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You will need to make a REST call to get the sprint(s) start and end dates, plus the estimation statistic in use, then a second REST call to search for all the issues you want to calculate the velocity from, including the data for their estimates, sprints, and changes of status from backlog to/from in-sprint, and to/from not-done-status to done-status (done status being "mapped into the last column on the board")
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