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This vignette examines whether there is a relationship between total
team salaries (payroll) and World Series success. It was inspired by
Nolan & Lang (2015), “Baseball: Exploring Data in a Relational
Database”, Chapter 10 in Data Science in R.
They use SQL
on the raw Lahman files .csv
,
rather than the Lahman package.
Here, We largely use dplyr
for data munging and
ggplot2
for plotting. In the process, we discover a few
errors in the data sets.
Start with loading the files we will use here. We do some pre-processing to make them more convenient for the analyses done later.
Salaries
dataThe Salaries
data.frame contains data on all players’
salaries from 1985-2016 in the latest release, v. 11.0.0, of the
Lahman
package. (Additions to the Salaries
table in San Lahman’s database were discontinued after 2016.) We use the
sample_n
function to display a random sample of
observations.
data("Salaries", package="Lahman")
str(Salaries)
## 'data.frame': 26428 obs. of 5 variables:
## $ yearID : int 1985 1985 1985 1985 1985 1985 1985 1985 1985 1985 ...
## $ teamID : Factor w/ 35 levels "ANA","ARI","ATL",..: 3 3 3 3 3 3 3 3 3 3 ...
## $ lgID : Factor w/ 2 levels "AL","NL": 2 2 2 2 2 2 2 2 2 2 ...
## $ playerID: chr "barkele01" "bedrost01" "benedbr01" "campri01" ...
## $ salary : int 870000 550000 545000 633333 625000 800000 150000 483333 772000 250000 ...
sample_n(Salaries, 10)
## yearID teamID lgID playerID salary
## 1 1995 BAL AL benitar01 125000
## 2 1995 NYA AL fernato01 1633335
## 3 1994 PHI NL chambwe01 350000
## 4 1995 OAK AL aldremi01 430000
## 5 2013 NYN NL wrighda03 10192071
## 6 1996 SEA AL strando01 380000
## 7 1986 BOS AL hoffmgl01 350000
## 8 2003 MIL NL sexsori01 5125000
## 9 1998 NYA AL seabosc01 170000
## 10 1986 ML4 AL higuete01 195000
Teams
dataThe Teams
data.frame contains a lot of information about
all teams that have ever played, with a separate observation for each
year. Here, we will mainly use this to get the team name
(team
) from teamID
and also to get the
information about World Series winners.
data("Teams", package="Lahman")
dim(Teams)
## [1] 3015 48
names(Teams)
## [1] "yearID" "lgID" "teamID" "franchID"
## [5] "divID" "Rank" "G" "Ghome"
## [9] "W" "L" "DivWin" "WCWin"
## [13] "LgWin" "WSWin" "R" "AB"
## [17] "H" "X2B" "X3B" "HR"
## [21] "BB" "SO" "SB" "CS"
## [25] "HBP" "SF" "RA" "ER"
## [29] "ERA" "CG" "SHO" "SV"
## [33] "IPouts" "HA" "HRA" "BBA"
## [37] "SOA" "E" "DP" "FP"
## [41] "name" "park" "attendance" "BPF"
## [45] "PPF" "teamIDBR" "teamIDlahman45" "teamIDretro"
We are only going to use the observations from 1985 on, and a few
variables, so we filter and select them now. Keep only the levels of
teamID
in the data.
<- Teams %>%
Teams select(yearID, lgID, teamID, name, divID, Rank, WSWin, attendance) %>%
filter(yearID >= 1985) %>%
mutate(teamID = droplevels(teamID))
sample_n(Teams, 10)
## yearID lgID teamID name divID Rank WSWin attendance
## 1 1999 NL PHI Philadelphia Phillies E 3 N 1825337
## 2 2016 AL KCA Kansas City Royals C 3 N 2557712
## 3 1988 NL PIT Pittsburgh Pirates E 2 N 1866713
## 4 2010 AL NYA New York Yankees E 2 N 3765807
## 5 1997 NL CHN Chicago Cubs C 5 N 2190308
## 6 2015 NL SLN St. Louis Cardinals C 1 N 3520889
## 7 1995 NL CHN Chicago Cubs C 3 N 1918265
## 8 1992 AL BAL Baltimore Orioles E 3 N 3567819
## 9 2005 NL MIL Milwaukee Brewers C 3 N 2211023
## 10 1985 AL CAL California Angels W 2 N 2567427
SeriesPost
dataPost season records go back to 1884. There are 378 observations covering all aspects of post-season play.
data("SeriesPost", package="Lahman")
names(SeriesPost)
## [1] "yearID" "round" "teamIDwinner" "lgIDwinner" "teamIDloser"
## [6] "lgIDloser" "wins" "losses" "ties"
For each year, there are number of observations for the various levels of post-season play (Division titles, League titles, etc. A number of these designations have changed over the years, and I don’t know what they all mean.)
table(SeriesPost$round)
##
## AEDIV ALCS ALDS1 ALDS2 ALWC ALWC1 ALWC2 ALWC3 ALWC4 AWDIV CS NEDIV NLCS
## 1 53 28 28 9 2 2 1 1 1 1 1 53
## NLDS1 NLDS2 NLWC NLWC1 NLWC2 NLWC3 NLWC4 NWDIV WS
## 28 28 9 2 2 1 1 1 125
We are interested only in the World Series (WS
), which
was first played in 1903. We filter for the years for which we have
salary data, and drop a couple of variables. The league IDs of the
winner and loser are factors, so we use droplevels
to
include only the levels in recent history.
<- SeriesPost %>%
WS filter(yearID >= 1985 & round == "WS") %>%
select(-ties, -round) %>%
mutate(lgIDloser = droplevels(lgIDloser),
lgIDwinner = droplevels(lgIDwinner))
dim(WS)
## [1] 37 7
sample_n(WS, 6)
## yearID teamIDwinner lgIDwinner teamIDloser lgIDloser wins losses
## 1 1988 LAN NL OAK AL 4 1
## 2 2006 SLN NL DET AL 4 1
## 3 2005 CHA AL HOU NL 4 0
## 4 1987 MIN AL SLN NL 4 3
## 5 2016 CHN NL CLE AL 4 3
## 6 2014 SFN NL KCA AL 4 3
Salaries
How many players do we have in each year?
table(Salaries$yearID)
##
## 1985 1986 1987 1988 1989 1990 1991 1992 1993 1994 1995 1996 1997 1998 1999 2000
## 550 738 627 663 711 867 685 769 923 884 986 931 925 998 1006 836
## 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010 2011 2012 2013 2014 2015 2016
## 860 846 827 831 831 819 842 856 813 830 839 848 815 802 817 853
What is the range of salaries, across all years?
range(Salaries$salary)
## [1] 0 33000000
And, year by year?
%>%
Salaries group_by(yearID) %>%
summarise(min=min(salary),
max=max(salary))
## # A tibble: 32 × 3
## yearID min max
## <int> <int> <int>
## 1 1985 60000 2130300
## 2 1986 60000 2800000
## 3 1987 62500 2127333
## 4 1988 62500 2340000
## 5 1989 62500 2766667
## 6 1990 100000 3200000
## 7 1991 100000 3800000
## 8 1992 109000 6100000
## 9 1993 0 6200000
## 10 1994 50000 6300000
## # ℹ 22 more rows
Hmm, there is a salary==0
in 1993, maybe there are
others.
which(Salaries$salary==0)
## [1] 6180 12008
Who are they? (We could also look up their playerID
s in
Lahman::People
.)
which(Salaries$salary==0),]
Salaries[## yearID teamID lgID playerID salary
## 6180 1993 NYA AL jamesdi01 0
## 12008 1999 PIT NL martija02 0
These must be errors. Get rid of them. Reminder: Check further; maybe file an issue in the Lahman package!
<- Salaries %>%
Salaries filter(salary !=0)
We want to sum the salary
for each team for each year.
We might as well make it in millions. All those zeros hurt my eyes.
<- Salaries %>%
payroll group_by(teamID, yearID) %>%
summarise(payroll = sum(salary)/1000000)
head(payroll)
## # A tibble: 6 × 3
## # Groups: teamID [1]
## teamID yearID payroll
## <fct> <int> <dbl>
## 1 ANA 1997 31.1
## 2 ANA 1998 41.3
## 3 ANA 1999 55.4
## 4 ANA 2000 51.5
## 5 ANA 2001 47.5
## 6 ANA 2002 61.7
payroll
It will be more convenient to have the team names included in the
payroll
data.frame. The Teams
data frame also
contains the Y/N
indicator WSWin
for World
Series winners, so we might as well include this too.
<- merge(payroll, Teams[,c("yearID", "teamID","name", "WSWin")],
payroll by=c("yearID", "teamID"))
sample_n(payroll, 10)
## yearID teamID payroll name WSWin
## 1 2007 MIL 70.99 Milwaukee Brewers N
## 2 2016 LAA 137.25 Los Angeles Angels of Anaheim N
## 3 2005 OAK 55.43 Oakland Athletics N
## 4 2003 FLO 49.45 Florida Marlins Y
## 5 2009 COL 75.20 Colorado Rockies N
## 6 2000 MIL 36.51 Milwaukee Brewers N
## 7 1999 ANA 55.39 Anaheim Angels N
## 8 2013 NYA 231.98 New York Yankees N
## 9 1989 CAL 15.10 California Angels N
## 10 1990 ATL 14.56 Atlanta Braves N
Note that we could also do this using left_join
in the
dplyr
package. There is probably a more tidy
way to subset the variables from the Teams
data set than
using Teams[, c()]
, but, hey– this works.
left_join(payroll, Teams[,c("yearID", "teamID","name", "WSWin")],
by=c("yearID", "teamID")) %>%
sample_n(10)
WSWin
is a character variable. Convert it to a
factor.
<- payroll %>%
payroll mutate(WSWin = factor(WSWin))
Check the values:
table(payroll$WSWin, useNA="ifany")
##
## N Y <NA>
## 859 31 28
There is something wrong here! There shouldn’t be any
NA
s. We leave this for further study, and another
Reminder to file an issue if we figure out what the
problem is.
Let’s look at the distributions of payroll by year. The observations are teams.
boxplot(payroll ~ yearID, data=payroll, ylab="Payroll ($ millions)")
What are the outliers? Are there any teams that crop up repeatedly?
car::Boxplot
makes this easy, and also returns the labels
of the outliers. We don’t load the car
package, because
car
also contains a Salary
dataset.
<- car::Boxplot(payroll ~ yearID, data=payroll,
out id=list(n=1,
labels=as.character(payroll$teamID)),
ylab="Payroll ($ millions)")
Most of the outliers are the New York Yankees (NYA
):
table(out)
## out
## CLE LAN MON NYA PIT SEA
## 1 2 1 11 1 1
Payroll has obviously increased dramatically over time. So has the
variability across teams. For any modelling, we would probably want to
use \log(payroll)
. We might also want to look separately at
the American and National leagues.
For proper comparisons, we should correct for inflation. Lets do this by scaling salary back to 1985 dollars, The data below gives inflation rates for all subsequent years. It comes from Nolan & Lang, extended to 2015 using (https://www.in2013dollars.com/).
= c(1, 1.02, 1.06, 1.10, 1.15, 1.21,
inflation 1.27, 1.30, 1.34, 1.38, 1.42, 1.46, 1.49, 1.51, 1.55, 1.60,
1.65, 1.67, 1.71, 1.76, 1.82, 1.87, 1.93, 2.00, 1.99, 2.03,
2.09, 2.13, 2.16, 2.20, 2.20 )
<- data.frame(year=1985:2015, inflation)
inflation.df
# plot inflation rate
ggplot(inflation.df, aes(y=inflation, x=year)) +
geom_point() +
geom_line() +
geom_smooth(method="lm")
This is close enough to linear, that we could use the linear
regression predicted value as a simple computation of the inflation
rate. (A better way, of course, would be to use the actual inflation
rate; this would entail merging payroll
with
inflation.df
by year, and doing the computation.)
<- lm(inflation ~ year, data=inflation.df)
infl.lm <- coef(infl.lm))
(coefs ## (Intercept) year
## -81.57032 0.04159
Scale payroll
by dividing by linear prediction of
inflation rate, producing payrollStd
.
<- payroll %>%
payroll mutate(payrollStd = payroll / (coefs[1] + coefs[2] * yearID))
Boxplot again, of inflation-adjusted payroll. The increase after 2000 doesn’t seem so large.
::Boxplot(payrollStd ~ yearID, data=payroll,
carid = list(labels=as.character(payroll$teamID)),
ylab="Payroll (1985-adjusted $ millions)")
## [1] "SEA" "CLE" "MON" "PIT" "NYA" "NYA" "NYA" "NYA" "NYA" "NYA" "NYA" "NYA"
## [13] "NYA" "NYA" "LAN" "NYA" "LAN" "NYA" "BOS" "DET" "LAN" "NYA"
To what extent are the World Series winners those among the highest in payroll? A simple way to look at this is to plot the team payrolls across years, and mark the World Series winner for each year.
This plot shows inflation-adjusted payroll on a log scale to avoid the dominating influence of the most recent years. We jitter the points to avoid overplotting, and use a transparent gray color for the non-winners, red for the winner in each year.
<- ifelse(payroll$WSWin=='Y', "red", gray(.7, alpha=0.5))
Cols with(payroll, {
plot(payrollStd ~ jitter(yearID, 0.5),
ylab = "Payroll (inflation-adjusted $ millions)",
ylim = c(5,125), log = "y",
xlab = "Year",
pch = 19, cex = 0.8, col = Cols)
})with(payroll[payroll$WSWin == 'Y',],
text(y = payrollStd, x = yearID, labels = teamID, pos = 3, cex = 0.8) )
By and large, the World Series winners tend to be in the upper portion of the payrolls for each year.
Here are some questions to provoke further analyses of these data sets. If you find something interesting, post it in a Github Gist or forward it to Team Lahman as in a Lahman issue.
Our boxplots used total payroll in millions. Would the plots be clearer if we plotted payroll on a log scale?
Follow-up the suggestion to fit a linear model predicting
log(payroll)
from some of the available
predictors.
Examine the trend of team salaries over time for World Series losers. Does it look the same or different than that for the winning teams?
What kind of analysis would you do to address this statement: “For teams that make it to the World series, the one with the larger payroll is more likely to win.”
Is there any relationship between the number of team wins in a season and winning the World series?
These binaries (installable software) and packages are in development.
They may not be fully stable and should be used with caution. We make no claims about them.