normalized_scores

Table actions
rigid
the simplest possible normalization: 5 points for 1st (equal), 4 for 2nd (equal), etc.; null for team tasks (only two ranks)
spread
Distribute points from a pool of {5, 4, 3, 2, 1}, with rank ties between N people sharing the next N available point values. (〃)
scale
Multiply every score by some common factor to achieve a sum of 15 for the task; where this causes any individual score to exceed 5, regrettably abandon the 15-point target and scale down to ensure a maximum of 5. Note that this value does exist for team tasks due to being point- rather than rank-based.
5+3, 3+2, 3½+2½
various ways to normalize team tasks based on rank

5 rows where task = 542

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id ▲ task contestant base ± points rank rigid spread scale 5+3 3+2 3½+2½
2607 The nicest thing to sit on 542 Alan Davies 68 4   4 2 4 4 4      
2608 The nicest thing to sit on 542 Desiree Burch 69 5   5 1 5 5 5      
2609 The nicest thing to sit on 542 Guz Khan 70 1   1 5 1 1 1      
2610 The nicest thing to sit on 542 Morgana Robinson 71 2   2 4 2 2 2      
2611 The nicest thing to sit on 542 Victoria Coren Mitchell 72 3   3 3 3 3 3      

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CREATE TABLE normalized_scores (
   id         INTEGER PRIMARY KEY,
   task       INTEGER REFERENCES tasks(id),
   contestant INTEGER REFERENCES people(id),
   base       INTEGER,
   adjustment INTEGER,
   points     INTEGER,
   rank       TEXT,
   rigid      REAL,
   spread     REAL,
   scale      REAL,
   '5+3'      REAL,
   '3+2'      REAL,
   '3½+2½'    REAL
);