At the core, a SaaS business model is relatively easy to understand: your goal is to attract customers at an acceptable cost and provide them with a delightful service so they stick around, happily paying their monthly subscription fee.
The core metrics for a SaaS business are therefore:
CAC or Cost of Acquisition, the cost of attracting a new customer
CLTV or Life Time Value, the revenue you make on an individual customer, over the entire course of the relationship with that customer. The inverse of CLTV is churn.
Net MRR Growth, net monthly recurring revenue growth, the ultimate metric to track the speed of growth.
SaaS companies deploy numerous tactics to influence their metrics. You'll see SaaS companies use free trials, onboarding tutorials, content marketing and what not to attract and retain customers at scale. The interesting part of the SaaS business, is that most of these activities are digital, i.e. they can be tracked and analysed. This is where predictive analytics comes in: once a SaaS company can predict the likelihood if a given trail user is going to convert into a paying user, it can deploy specific tactics to increase that likelihood. E.g. for those trail users that are relatively likely to convert, one could send a discount coupon, or schedule a short intro skype call to get them over the edge, while one could simply ignore those trial users that are highly unlikely to convert at all.
Flex4Apps partner Datastories.com is developing a platform that will allow SaaS companies to leverage predictive analytics, without the need to have dedicated data scientists on board. You can find more info on the datastories platform at http://datastories.com/data-driven-product-management