How can you not be romantic about baseball?
— Billy Beans

Last week, we discussed how Billy Beans and Paul DePosta predicted, using linear regression, about the conditions necessary for Oakland A’s to make it to the 2002 playoffs. Although A’s made it to the playoffs yet they didn’t succeed to win the World Series. Billy Beans justified this by making a claim that sabermatrics can’t be used to predict baseball champions. Today, we’ll try to analyze why no prediction can’t be made for winning the baseball World Series.

We’ll try to make prediction using logistic regression in R with the same dataset baseball.csv used last week.

# load in the dataset
> baseball = read.csv ( "baseball.csv" )
> table ( baseball $ Year ) # 1972, 1981, 1994, and 1995 are missing
1962 1963 1964 1965 1966 1967 1968 1969 1970 1971 1973 1974 1975 1976 1977 1978 1979
20 20 20 20 20 20 20 24 24 24 24 24 24 24 26 26 26
1980 1982 1983 1984 1985 1986 1987 1988 1989 1990 1991 1992 1993 1996 1997 1998 1999
26 26 26 26 26 26 26 26 26 26 26 26 28 28 28 30 30
2000 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010 2011 2012
30 30 30 30 30 30 30 30 30 30 30 30 30
# we're only analyzing teams that made the playoffs
> baseball = subset ( baseball , Playoffs == 1 )
# no of teams making to the playoffs in particular year
> table ( baseball $ Year )
1962 1963 1964 1965 1966 1967 1968 1969 1970 1971 1973 1974 1975 1976 1977 1978 1979
2 2 2 2 2 2 2 4 4 4 4 4 4 4 4 4 4
1980 1982 1983 1984 1985 1986 1987 1988 1989 1990 1991 1992 1993 1996 1997 1998 1999
4 4 4 4 4 4 4 4 4 4 4 4 4 8 8 8 8
2000 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010 2011 2012
8 8 8 8 8 8 8 8 8 8 8 8 10
> table ( table ( baseball $ Year ))
2 4 8 10
7 23 16 1

Note that it’s much harder to win the World Series if there are 10 teams competing for the championship versus just two. Therefore, we will add the predictor variable `NumCompetitors`

to the baseball data frame. It will contain the number of total teams making the playoffs in the year of a particular team/year pair.

> playoffTable = table ( baseball $ Year )
> str ( names ( playoffTable ))
chr [ 1 : 47 ] "1962" "1963" "1964" "1965" "1966" "1967" "1968" "1969" ...
> playoffTable [ c ( "1990" , "2001" )]
1990 2001
4 8
> baseball $ NumCompetitors = playoffTable [ as.character ( baseball $ Year )]
> table ( baseball $ NumCompetitors )
2 4 8 10
14 92 128 10
# Add a variable named WorldSeries to the baseball data frame (takes value 1 if a team won the World Series)
> baseball $ WorldSeries = as.numeric ( baseball $ RankPlayoffs == 1 )
> table ( baseball $ WorldSeries )
0 1
197 47

When we’re not sure which of our variables are useful in predicting a particular outcome, it’s often helpful to build bivariate models, which are models that predict the outcome using a single independent variable.

# logistic regression models with a single independent variable
> summary ( glm ( WorldSeries ~ Year , data = baseball , family = "binomial" ))
Call :
glm ( formula = WorldSeries ~ Year , family = "binomial" , data = baseball )
Deviance Residuals :
Min 1 Q Median 3 Q Max
-1.0297 -0.6797 -0.5435 -0.4648 2.1504
Coefficients :
Estimate Std. Error z value Pr ( >| z | )
( Intercept ) 72.23602 22.64409 3.19 0.00142 **
Year -0.03700 0.01138 -3.25 0.00115 **
---
Signif. codes : 0 ‘ *** ’ 0.001 ‘ ** ’ 0.01 ‘ * ’ 0.05 ‘ . ’ 0.1 ‘ ’ 1
( Dispersion parameter for binomial family taken to be 1 )
Null deviance : 239.12 on 243 degrees of freedom
Residual deviance : 228.35 on 242 degrees of freedom
AIC : 232.35
Number of Fisher Scoring iterations : 4
> summary ( glm ( WorldSeries ~ RS , data = baseball , family = "binomial" ))
Call :
glm ( formula = WorldSeries ~ RS , family = "binomial" , data = baseball )
Deviance Residuals :
Min 1 Q Median 3 Q Max
-0.8254 -0.6819 -0.6363 -0.5561 2.0308
Coefficients :
Estimate Std. Error z value Pr ( >| z | )
( Intercept ) 0.661226 1.636494 0.404 0.686
RS -0.002681 0.002098 -1.278 0.201
( Dispersion parameter for binomial family taken to be 1 )
Null deviance : 239.12 on 243 degrees of freedom
Residual deviance : 237.45 on 242 degrees of freedom
AIC : 241.45
Number of Fisher Scoring iterations : 4
> summary ( glm ( WorldSeries ~ RA , data = baseball , family = "binomial" ))
Call :
glm ( formula = WorldSeries ~ RA , family = "binomial" , data = baseball )
Deviance Residuals :
Min 1 Q Median 3 Q Max
-0.9749 -0.6883 -0.6118 -0.4746 2.1577
Coefficients :
Estimate Std. Error z value Pr ( >| z | )
( Intercept ) 1.888174 1.483831 1.272 0.2032
RA -0.005053 0.002273 -2.223 0.0262 *
---
Signif. codes : 0 ‘ *** ’ 0.001 ‘ ** ’ 0.01 ‘ * ’ 0.05 ‘ . ’ 0.1 ‘ ’ 1
( Dispersion parameter for binomial family taken to be 1 )
Null deviance : 239.12 on 243 degrees of freedom
Residual deviance : 233.88 on 242 degrees of freedom
AIC : 237.88
Number of Fisher Scoring iterations : 4
> summary ( glm ( WorldSeries ~ NumCompetitors , data = baseball , family = "binomial" ))
Call :
glm ( formula = WorldSeries ~ NumCompetitors , family = "binomial" ,
data = baseball )
Deviance Residuals :
Min 1 Q Median 3 Q Max
-0.9871 -0.8017 -0.5089 -0.5089 2.2643
Coefficients :
Estimate Std. Error z value Pr ( >| z | )
( Intercept ) 0.03868 0.43750 0.088 0.929559
NumCompetitors -0.25220 0.07422 -3.398 0.000678 ***
---
Signif. codes : 0 ‘ *** ’ 0.001 ‘ ** ’ 0.01 ‘ * ’ 0.05 ‘ . ’ 0.1 ‘ ’ 1
( Dispersion parameter for binomial family taken to be 1 )
Null deviance : 239.12 on 243 degrees of freedom
Residual deviance : 226.96 on 242 degrees of freedom
AIC : 230.96
Number of Fisher Scoring iterations : 4
> LogModel = glm ( WorldSeries ~ Year + RA + RankSeason + NumCompetitors , data = baseball , family = "binomial" )
> summary ( LogModel )
Call :
glm ( formula = WorldSeries ~ Year + RA + RankSeason + NumCompetitors ,
family = "binomial" , data = baseball )
Deviance Residuals :
Min 1 Q Median 3 Q Max
-1.0336 -0.7689 -0.5139 -0.4583 2.2195
Coefficients :
Estimate Std. Error z value Pr ( >| z | )
( Intercept ) 12.5874376 53.6474210 0.235 0.814
Year -0.0061425 0.0274665 -0.224 0.823
RA -0.0008238 0.0027391 -0.301 0.764
RankSeason -0.0685046 0.1203459 -0.569 0.569
NumCompetitors -0.1794264 0.1815933 -0.988 0.323
( Dispersion parameter for binomial family taken to be 1 )
Null deviance : 239.12 on 243 degrees of freedom
Residual deviance : 226.37 on 239 degrees of freedom
AIC : 236.37
Number of Fisher Scoring iterations : 4
# and so on ... there will be 12 models!!

After analyzing the above models, we found that `Year`

, `RA`

, `RankSeason`

and `NumCompetitors`

are significant .
Let’s build a regression model using above four variables.

# a logistic regression model
> LogModel = glm ( WorldSeries ~ Year + RA + RankSeason + NumCompetitors , data = baseball , family = "binomial" )
> summary ( LogModel )
Call :
glm ( formula = WorldSeries ~ Year + RA + RankSeason + NumCompetitors ,
family = "binomial" , data = baseball )
Deviance Residuals :
Min 1 Q Median 3 Q Max
-1.0336 -0.7689 -0.5139 -0.4583 2.2195
Coefficients :
Estimate Std. Error z value Pr ( >| z | )
( Intercept ) 12.5874376 53.6474210 0.235 0.814
Year -0.0061425 0.0274665 -0.224 0.823
RA -0.0008238 0.0027391 -0.301 0.764
RankSeason -0.0685046 0.1203459 -0.569 0.569
NumCompetitors -0.1794264 0.1815933 -0.988 0.323
( Dispersion parameter for binomial family taken to be 1 )
Null deviance : 239.12 on 243 degrees of freedom
Residual deviance : 226.37 on 239 degrees of freedom
AIC : 236.37
Number of Fisher Scoring iterations : 4

Oops, none of the variables are significant in the multivariate model!
It maybe due to correlation between the variables.

> cor ( baseball [ c ( "Year" , "RA" , "RankSeason" , "NumCompetitors" )])
Year RA RankSeason NumCompetitors
Year 1.0000000 0.4762422 0.3852191 0.9139548
RA 0.4762422 1.0000000 0.3991413 0.5136769
RankSeason 0.3852191 0.3991413 1.0000000 0.4247393
NumCompetitors 0.9139548 0.5136769 0.4247393 1.0000000

The above correlation matrix indicates that `Year/NumCompetitors`

has high degree of correlation (0.91).

Now, let’s try to build two-variable model.

> summary ( glm ( WorldSeries ~ Year + RA , data = baseball , family = binomial ))
Call :
glm ( formula = WorldSeries ~ Year + RA , family = binomial , data = baseball )
Deviance Residuals :
Min 1 Q Median 3 Q Max
-1.0402 -0.6878 -0.5298 -0.4785 2.1370
Coefficients :
Estimate Std. Error z value Pr ( >| z | )
( Intercept ) 63.610741 25.654830 2.479 0.0132 *
Year -0.032084 0.013323 -2.408 0.0160 *
RA -0.001766 0.002585 -0.683 0.4945
---
Signif. codes : 0 ‘ *** ’ 0.001 ‘ ** ’ 0.01 ‘ * ’ 0.05 ‘ . ’ 0.1 ‘ ’ 1
( Dispersion parameter for binomial family taken to be 1 )
Null deviance : 239.12 on 243 degrees of freedom
Residual deviance : 227.88 on 241 degrees of freedom
AIC : 233.88
Number of Fisher Scoring iterations : 4
> summary ( glm ( WorldSeries ~ Year + RankSeason , data = baseball , family = binomial ))
Call :
glm ( formula = WorldSeries ~ Year + RankSeason , family = binomial ,
data = baseball )
Deviance Residuals :
Min 1 Q Median 3 Q Max
-1.0560 -0.6957 -0.5379 -0.4528 2.2673
Coefficients :
Estimate Std. Error z value Pr ( >| z | )
( Intercept ) 63.64855 24.37063 2.612 0.00901 **
Year -0.03254 0.01231 -2.643 0.00822 **
RankSeason -0.10064 0.11352 -0.887 0.37534
---
Signif. codes : 0 ‘ *** ’ 0.001 ‘ ** ’ 0.01 ‘ * ’ 0.05 ‘ . ’ 0.1 ‘ ’ 1
( Dispersion parameter for binomial family taken to be 1 )
Null deviance : 239.12 on 243 degrees of freedom
Residual deviance : 227.55 on 241 degrees of freedom
AIC : 233.55
Number of Fisher Scoring iterations : 4
> summary ( glm ( WorldSeries ~ Year + NumCompetitors , data = baseball , family = binomial ))
Call :
glm ( formula = WorldSeries ~ Year + NumCompetitors , family = binomial ,
data = baseball )
Deviance Residuals :
Min 1 Q Median 3 Q Max
-1.0050 -0.7823 -0.5115 -0.4970 2.2552
Coefficients :
Estimate Std. Error z value Pr ( >| z | )
( Intercept ) 13.350467 53.481896 0.250 0.803
Year -0.006802 0.027328 -0.249 0.803
NumCompetitors -0.212610 0.175520 -1.211 0.226
( Dispersion parameter for binomial family taken to be 1 )
Null deviance : 239.12 on 243 degrees of freedom
Residual deviance : 226.90 on 241 degrees of freedom
AIC : 232.9
Number of Fisher Scoring iterations : 4
> summary ( glm ( WorldSeries ~ RA + RankSeason , data = baseball , family = binomial ))
Call :
glm ( formula = WorldSeries ~ RA + RankSeason , family = binomial ,
data = baseball )
Deviance Residuals :
Min 1 Q Median 3 Q Max
-0.9374 -0.6933 -0.5936 -0.4564 2.1979
Coefficients :
Estimate Std. Error z value Pr ( >| z | )
( Intercept ) 1.487461 1.506143 0.988 0.323
RA -0.003815 0.002441 -1.563 0.118
RankSeason -0.140824 0.110908 -1.270 0.204
( Dispersion parameter for binomial family taken to be 1 )
Null deviance : 239.12 on 243 degrees of freedom
Residual deviance : 232.22 on 241 degrees of freedom
AIC : 238.22
Number of Fisher Scoring iterations : 4
> summary ( glm ( WorldSeries ~ RA + NumCompetitors , data = baseball , family = binomial ))
Call :
glm ( formula = WorldSeries ~ RA + NumCompetitors , family = binomial ,
data = baseball )
Deviance Residuals :
Min 1 Q Median 3 Q Max
-1.0433 -0.7826 -0.5133 -0.4701 2.2208
Coefficients :
Estimate Std. Error z value Pr ( >| z | )
( Intercept ) 0.716895 1.528736 0.469 0.63911
RA -0.001233 0.002661 -0.463 0.64313
NumCompetitors -0.229385 0.088399 -2.595 0.00946 **
---
Signif. codes : 0 ‘ *** ’ 0.001 ‘ ** ’ 0.01 ‘ * ’ 0.05 ‘ . ’ 0.1 ‘ ’ 1
( Dispersion parameter for binomial family taken to be 1 )
Null deviance : 239.12 on 243 degrees of freedom
Residual deviance : 226.74 on 241 degrees of freedom
AIC : 232.74
Number of Fisher Scoring iterations : 4
> summary ( glm ( WorldSeries ~ RankSeason + NumCompetitors , data = baseball , family = binomial ))
Call :
glm ( formula = WorldSeries ~ RankSeason + NumCompetitors , family = binomial ,
data = baseball )
Deviance Residuals :
Min 1 Q Median 3 Q Max
-1.0090 -0.7592 -0.5204 -0.4501 2.2562
Coefficients :
Estimate Std. Error z value Pr ( >| z | )
( Intercept ) 0.12277 0.45737 0.268 0.78837
RankSeason -0.07697 0.11711 -0.657 0.51102
NumCompetitors -0.22784 0.08201 -2.778 0.00546 **
---
Signif. codes : 0 ‘ *** ’ 0.001 ‘ ** ’ 0.01 ‘ * ’ 0.05 ‘ . ’ 0.1 ‘ ’ 1
( Dispersion parameter for binomial family taken to be 1 )
Null deviance : 239.12 on 243 degrees of freedom
Residual deviance : 226.52 on 241 degrees of freedom
AIC : 232.52
Number of Fisher Scoring iterations : 4

None of the models with two independent variables has both variables significant, so none seem promising as compared to a simple bivariate model. Indeed the model with the lowest AIC value is the model with just `NumCompetitors`

as the independent variable.

This seems to confirm the claim made by Billy Beane in Moneyball that all that matters in the Playoffs is luck, since `NumCompetitors`

has nothing to do with the quality of the teams!
Hence, no prediction can be made for baseball champion.