Hey,
If, like with many other areas of law, you are asked to judge the effectiveness, police discretion can be a very heated debate.
You are correct in its definition i.e. the ability for officers to choose to enforce the law or not too and also the extent to which this occurs (similar to judicial discretion).
In relation to effectiveness you can explore the positives such as the ability for officers to overlook poor judgement of law abiding citizens, to incorporate underlying circumstances etc.
However, I found one point very interesting as a negative...explore the way in which personal context influences Police choices especially in relation to race, religion, sex etc.
I know this is not what you asked originally but its a great topic to explore in debate in relation to effectiveness. So sorry if this is a waste of time lol
Cheers,
BC