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

10 rows where contestant = 28

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Suggested facets: base, points, rank, rigid, spread, scale

id ▲ task contestant base ± points rank rigid spread scale 5+3 3+2 3½+2½
912 The most embarrassing item 195 Bob Mortimer 28 2   2 4 2 2 2      
917 Throw an exercise ball into a bath or put the coconuts in a trolley 196 Bob Mortimer 28 2   2 4 2 2 2      
922 Blow something substantial off a table 197 Bob Mortimer 28 2   2 4 2 2 1.88      
927 Perform a miracle 198 Bob Mortimer 28 4   4 3= 3 2.5 2.86      
932 The second longest T-word 199 Bob Mortimer 28 1   1 5 1 1 0.833      
938 The best thing 201 Bob Mortimer 28 3   3 3= 3 2.5 2.81      
943 Find out what’s in the briefcase 202 Bob Mortimer 28 2   2 4 2 2 2      
948 Make a delicious mask 203 Bob Mortimer 28 5   5 1 5 5 4.69      
953 Make a mess and then clean it up 204 Bob Mortimer 28 1   1 5 1 1 0.882      
958 Record the most steps on your pedometers 205 Bob Mortimer 28 2   2 4 2 2 2      

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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
);