I understand the concepts of quantity and productivity. I understand the purpose of these metrics is quality neutral. But I'm not sure if the BA output can be easily or accurately measured using metrics. BA output is not the equivalent of counting the number of sales or looking at the variation on a chart of widget output.

It's the old apples and oranges argument. Some projects will be more complex. Some will have difficult to reach stakeholders or complex requirements. They all will continue to remain vulnerable to senior management re-prioritization and development resource squeezes. Project Managers, who focus on timelines, budget and resource allocation, may have more measurable units for "productivity" - but again, as stated, this isn't quality.

BA productivity also feels like a common problem with Sales Managers and Sales People. Sometimes a top salesperson will receive pressure that although their sales are high and their quality excellent, they aren't making the required number of contacts. This is often due to their having a time intensive approach. To increase the numbers, you change the approach and reduce their effectiveness.

I tend to agree with the Agile philosophy here. The TEAM should be measured, not the individual. The whole approach to projects is more that of a sports team or relay team. Some members of a team might "shine" more than others and have stats that can be evaluated, but the sum is greater than the parts when you have a high-performing team. A JIT or YAGNI approach from an approachable BA might be more effective for the team than a box load of documents delivered en masse from a BA without close relationships to the team. So what and how do you measure? In this case, it's a sensitive project manager or BA manager who has to assess the effectiveness, not the "productivity" of the BA.