One of my teams was so obsessed with velocity; they constantly stressed about doing 'more.' Yet, at the same time, they were not even able to get their velocity to a stable point. It turns out they cheated themselves out of good results.
From the outside, their anxiety was very puzzling, because they did such good work and delivered consistently. So, my agile coach and I started working with them closely to understand what the real issue was. The only thing that skewed the numbers was carry-over: When a story did not get done in one sprint, they would carry it over into the next sprint and – here is the kicker – would re-estimate it.
Take this example: Three stories, all 8 for a total of 24 points are taken into sprint one. They would finish one of those stories and carry over the other two. The team also agrees to re-estimate them to 3. Because the old velocity was 8, they take on those 6 points and assume to be able to complete them. They finish those as well, completing 6 points of velocity for this sprint, for an average of 7.
With a velocity of 7, 24 points would take a little more than three sprints, but they just completed 24 points in a little less than two sprints, with a velocity of 12. This number would be way more realistic.
So, they really cheated themselves out of almost half their velocity, because it made sense to them, to re-estimate the stories.
We did keep the practice of estimating what was left to do to plan the current sprint, but we kept the original estimation on the ticket to calculate the velocity. Suddenly having reliable numbers and predictability lifted so much of a burden off the team that over the next month, they even managed to increase their velocity just by not stressing about it anymore.