Thursday, October 18, 2007

The Tigers were what they were in 2007

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 2007 Tigers scored 887 runs and allowed 797. Plugging those numbers into the above formula yields a winning percentage of .553 which translates into 90 predicted wins (PW1). In reality, they won 88 games so theory was very close to reality. Alternatively, we can use runs created (RC) and runs created against (RCA), both of which I discussed in articles last week. In that case, the formula works like this:

PCT=(RC squared)/(RC squared + RCA squared)

The Tigers had 891 RC and 815 RCA allowed in 2007 which translates into 88 predicted wins (PW2) according to the formula. This matches their actual wins precisely so they Tigers were a very sabermetrically correct team this year.

Tables 1 and 2 below show that the formula did not work as well for all teams in 2007. In the tables, R, RA, PW1, RC, RCA, and PW2 are as defined above. D1 is the difference between wins and PW1 and D2 is the difference between wins and PW2.

Using PW2 and D2, we can see that the formula worked better for the National League in 2007 as all but 1 team came within 5 wins of their pythagorean estimate. The one team was the Arizona Diamondbacks who finished a whopping 14 games ahead of their predicted wins. This tells me that the DBacks were probably very lucky this year. Teams which substantially outperform their expected win totals one year tend to slip back in the following year. It doesn't work that way all the time but it works often enough to make me think the DBacks are a candidate to fall in the standings next year.

In the American League, 4 teams fell 6 or more wins away from their predicted wins. The Mariners (+11) and Angels (+9) outperformed their predicted wins which makes me think they could regress next year if they don't improve significantly. On the other hand, the Red Sox and Athletics underperformed their Pythagorean estimates by 7 wins which makes them candidates to improve their records next year. I'm sure that Billy Beane, Theo Epstein and Bill James are well aware of that.


Table 1: Pythagorean estimates for American League teams in 2007

TEAM

Wins

R

RA

PW1

D1

RC

RCA

PW2

D2

SEA

88

794

813

79

9

786

830

77

11

LAA

94

822

731

90

4

787

753

85

9

CHA

72

693

839

66

6

682

827

66

6

CLE

96

811

704

92

4

821

730

90

6

KC

69

706

778

73

-4

669

834

63

6

MIN

79

718

725

80

-1

707

766

75

4

TEX

75

816

844

78

-3

769

845

73

2

DET

88

887

797

90

-2

891

815

88

0

NYA

94

968

777

99

-5

962

799

96

-2

TB

66

782

944

66

0

812

934

70

-4

TOR

83

753

699

87

-4

751

692

88

-5

BAL

69

756

868

70

-1

771

832

75

-6

BOS

96

867

657

103

-7

898

680

103

-7

OAK

76

741

758

79

-3

768

748

83

-7



Table 2: Pythagorean estimates for National League teams in 2007

TEAM

Wins

R

RA

PW1

+/-

RC

RCA

PW2

+/-

ARI

90

712

732

79

11

722

768

76

14

WAS

73

673

783

69

4

691

816

68

5

HOU

73

723

813

72

1

749

868

69

4

STL

78

725

829

70

8

738

807

74

4

PHI

89

892

821

88

1

932

865

87

2

PIT

68

724

846

68

0

732

875

67

1

SD

89

741

666

90

-1

739

678

89

0

COL

90

860

758

92

-2

877

780

91

-1

MIL

83

801

776

84

-1

827

792

85

-2

NYN

88

804

750

87

1

846

759

90

-2

SF

71

683

720

77

-6

685

753

73

-2

CHN

85

752

690

88

-3

780

716

88

-3

CIN

72

783

853

74

-2

811

876

75

-3

ATL

84

810

733

89

-5

822

753

88

-4

FLA

71

790

891

71

0

846

913

75

-4

LAN

82

735

727

82

0

772

715

87

-5

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