether these properties could be measured.

The fact that three different queries with three different result sets purport to describe the same quantity is not a cause to abandon the quantity itself.  Rather, the point of this semantic analysis is to refine the meaning of a term so that it provides a clear picture of what is meant by enforcement.  This needn’t be the only picture of enforcement out there, of course, but somebody looking at it should be able to figure out what’s going on.