This paper was inspired by my own futility as a baseball prognosticator. Every spring I'd sit down with the spring training rosters and last season's statistics, calibrating and calculating the effect of changes which, in my “expert” opinion, would inevitably catapult Team A to a division championship while Team B collapsed to a pathetic sixth place. Every spring I'd share my picks with friends -- and every fall's final standings would reconfirm my incompetence. Am I really that stupid, or is there another explanation? Read on and draw your own conclusions...


Tinkering

Ever with

Chance


Or...How Well Do Statistics Predict the Present?

 

Doug Pappas

SABR 23

June 25, 1993





This research was inspired by Bill James's essay "How Often Do the Best Teams Actually Win," which appeared in the 1989 Baseball Abstract (the Brock Hanke/Rob Wood collaboration). For that essay, James simulated 1,000 complete seasons on his computer, using teams of a known quality whose chances of winning a particular game could be precisely calculated. He found that the best team in a division won only 2,185 of 4,000 divisional races, or 54.6%. The best team in all of baseball won its division only 71.5% of the time, and won the World Series only 29.3% of the time...and this in a simplified model where "the best team in baseball" could be objectively identified.


This bothered me...until I stopped to think about how "real" baseball works. The final standings summarize the results of 162 individual games, while each game in turn represents the results of nine (or more) innings of batter-pitcher duels. At each stage of the contest, chance plays a major role:

 

--          Within an inning: Batters don't "win games"; they hit doubles, draw bases on balls, and strike out. The order of events is critically important. If a team's first three batters produce an infield single, a walk, and a double high off the outfield wall, it will score no runs if the double comes first, one run if it comes second, and two runs if it comes third, yet the individual players have performed the same.

 

--          Within a game: A team wins only by scoring more runs than it allows, so great pitching performances, like Harvey Haddix's 12-inning perfect game in 1959, aren't enough if the team doesn't score. Twenty years later, the Cubs scored 22 runs and lost; just last week, Carlos Baerga hit three home runs against Detroit in a losing effort. Teams can't create a "runs bank" to store the excess from ten-run wins for use during later one-run losses.

 

--          Within a season: If success is defined as winning a pennant or division championship, it's not enough just to win a lot of games. Casey Stengel's 1954 Yankees won 103 games, more than any other Yankee team he managed...but it lost the pennant because Cleveland won 111 games. Meanwhile, the 1973 Mets captured their division with 82 wins, and the 1987 Twins rode an 87-win season (in which they were actually outscored by their opponents!) all the way to a World Championship.


In recent years, new measurements have been developed to estimate how many games a team should win with a given offensive and defensive performance. The first of these was Bill James' Pythagorean Formula, which focuses on the number of runs scored and allowed over the course of a season:


Winning percentage = (Runs scored)2 / (Runs scored)2 + (Runs allowed)2.


Thus a team which scores as many runs as it allows should win half the time; one that scores 700 and allows 600 should win at about a .576 percentage. Teams performing significantly better or significantly worse are "clutch" and "choke" teams, if you believe in such concepts, "lucky" and "unlucky" if you don't.


More recently, Pete Palmer has developed a "linear weights" system which evaluates each player's batting, pitching and fielding to determine whether he's better or worse than the league average and converting that into his effect on the team's won/lost record. This system concluded, for example, that because of Barry Bonds' outstanding 1992 season, the Pirates won nine games more than if they'd have won with an average left fielder. (Bonds' nine-win 1992 is the fifth best single season in history, according to Palmer's formulas.) Each team's expected performance is simply the sum of the positive and negative values for each of its players, with a .500 team scoring zero. The formulas are too complex to reproduce here, but can be found in the Appendix to Total Baseball; the sum of each team's batting, pitching and fielding Linear Weights for a given season is contained in Total Baseball's Annual Record of that season. Again, teams which outperform their collective statistics are "clutch" or "lucky." (Don't ask me to explain why Total Baseball's system for rating managers is a variant of the Pythagorean Formula, attributing all differences between expected and actual record to managerial skill and thereby concluding that Joe McCarthy, John McGraw and Casey Stengel were below-average managers.)


For easy reference, the three right-hand columns on the first page of reports for each set of simulated seasons lists the team's actual number of wins; the number predicted by the Pythagorean Formula; and the number predicted by Linear Weights. In 1992, for example, the Bluejays and Pirates were "lucky"; the Mariners and Dodgers, "unlucky."


************************************************************************************


Keeping these principles in mind, I developed a different type of simulation -- one which, using actual players and teams, controlled for every variable except the effect of chance on the outcome. I used version 4.0 of the Pursue the Pennant computer game to replay every season from 1986 through 1992 using each team's actual rosters and statistics. The computer chose starting lineups and pitching rotations and made all in-game decisions for each team, replaying an entire league's schedule in about an hour and a half. When a season was complete, I collected the results, cleared them from the computer's memory, and ran the simulation again...ten times for the 1986-91 seasons, 20 times for the 1992 season. The same players with the same statistics, using the same batting orders, pitching rotations, and managerial strategies -- how much could the results vary?


A LOT. In the twenty 1992 simulations, for example, four different teams won the NL East, with real-world champion Pittsburgh accounting for only three of those wins. Houston tied Atlanta for one division title, while finishing last two other times; world champion Toronto won as many as 103 games, as few as 74. In fact, every single team in baseball had at least an eighteen-game spread between its best and worst record.


For the 1990 and 1991 seasons, I extracted a few players' key statistics for each simulation to show variance in individual player performances. AL MVP Rickey Henderson's 1990 Runs Created/27 Outs (the number of runs a team of nine Rickey Hendersons would score) varied from 8.62 to 12.68, while Cecil Fielder's 1990 home run total ranged from a low of 41 to a high of 63(!). Leaguewide ERAs for that season varied only from 4.07 to 4.24.



1992


AL EAST                  Consolidated Standings   GB   RealPythLin Wt

Divisional wins:         Baltimore      92-70     --   89  87 90

Baltimore - 7            Toronto        91-71     1   96  91  90

Milwaukee - 5            Milwaukee      91-71     1   92  97  90

Toronto - 8              New York       84-78     8   76  73  81

                         Detroit        74-88     18 75  81  76

                         Cleveland      74-88     18   76  80  76

                         Boston         67-95     25   73  72  75

 

AL WEST                  Consolidated Standings   GB

Divisional wins:         Minnesota      97-65     --   90  92  89

Chicago - 1              Oakland        92-70     5   96  89  91

Minnesota - 13           Chicago        84-78     13   86  86  85

Oakland - 6              Kansas City    82-80     15   72  69  75

                         Texas          73-89     24   77  73  76

                         Seattle        73-89     24   64  68  73

                         California     60-102    37   72  69  65

 

NL EAST                  Consolidated Standings   GB

Divisional wins:         St. Louis      92-70     --   83  85  87

Chicago - 1              Montreal       90-72     2   87  90  87

Montreal - 8             Pittsburgh     89-73     3   96  93  89

Pittsburgh - 3           Chicago        79-83     13   78  77  79

St. Louis - 8            Philadelphia   75-87     17   70  77  75

                         New York       73-89     19   72  74  73

 

NL WEST                  Consolidated Standings   GB

Divisional wins:         Atlanta        93-69     --   98  96  90

Atlanta - 18.5           Cincinnati     83-79     10   90  88  88

Cincinnati - 1           San Francisco 79-83     14   72  71  73

Houston - 0.5            Houston        76-86     17   81  73  77

                         San Diego      73-89     20   82  79  81

                         Los Angeles    68-94     25   63  69  73

 

"Real" -- Actual number of wins for the team

"Pyth" -- Number of wins predicted by Bill James' Pythagorean Formula

"Lin Wt" -- Number of wins predicted by Pete Palmer's Linear Weights formula




1991

 

AL EAST                  Consolidated Standings   GB   RealPythLin Wt

Divisional wins:         Toronto        98-64     --   91  88  90 

Boston - 1*              Boston         87-75     11   84  83 86

Detroit - 1              Detroit    85-77     13   84  83  81

Toronto - 8*             Baltimore      78-84     20   67  69  73

                         New York       72-90     26 71  70  72

*Two Boston-Toronto tiesMilwaukee      70-92     28   83  87  82

                         Cleveland      63-99     35   57  59  65

 

AL WEST                  Consolidated Standings   GB

Divisional wins:         Minnesota      90-72     --   95  95  96

Chicago - 5              Chicago        88-64     2   87 90 87

Minnesota - 3            Texas          86-76     4   85  82  83

Oakland - 0.5            Oakland    82-80     8   84  79  74

Texas - 1.5              Kansas City    80-82     10   82  82  83

                         California     77-85     13   81 81  80

                         Seattle        71-91     19   83  84  85

 

NL EAST                  Consolidated Standings   GB

Divisional wins:         Pittsburgh     89-73     --   98  97  97

Chicago - 1              St. Louis      85-77     4   84 81  80

New York - 1             Chicago     78-84     11   77  77  76

Pittsburgh - 7           Philadelphia 76-86     13   78  75  74

St. Louis - 1            Montreal   74-88     15   71 70  76

                         New York       74-88     19   77  80  81

 

 

NL WEST                  Consolidated Standings   GB

Divisional wins:         Los Angeles    90-72     --   93  93  91

Atlanta - 4            Atlanta     89-73     1   94  94  90

Cincinnati - 1           Cincinnati     87-75     3   74 81 84

Los Angeles - 4*         San Diego      83-79     7   84  80  79

San Diego - 1*           San Francisco  80-82     10   75  75  75

* Two LA-SD ties         Houston    67-75     23   65  67  68

 

Frank Thomas, OBP:  .458.461.440.428.425.454.427.451.447.429

 

David Cone, K/9 IP: 10.10 9.72 10.73 9.67 9.40 10.61 9.23 9.73 10.28 9.34

 



1990

 

AL EAST                  Consolidated Standings   GB   RealPythLin Wt

Divisional wins:         Boston         85-77     --   88  85 88

Baltimore - 1.5*         Toronto        83-79     2   86  93  89

Boston - 5.5*            Baltimore      79-83     6   76  78  78

Cleveland - 1            Cleveland      77-85     8   77  80  76

Toronto - 2              Detroit        76-86     9 79  81  78

                         Milwaukee      76-86     9   74  78  75

*One Bal-Bos tie         New York       70-92     15   67  64  66

 

AL WEST                  Consolidated Standings   GB

Divisional wins:         Oakland 102-59    --   103  101  99

Oakland - 10             Chicago        87-75     15   94  87  81

                         Seattle        85-77     17   77  76  83

                         Kansas City    85-77     17   75  81  81

                         Texas          79-83     23   83  79  81

                         Minnesota      77-85     25   74  74  76

                         California     73-89     29   80  79  82

 

NL EAST                  Consolidated Standings   GB

Divisional wins:         New York      90-72     --   91  100  92

Montreal - 1.5           Pittsburgh     88-74     2   95  95  94

New York - 3.5           Montreal     86-76     4   85  89  88

Philadelphia - 1.5       Philadelphia   82-80     8   77  72  76

Pittsburgh - 3.5         St. Louis   80-82     10   70  69  76

St. Louis - 1            Chicago        76-86     14   77  71  72

One Montreal-NY tie; one Philadelphia-Pittsburgh tie

 

NL WEST                  Consolidated Standings   GB

Divisional wins:         Cincinnati     93-69     --   91  93  92

Cincinnati 8.3           Los Angeles    87-75     6   86  86  83

Los Angeles 1.3          San Diego 82-80     11   75  81  81

San Diego 0.3            San Francisco  77-85     16   85  82  79

                         Atlanta        66-96     27   65  66  64

                         Houston       66-96     27   75  70  75

One three-way tie between Cincinnati, Los Angeles and San Diego

 

 

Cecil Fielder, home runs: 52 63 58 44 60 41 54 51 46 51

 

Rickey Henderson,

Runs Created/27 outs:    10.87 11.40 8.62 9.87 11.06 12.68 9.44 9.25 9.45 11.65

 

American League ERA:     4.08 4.17 4.10 4.12 4.07 4.24 4.15 4.08 4.08 4.14



1989

 

AL EAST                  Consolidated Standings   GB   RealPythLin Wt

Divisional wins:         Toronto        91-71     --   89  90 88

Boston - 1*              Milwaukee      84-78     7   81  84  79

Milwaukee - 1.5*         Boston         82-80     9   83  85  88

Toronto - 7.5*           Cleveland      79-83     12   73  75  77

*Two Bos-Tor ties;       New York       77-85     14 74  71  74

 one Mil-Tor tie          Baltimore      74-88     17   87  84  81

                         Detroit        61-91     30   59  59  63

 

AL WEST                  Consolidated Standings   GB

Divisional wins:         Oakland        93-69     --   99  98  95

California - 2           Kansas City    90-72     3   92  88  87

Kansas City 2.5*         Texas          89-73     4   83  79  82

Oakland - 4              California    87-75     6   91  93  89

Texas - 1.5*             Seattle        76-86     17   73  77  75

*One KC-Tex tie          Chicago        68-94     25   69  75 74

                         California     60-102    37   72  69  65

 

NL EAST                  Consolidated Standings   GB

Divisional wins:         St. Louis      94-68     --   86  84  88

Chicago - 4*             Chicago       89-73     5   93  91  89

St. Louis - 6*           New York     82-80     12   87  92  88

                         Montreal      81-81     13   81  81  83

*Two Chi-St.L ties       Pittsburgh     81-81     13   74  76  76

                         Philadelphia   64-98     30   67  68 73

 

 

NL WEST                  Consolidated Standings   GB

Divisional wins:         San Francisco  88-74     --   92  93 90

Cincinnati - 1           Houston     84-78     4   86  78  74

Houston - 4              Cincinnati 82-80     6   75  74  77

San Diego - 1            Los Angeles    80-82     8   77  84  82

San Francisco - 5        San Diego      77-85     11   89 83  84

                         Atlanta        69-93     19   63  69  68




1988

 

AL EAST                  Consolidated Standings   GB   RealPythLin Wt

Divisional wins:         Boston         93-69     --   89  94 96

Boston - 4               Milwaukee      91-71     2   87  90  91

Milwaukee - 3            Toronto        85-77     8   87  89  84

New York - 1             Detroit       83-79     10   88  86  84

Toronto - 2              New York       82-80     11 85  84  80

                         Cleveland      78-84     15   78  73  74

                         Baltimore      54-108    39   54  53  61

 

AL WEST                  Consolidated Standings   GB

Divisional wins:         Oakland      94-68     --   104  101  95

Kansas City - 2          Minnesota      92-70     2   91  91  92

Minnesota - 1.5*         Seattle        82-80     12   68  72  77

Oakland - 6.5*           Kansas City    82-80     12   84  88  85

                         California     74-88     20   75  75  72

*One Min-Oak tie         Texas        73-89     21   70  69  74

                         Chicago        71-91     23   71  66  67

 

NL EAST                  Consolidated Standings   GB

Divisional wins:         New York 101-61    --   100  103  100

New York - 9             Montreal       88-74     13   81  86 87

St. Louis - 1            St. Louis     84-78     17   76  74  79

                         Pittsburgh     81-81     20   85 85  83

                           Chicago   81-81     20   77  77  78

                         Philadelphia   65-97     36   65  65  66

 

 

NL WEST                  Consolidated Standings   GB

Divisional wins:         Cincinnati     92-70     --   87  87  85

Cincinnati - 4*          San Francisco  88-74     4   83  86  83

Houston - 0.5            San Diego 84-78     8   83  83  82

San Diego - 2            Houston        81-81     11   82  79  79

San Francisco - 3.5      Los Angeles    76-86     16   94  92  85

*One Cin-Hou tie; one    Atlanta    51-111    41   54  58  60

 Cin-SF tie




1987

 

AL EAST                  Consolidated Standings   GB   RealPythLin Wt

Divisional wins:         Toronto       90-72     --   96  101 96

Boston - 1               New York       89-73     1   89  84  83

Detroit - 0.3*           Milwaukee      85-77     5   91  85  81

Milwaukee - 0.3*         Boston       82-80     8   78  83 81

New York - 5             Detroit        79-83     11 98  97  96

Toronto - 3.3*           Baltimore     69-93     21   67  66  69

*One Det-Mil-Tor tie     Cleveland     65-97     23   61  61  65

 

AL WEST                  Consolidated Standings   GB

Divisional wins:         Kansas City    86-76     --   83  84  86

California - 2           Minnesota      85-77     1   85  79  79

Chicago - 1              Chicago        84-78     2   77  81  79

Kansas City - 3          California    84-78     2   75  78  77

Minnesota - 3            Seattle        83-79     3   78  77  82

Seattle - 1              Oakland        79-83     7   81  83  82

                         Texas          75-87     11   75  78  77

 

NL EAST                  Consolidated Standings   GB

Divisional wins:         New York      94-68     --   92  94  93

New York - 7             St. Louis      90-72     4   95  92  85

St. Louis - 3            Montreal     82-80     12   91  83  82

                         Pittsburgh     81-81     13   80  76  80

                         Chicago   77-85     17   76  72  77

                         Philadelphia   77-85     17   80  79  81

 

 

NL WEST                  Consolidated Standings   GB

Divisional wins:         San Francisco  92-70     --   90  94 88

Cincinnati - 0.5*        Cincinnati     80-72     12   84  82  84

Houston - 1              Houston 79-83     13   76  77  79

San Francisco - 8.5*     San Diego      77-85 15  65  70  74

                         Atlanta      72-90     20   69  73  75

*One Cin-SF tie          Los Angeles    71-91     21   73  76  74




1986

 

AL EAST                  Consolidated Standings   GB   RealPythLin Wt

Divisional wins:         New York       99-63     --   90  87 92

Boston - 1               Toronto        94-68     5   86  89 86

Detroit - 2              Detroit      93-69     6   87  90  90

New York - 6.5*          Boston       86-76     13   95  92  89

Toronto - 0.5*           Milwaukee      81-81     18 77  73  76

                         Cleveland      76-86     23   84  80  80

*One NY-Tor tie          Baltimore      76-86     23   73  75  76

 

AL WEST                  Consolidated Standings   GB

Divisional wins:         California     95-67     --   92  92  91

California - 8           Kansas City    77-85     18   76  79  79

Kansas City - 1          Texas        76-86     19   87  84  84

Texas - 1                Minnesota    75-87     20   71  71  73

                         Oakland        73-89     22   76  78  75

                         Chicago        71-91     24   72  74 74 

                         Seattle     61-101    34   67  69  68

 

NL EAST                  Consolidated Standings   GB

Divisional wins:         New York      93-69     --   108  105  100

Montreal - 1             St. Louis      89-73     4   79  80  77

New York - 4.5*          Philadelphia   87-75     6   86  84 84

Philadelphia - 2         Montreal       83-79     10   78  75  80

St. Louis - 2.5*         Pittsburgh   70-92     23   64  77  76

* One NY-St.L tie        Chicago       68-94     25   70  70  70

 

 

NL WEST                  Consolidated Standings   GB

Divisional wins:         Houston        93-69     --   96 92  92

Cincinnati - 1           San Francisco  92-70     1   83  91  85

Houston - 4              Cincinnati 82-80     11   86  83  81

San Francisco - 5        San Diego      74-88     19   74  73  76

                         Atlanta      73-89     20   72  68  74

                         Los Angeles    68-94     25   73  76  74



Copyright © 1993 Doug Pappas. All rights reserved.
Originally presented at the 1993 SABR convention.



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