Tuesday, April 30, 2013

Application of Baye's theorem to baseball.



This question is from my 1996 book Statistical Applications of Baseball.   First edition is on Kindle. 
I will eventually create a drastically improved second edition.

Question: 

The Eastern Division teams are (NY, BA, BO, TO and DE), the Central Division teams are (CL, CH, ML, MN and KC) and the remainder of the Western Division teams are (SE, OA and CA).  Summarize the Texas Rangers' win/loss record against each conference.  What are the P(Win/Western Division) and P(Western Division/Win)?  Use Baye's Theorem to confirm these conditional probabilities.
 




NY

BA

BO

TO

DE

CL

CH

ML

MN

KC

SE

OA

CA

W

7

10

6

10

9

8

4

7

5

6

3

6

9

L

5

3

6

2

4

4

8

6

7

6

10

7

4
Texas Ranger 1996 win/loss season by team


Answer: 

The consolidated win/loss record for Texas against each conference is presented below.




Eastern

Central

Western

Total

Wins

42

30

18

90

Losses

20

31

21

72

Totals

62

61

39

162

The P(Win/Western) is 0.461 (18/39).  The P(Western/Win) is 0.200 (18/90).

Baye’s law confirms that P(Win/Western) is 0.461 since (0.556x(0.111/0.556) divided by (0.556x(0.111/0.556)+0.444x(0.130/0.444)) is 0.461.

Baye’s law also confirms  P(Western/Win) is 0.200  since (0.241x(0.111/0.241)) divided by (0.241x0.(111/0.241)+0.337x(0.186/0.0.337)) is 0.200




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