The best teams I work with burn down story points. They only burn down when a story is done.
To do this, the team needs to have small stories. They will need to work with the product owner to make this happen. In disciplined teams this saves a lot of overhead and makes them go faster.
For new teams, breaking down the Sprint Backlog into tasks and estimating in hours is done but no longer recommended. Intronis, one of my venture group portfolio companies, started their first Scrum with burning down story points and has never looked back. They tripled their velocity in a few months.
This strategy is recommended for teams that can deliver working software at the end of each Sprint. This means tested at the feature level, i.e. potentially shippable code.
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