# Team Payroll and the World Series

# set some default options for chunks knitr::opts_chunk$set( warning = FALSE, # avoid warnings and messages in the output message = FALSE, collapse = TRUE, # collapse all output into a single block tidy = FALSE, # don't tidy our code-- assume we do it ourselves fig.height = 5, fig.width = 5 ) options(digits=4) # number of digits to display in output; can override with chunk option R.options=list(digits=) par(mar=c(3,3,1,1)+.1) set.seed(1234) # reproducibility library(Lahman) # Load additional packages here library(ggplot2) library(dplyr) 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. ## The data files Start with loading the files we will use here. We do some pre-processing to make them more convenient for the analyses done later. ### The Salaries data The Salaries data.frame contains data on all players' salaries from 1985-2015 in the latest release, v. r packageVersion("Lahman"), of the Lahman package. We use the sample_n function to display a random sample of observations. data("Salaries", package="Lahman") str(Salaries) sample_n(Salaries, 10) ### The Teams data The 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) names(Teams) 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) ### The SeriesPost data Post season records go back to 1884. There are r nrow(Lahman::SeriesPost) observations covering all aspects of post-season play. data("SeriesPost", package="Lahman") names(SeriesPost) 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)

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.

WS <- SeriesPost %>% filter(yearID >= 1985 & round == "WS") %>% select(-ties, -round) %>% mutate(lgIDloser = droplevels(lgIDloser), lgIDwinner = droplevels(lgIDwinner)) dim(WS) sample_n(WS, 6)

## A first look at Salaries

How many players do we have in each year?

table(Salaries$yearID) What is the range of salaries, across all years? range(Salaries$salary)

And, year by year?

Salaries %>% group_by(yearID) %>% summarise(min=min(salary), max=max(salary))

Hmm, there is a salary==0 in 1993, maybe there are others.

which(Salaries$salary==0) Who are they? (We could also look up their playerIDs in Lahman::People.) Salaries[which(Salaries$salary==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)

### Get team payrolls

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.

payroll <- Salaries %>% group_by(teamID, yearID) %>% summarise(payroll = sum(salary)/1000000) head(payroll)

### Merge team names into 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.

payroll <- merge(payroll, Teams[,c("yearID", "teamID","name", "WSWin")], by=c("yearID", "teamID")) sample_n(payroll, 10)

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$WSWin, useNA="ifany") There is something wrong here! There shouldn't be any NAs. We leave this for further study, and another Reminder to file an issue if we figure out what the problem is. ## Boxplots of payroll Let's look at the distributions of payroll by year. The observations are teams. boxplot(payroll ~ yearID, data=payroll, ylab="Payroll ($ 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.

out <- car::Boxplot(payroll ~ yearID, data=payroll, id=list(n=1, labels=as.character(payroll$teamID)), ylab="Payroll ($ millions)")

Most of the outliers are the New York Yankees (NYA):

table(out)

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.

### Correcting for inflation

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 (http://www.in2013dollars.com/).

inflation = c(1, 1.02, 1.06, 1.10, 1.15, 1.21, 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 ) inflation.df <- data.frame(year=1985:2015, inflation) # 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.)

infl.lm <- lm(inflation ~ year, data=inflation.df) (coefs <- coef(infl.lm))

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.

car::Boxplot(payrollStd ~ yearID, data=payroll, id = list(labels=as.character(payroll$teamID)), ylab="Payroll (1985-adjusted$ millions)")

## Salaries of World Series winning teams

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.

Cols <- ifelse(payroll$WSWin=='Y', "red", gray(.7, alpha=0.5)) with(payroll, { plot(payrollStd ~ jitter(yearID, 0.5), ylab = "Payroll (inflation-adjusted$ 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.

• Follow-up the suggestion to fit a linear model predicting log(payroll) from some of the available predictors.