Employing economic and military spies is really helpful towards the middle of the game and onward. Typically, I've hit a bunch of capitals and Im flush with cash and the map starts to form up into multiple coalitions. Anyway..at this point of the game, flush with cash, the best way to use that extra cash (assuming you can't purchase goods/food anymore) is to put a bunch of spies in the core countries that are producing whatever that map is short of. So wheat or goods or whatever is going to hurt your enemy or future enemy the most.
I typically put multiple spies in each of these countries. So you may have 5 counter spies but if I have 3 economic and 3 military than there is a really good chance one of my spies is going to be successful each round. In the example above you have to consider that the news reports, etc. aren't telling you how many spies are in each country. You might have 6 counter spies but your enemy (or multiple enemies) may have a few each. I'd say its hard to catch spies in real life before they act. After they act its typically easier to catch a spy in real life.
Whatever the equations they use to catch spies or to see if they actually do anything can't be 50/50. That would be too easy. Looks like to me that only one spy is ever successful in any one area. Perhaps there has been another post on this that someone can point us to explain the mechanics of how the game figures out if and when a spy is successful.