The algorithm is described in the tournament section of the manual. However, often the data to reproduce the results is not always available.
Quote:
5.3.4 All Teams in attendance are seeded during the Qualification MATCHES. If the number of Teams in attendance is 'n',
they are seeded '1' through 'n', with '1' being the highest seeded Team and 'n' being the lowest seeded Team.
The FMS ranks all Teams in decreasing order, using the following sorting criteria:
1st order sort Qualification Score
2nd order sort Cumulative sum of AUTO GOAL points
3rd order sort Cumulative sum of CLIMB points
4th order sort Cumulative sum of TELEOP GOAL points and FOUL points
5th order sort Random sorting by the FMS
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Most of that data isn't available except via the
FMS twitter feed which isn't always reliable. If your scouting team has internet access to get the FMS twitter feed, you might as well look up the standings on the FIRST website, which are updated after every match.