VSTS has a really nice ability to show you the utilized versus available capacity in the work details section that's on the right hand side on the current sprint's backlog.
I would like to see what it was historically for previous sprints, but the work details section for previous sprints is more or less blank. Does anyone know if this is possible?
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You should to check history via burndown chart that is used to determine if your team is on track to complete its sprint plan.
I assume you are using the Scrum process template for your Team Project as you mentioned Sprint's backlog (instead of Iteration of an Agile template).
The Work Details in the backlog of the sprint is based on capacity assigned to each member, and on Remaining Work (either hours or days) assigned to each Task.
When the task is Done, its Remaining Work is set to 0, hence the assignee gets the 'Work By: assigned to' work decreased by the same amount. The amount is graphically represented by the green or the red bar.
The same stands for the team, the 'Work' quantity is decreased by the same amount.
This is the reason you see that in a past sprint there is no work to do, because most of the tasks have been (luckily :-) ) completed.
This is sensible as during a sprint you want to track the progress, and you want to see each day the remaining work decreasing (i.e. Burndown chart, which is again based on the Remaining Work of the tasks).
Only the capacity remains unmodified at the end of the sprint, as the capacity is defined explicitly for each sprint.