Saturday, October 04, 2008

Under performing Tigers

One of the fundamental concepts of sabermetrics is the Pythagorean Theorem. Invented by Bill James in the late 1970s, the Pythagorean Theorem is a formula that shows the relationship between a team's runs scored (RS), runs allowed (RA) and winning percentage (PCT). It is as follows:

PCT=(RS squared)/(RS squared + RA squared)

The formula works reasonably well in most years for most teams. This indicates that winning games is essentially a function of how many runs a team scores and allows and when the runs were scored is not so important in most cases.

For example, the 2008 Tigers scored 821 runs and allowed 857. Plugging those numbers into the above formula yields a winning percentage of .479 which translates into 78 predicted wins. In reality, they won 74 games so they underperformed their pythagorean estimate by four wins.

When a team under performs like the Tigers did, it usually means they either they did poorly in close games or they won a disproportionate number of blowouts. In this case, both were true. They were 16-25 in one run games and 4-0 in games decided by 13 runs or more.

The results for all American and National League teams are presented in tables 1 and 2 below. All American League teams but two finished within five runs of their Pythagorean estimate. Thanks to an outstanding record of 61-28 in games decided by one or two runs, the Angels out did their estimate by 11 wins. The Blue Jays, on the other hand, fell eight wins below their predicted wins. This is because they were 9-1 in games decided by eight or more runs and 16-25 in one run games.

There were also only two National League teams that fell more than five wins outside their Pythagorean estimate. The Braves under performed by 6 wins partly because of their 11-30 record in one run games. The Astros over performed by 9 wins thanks, in part, to a 2-9 record in games decided by eight or more runs.

Because performance in close games and blow outs are not consistent from year to year, there is good chance that the Braves and Blue Jays will win more games next year. Conversely, the Angels and Astros might have a difficult time matching their 2008 win totals next year.

Table 1: Pythagorean estimates for American League teams in 2008

team

runs

runs allowed

actual wins

pred wins

difference

% difference

LAA

765

697

100

89

11

12.4

TB

774

671

97

92

5

5.4

KC

691

781

75

71

4

5.6

TEX

901

967

79

75

4

5.3

NYA

789

727

89

88

1

1.1

OAK

646

690

75

75

0

0.0

CHA

811

729

89

90

-1

-1.1

BOS

845

694

95

97

-2

-2.1

MIN

829

745

88

90

-2

-2.2

BAL

782

869

68

72

-4

-5.6

DET

821

857

74

78

-4

-5.1

CLE

805

761

81

86

-5

-5.8

SEA

671

811

61

66

-5

-7.6

TOR

714

610

86

94

-8

-8.5



Table 2: Pythagorean estimates for National League teams in 2008

team

runs

runs allowed

actual wins

pred wins

difference

% difference

HOU

712

743

86

77

9

11.7

SF

640

759

72

67

5

7.5

CIN

704

800

74

71

3

4.2

FLA

770

767

84

81

3

3.7

MIL

750

689

90

88

2

2.3

COL

747

822

74

73

1

1.4

PIT

735

884

67

66

1

1.5

ARI

720

706

82

83

-1

-1.2

NYN

799

715

89

90

-1

-1.1

STL

779

725

86

87

-1

-1.1

PHI

799

680

92

94

-2

-2.1

WAS

641

825

59

61

-2

-3.3

CHN

855

671

97

100

-3

-3.0

LAN

700

648

84

87

-3

-3.4

SD

637

764

63

66

-3

-4.5

ATL

753

778

72

78

-6

-7.7

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