“Simpson’s Paradox” is a statistical quirk in that one side
wins more points yet loses the contest.
1) Basketball
There are 2 levels:
Points-->Game
Whoever wins most points wins the game.
“Simpson’s Paradox” is not possible.
2) Soccer
There are 2 levels:
Points-->Game
Whoever wins most points wins the game.
“Simpson’s Paradox” is not possible.
3) Volleyball
There are 3 levels:
Points-->Set-->Match
Whoever wins most points wins the set.
Whoever wins most sets wins the match.
“Simpson’s Paradox” is possible.
Example: A vs B: 25:0, 25:0, 23:25, 23:25, 13:15.
A got 103 points, B got 65 points, yet B won the match.
4) Baseball
There are 2 levels:
Runs ->Game
Whoever wins most runs wins the game.
“Simpson’s Paradox” is not possible.
5) American
Football
There are 2 levels:
Points-->Game
Whoever wins most points wins the game.
“Simpson’s Paradox” is not possible.
6) Tennis
There are 4 levels:
Points-->Game-->Set-->Match
Whoever wins most points wins the game.
Whoever wins most games wins the set.
Whoever wins most sets wins the match.
“Simpson’s Paradox” is possible.
Example: A vs B: 6:0, 4:6, 4:6.
A won 14 games, B won 12 games, yet B won the match.
7) Badminton
There are 3 levels:
Points->Set->Match
Whoever wins most points wins the set.
Whoever wins most sets wins the match.
“Simpson’s Paradox” is possible.
Example: A vs B: 21:0, 19:21, 19:21.
A won 59 points, B won 42 points, yet B won the match.
8) Ping pong
There are 3 levels:
Points->Set->Match
Whoever wins most points wins the set.
Whoever wins most sets wins the match.
“Simpson’s Paradox” is not possible.
Example: A vs B: 21:0, 19:21, 19:21.
A won 59 points, B won 42 points, yet B won the match.
9) American
Election
There are 3 levels:
Individual votes->Electoral College votes->Presidency
Whoever wins most Individual votes wins the Electoral College
votes in the state.
Whoever wins most Electoral College votes wins the
presidency.
“Simpson’s Paradox” is possible.
Example: John vs Mike. Each of the 3 states has 100 million voters and 10 Electoral College votes.
|
State A
|
State B
|
State C
|
Total
|
John # votes
|
100M
|
49M
|
49M
|
198M
|
John EC
votes
|
10
|
0
|
0
|
10
|
Mike # votes
|
0M
|
51M
|
51M
|
102M
|
Mike EC
votes
|
0
|
10
|
10
|
20
|
John won 198 million individual votes, Mike won 102 million
individual votes, yet Mike won the presidency.
10) French Election
There are 2 levels:
Individual votes->Presidency
Whoever wins most Individual votes wins the Presidency.
“Simpson’s Paradox” is not possible.