[jp10]

Warning: Generalized statements follow which are based on US military doctrine (but hold true for other military forces) and will have established exceptions:
Most counter battery assets will be at Division or Corps level which is above the level of command in both WINSP games.
Artillery assets are usually considered to be either General or Direct to the units they support or Dedicated to a specific task.
General Support Artillery fires in support of the operation as a whole rather than in support of a specific subordinate unit.
In WINSPMBT this would be the OFF MAP artillery. It could fire on map targets or be used to counter battery detected enemy artillery. It also can be considered to be supporting other commands not on the player's map.
Direct Support Artillery provides fire requested by the supported unit.
In WINSPMBT this would be the ON MAP artillery, supporting only the units on the map.

A battery assigned to one task rather than a unit (H&R, Interdiction, Counter-Battery...etc) can be considered Dedicated to that task. This is what a player is doing when they leave a battery idle for a chance of it to counter fire an enemy artillery unit.

My observation is that a dedicated CB battery would be considered to be quicker in support of that mission and deployed and supported for more efficient CB. Two ways to do this could be, 1. A new artillery unit 'Dedicated CB Arty' that the player buys that does not fire on map but has a higher % of firing. 2. No new units but arty capable of CB that remain idle gain a better % each turn they stay idle up to a capped % based on nationality/doctrine/training factors for each nation greater than the game currently simulates. In a perfect game world it would be able to CB enemy artillery on the player map without input from the player.
Oh to sleep, perchance to dream...