Bill James created a formula (which he called the Pythagorean formula) to estimate a team’s winning
percentage based on their runs for and against.
Winning Percentage = (Runs For)^2 / [ (Runs For)^2 + (Runs
Against)^2 ]
During the recent International Softball Federation World
Championship, I used this formula to calculate the winning percentage of the
teams during the round robin play of the tournament. Below are the results.
Team
|
Games
|
Wins
|
Runs For
|
Runs Against
|
Estimated Win Percentage
|
Predicted Wins
|
Difference in Wins
|
7
|
7
|
48
|
5
|
0.989
|
7
|
0
|
|
7
|
5
|
28
|
17
|
0.731
|
5
|
0
|
|
7
|
4
|
38
|
25
|
0.698
|
5
|
-1
|
|
7
|
4
|
31
|
25
|
0.606
|
4
|
0
|
|
7
|
3
|
20
|
18
|
0.552
|
4
|
-1
|
|
7
|
3
|
37
|
38
|
0.487
|
3
|
0
|
|
7
|
2
|
13
|
37
|
0.110
|
1
|
1
|
|
7
|
0
|
14
|
64
|
0.046
|
0
|
0
|
Pool B
Team
|
Games
|
Wins
|
Runs For
|
Runs Against
|
Estimated Win Percentage
|
Predicted Wins
|
Difference in Wins
|
7
|
6
|
44
|
12
|
0.931
|
7
|
-1
|
|
7
|
6
|
36
|
12
|
0.900
|
6
|
0
|
|
7
|
5
|
45
|
13
|
0.923
|
6
|
-1
|
|
7
|
5
|
24
|
6
|
0.941
|
7
|
-2
|
|
7
|
3
|
17
|
25
|
0.316
|
2
|
1
|
|
7
|
2
|
19
|
41
|
0.177
|
1
|
1
|
|
7
|
1
|
14
|
57
|
0.057
|
0
|
1
|
|
7
|
0
|
12
|
45
|
0.066
|
0
|
0
|
The James Win Percentage Formula did a relatively good job
of predicting the winning percentage and thus the number of wins in the round
robin portion of the tournament.
The only anomoly seems to be Argentina who allowed very fews runs but scored very few runs. The Bill James Formula over-estimated their winning percentage.
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