Scoring Systems in Sports and Politics

“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.