I think this article does a reasonably good job of describing advanced analytics and even goes on to explain some people's trepidation: http://www.articledashboard.com/Article/What-is-Predictive-Analytics-and-Why-Are-We-So-Afraid-of-It-/1175135
You ask about what metric to look at and that is an excellent question...and the answer is, you can’t know for sure until some analysis is done because everybody’s data is different. Here is a high level overview of how metrics are identified using advanced or predictive analytics. Say you have 30 variables related to each customer/donor/prospect (CDP) that may include information like: income, age, zip code, sales or donor history, education etc. and you are trying to determine who best to target with a particular marketing campaign. If you are using a standard BI tool (query and reporting), you can look at successes from past events and try to manually figure out who fits a particular profile, one variable at a time. But maybe there is not only one variable or two variables that are consistently present. Now, if you could take all associated variables into account simultaneously and let algorithms determine which variables are actually predictive and build a model that would essentially give each of those predictor variables a coefficient or predictability, you could then take that model and push it up against your database to score each CDP. You could then decide to send a particular marketing campaign to people who score in the top X% of the analysis and not send to people determined to be unlikely to respond. This way, you can reduce your marketing expense and increase the likelihood of responses because you will be sending campaigns to CDP that are statistically more relevant. Or you could even go a step further and take that model and use it to score people from a purchased list, thereby increasing the likelihood you will find additional, targeted CDPs. This is only one example how advanced analytics can help. I hope I explained this clearly enough that it makes sense.
Let me ask a question; if you had to guess, what is a typical marketing budget for a particular campaign for a small or medium sized NFP. $Hundreds? Thousands? Tens of thousands? Tough to answer about a “poor man’s” predictive model when I have no reference.