Before returning to the analysis of the NHL play-by-play data I’ve been looking at, here are some definitions to frame the project:

Enfoo:  The disposition to respond to aggressive play through retaliatory checking and fighting.
Enforcer: A person considered to have a high degree of Enfoo.
Enforcement: The kind of event that is the realization of an Enfoo.

Because no good names for the (dispositional) quantity under the scope came to mind, I chose a silly name.  Despite this, I think there’s sufficient reason to think that a crude order could be created by a group of hockey fans.  For a physical comparison, these three definitions are similar to the following:

Weight: The gravitational force on a body.
Heavy Person: A person considered to weigh a lot.
Gravitational Attraction: The kind of event where two objects attract one another due to their mass and mutual distance.

Dispositions can be tricky things to identify, so we’ll assert the following detection rule:

Detection Rule: An event is an enforcement if it is an Enforcer Action taking place within 2 minutes after a Violent Action against one of the teammates of the Enforcer.

The following definitions round out the necessary machinery:

Enforcer Action: An action penalized as fighting, cross-checking, roughing, or unsportsmanlike conduct.
Violent Action: An action penalized as charging, high-sticking, roughing, slashing, or unsportsmanlike conduct.

The goal of this analysis is to come up with a formal definition of enfoo and an appropriate measurement scale that can aid future analyses.  It would be nice if the order generated by the detection rule above was similar to rankings of enforcers by hockey analysts, but this is not necessary.  If this were a material definition of enfoo, then the goal would be to uncover the intended semantics of a group of hockey analysts that rank enforcers.  Instead, this formal definition of the disposition only depends on the semantics of the terms in its definitions (like Violent Action, Player, and Minutes).

Finally, a scale for measuring enfoo needs to be defined:

Barce: A scale for measuring the amount of enfoo a player had during a period of time.  A player has one barce when he is the agent of an enforcement once during the set period of time.  A player has (x+1) barce when he is the agent of (x+1) events of enforcement during the set period of time.

The barce scale unsurprisingly jives with the detection rule asserted above – to measure the enfoo of a player during a game on the barce scale, the enforcement events he is penalized for are tallied.  If a normalized barce scale is desired, then the tally for the game should be divided by the total possible number of enforcement events: the number of violent actions that the other team is penalized for.