Which of the following is most associated with the measurement of a shotgun barrel?

The measurement of a shotgun barrel is most commonly associated with gauge. The gauge of a shotgun refers to the diameter of the barrel and is determined by the number of lead balls of a certain diameter that equal one pound. For example, a 12-gauge shotgun means that 12 lead balls of the diameter equal the weight of one pound. This system is unique to shotguns and directly impacts the size and type of shot that can be used, as well as the effectiveness of the shotgun for various types of game.

The other options, while related to shotguns, do not define the measurement in the same widely recognized way as gauge does. Length of the barrel might be important for certain performance aspects but is not a standardized measurement like gauge. Width and thickness provide structural information about the barrel but do not serve as typical measures used to classify different shotgun types or their efficiency. Therefore, gauge is clearly the most relevant and recognized measurement associated with shotgun barrels.