Quality of hire can be measured via two types of performance data. Subjective: Ratings of observed behaviors, such as behaviorally anchored competency scales. Objective: Performance outcomes captured in the form of numbers.
When sound data is used to document quality of hire, evidence-based management is being deployed for the business process called staffing.
There is an underlying assumption with subjective measures that an individual rated higher on a valued behavior (job specific competency) is a more valuable employee. These are however, still opinions, and difficult to use in a calculation that documents value.
With objective measures, performance outcomes may be easily equated with dollar values, and thus contribute to a quantitative ROI analysis.
Some jobs do not have clear, specific performance metrics that are captured. Captured being the operative word.
Without data capture, there can be no analysis. Without analysis, no insights, and quality of hire remains elusive. As a practitioner, being well versed in methodology for HR analytics is important. If you are seeking assistance in this area, seek out an industrial organizational psychologist (IOP)
Quality, it has been said is determined by the customer. Who is the customer and what outcomes are important in talent acquisition? If it is hiring manager and their opinion, a survey will work for QOH If it is the hiring manager and their department production goals, then opinion may not be an adequate metric.
As an exercise, ask the hiring manager to produce a list of the objective performance metrics for the job. If there is enough people in the job to calculate a group average. (see more on performance variation here.) Quality of hire may then be viewed as new hire performance that lifts the average of the group. In accomplishing this you have delivered staffing process improvement
For more to think about, take a lesson from Lake Wobegon