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Arrieta for Cy Young

Michael Griffiths
November 19, 2015

<style type="text/css"> .section {overflow-x:scroll;} </style>

This is an effort to duplicate Greg Reida's iPython notebook on Cy Young in R, for kicks and giggles.

To begin, let's load the Hadley-verse.

library(readr)
library(dplyr)
library(tidyr)
library(ggplot2)

# For quick plot styles
library(ggthemes)
# Set to FiveThirtyEight default
theme_set(theme_fivethirtyeight())

# To customize output for HTML.
library(knitr)
library(pander)
knit_print.data.frame = function(x, options){ pander(x) }
knit_print.list = function(x, options){ pander(x) }
knit_print.matrix = function(x, options){ pander(x) }
knit_print.table = function(x, options){ pander(x) }

panderOptions('table.style', "rmarkdown")
panderOptions('table.split.table', Inf)
panderOptions('table.split.cells', Inf)
panderOptions('table.alignment.default', 'left')

Load game log files

First, let's load in some of the initial game files.

# Convert date column to an actual date object. 
# Note that date comes in as either "Apr 11" or "Jul 12(1)"; we don't care about the brackets.
to_date <- function(datestring){
  date_no_brackets = gsub("\\(.+\\)", "", datestring)
  dates <- as.Date(sprintf("%s 2015", date_no_brackets), "%b %d %Y")
  return(dates)
}

# Convert innings to fraction.
# See @url(https://en.wikipedia.org/wiki/Innings_pitched)
innings_pitched <- function(ip){
  inning = floor(ip)
  partial_inning = ip %% 1
  return(inning + partial_inning / .3)
}

# Load three files into one dataframe, with a new column for the filename.
files = c("arrieta", "greinke", "kershaw")
data = list()
for(file in files){
  read_csv(sprintf("data/gamelogs/%s2015.csv", file)) %>%
    mutate(Date = to_date(Date), 
           player = file,
           IP = innings_pitched(IP)) ->
    data[[file]]
}
data = bind_rows(data)
head(data)
Rk Gcar Gtm Date Tm [EMPTY] Opp Rslt Inngs Dec DR IP H R ER BB SO HR HBP ERA BF Pit Str StL StS GB FB LD PU Unk GSc IR IS SB CS PO AB 2B 3B IBB GDP SF ROE aLI WPA RE24 DFS(DK) DFS(FD) Entered Exited player
1 104 2 2015-04-08 CHC STL W2-0 GS-7 W(1-0) 99 7 3 0 0 3 7 0 0 0 27 104 65 20 4 7 10 3 2 0 75 NA NA 0 0 0 24 1 0 0 0 0 0 1.13 0.428 3.23 30.15 15 1t start tie 7t 3 out tie arrieta
2 105 7 2015-04-14 CHC CIN L2-3 GS-7 L(1-1) 5 6.667 7 3 3 1 5 0 0 1.98 27 110 73 20 7 9 12 5 2 0 52 NA NA 1 0 0 26 2 0 0 0 0 0 0.75 -0.105 -0.08 10.6 8.67 1t start tie 7t -2- 2 out d3 arrieta
3 106 12 2015-04-20 CHC @ PIT W5-2 GS-7 W(2-1) 5 7 4 1 1 0 7 0 0 1.74 26 100 69 18 15 13 6 5 0 0 72 NA NA 1 0 0 26 2 0 0 0 0 1 0.89 0.25 2.23 26.95 14 1b start tie 7b 3 out a3 arrieta
4 107 17 2015-04-26 CHC @ CIN W5-2 GS-6 W(3-1) 5 6 4 2 2 3 6 1 0 2.02 25 105 70 21 9 10 6 4 1 0 59 NA NA 1 0 0 22 0 0 0 0 0 0 1.16 0.18 0.79 20.7 11 1b start tie 6b 3 out a3 arrieta
5 108 22 2015-05-02 CHC MIL L1-6 GS-5 L(3-2) 5 5 7 4 4 1 6 1 0 2.84 22 90 62 12 8 6 9 5 1 0 42 NA NA 3 1 0 20 0 0 0 0 0 0 0.55 -0.239 -1.7 6.85 7 1t start tie 5t 3 out d4 arrieta
6 109 27 2015-05-07 CHC @ STL L1-5 GS-6 L(3-3) 4 5.333 9 5 4 1 7 0 0 3.41 25 106 66 16 10 10 7 5 0 0 38 NA NA 1 0 0 24 1 1 1 0 0 0 0.74 -0.207 -2.34 7.2 8.33 1b start tie 6b 1-3 1 out d4 arrieta

Calculate conversions

Now that we have the initial data loaded, let's calculate the summary statistics we want to look at on a per-player basis.

addStatisticsColumns <- function(dataframe){
  dataframe %>%
  mutate(rollingIP = cumsum(IP),
         IPGame = rollingIP / Rk,
         rollingER = cumsum(ER),
         rollingERA = rollingER / rollingIP * 9,
         rollingSO = cumsum(SO),
         strikeoutsPerIP = rollingSO / rollingIP,
         `K/9` = rollingSO / rollingIP * 9,
         strikeoutsPerBF = rollingSO / cumsum(BF),
         hitsPerIP = cumsum(H) / rollingIP,
         hitsPerAB = cumsum(H) / cumsum(AB),
         rollingWHIP = (cumsum(H) + cumsum(BB)) / rollingIP,
         # Opponents against
         `1B` = H - `2B` - `3B` - HR,
         AVG = cumsum(H) / cumsum(AB),
         OBP = (cumsum(H) + cumsum(BB) + cumsum(HBP)) / (cumsum(AB) + cumsum(BB) + cumsum(HBP) + cumsum(SF)),
         SLG = (cumsum(`1B`) + 2*cumsum(`2B`) + 3*cumsum(`3B`) + 4*cumsum(HR)) / cumsum(AB),
         OPS = OBP / SLG,
         # Rates
         BABIP = (cumsum(H) - cumsum(HR)) / (cumsum(AB) + cumsum(SO) + cumsum(HR) + cumsum(SF)),
         `HR%` = cumsum(HR) / cumsum(BF),
         `XBH%` = (cumsum(`2B`) + cumsum(`3B`) + cumsum(HR)) / cumsum(BF),
         `K%` = cumsum(SO) / cumsum(BF),
         `IP%` = (cumsum(AB) - cumsum(SO) - cumsum(HR) + cumsum(SF)) / cumsum(BF),
         `GB%` = cumsum(GB) / (cumsum(AB) - cumsum(SO) - cumsum(HR) + cumsum(SF))
         ) %>%
    return
}

data %>%
  group_by(player) %>%
  arrange(Date) %>%
  addStatisticsColumns %>%
  ungroup ->
  data

Since we've calculated all of out statistics (and there are a lot of them!) let's move on to the fun part - graphs:

data %>%
  ggplot(aes(x=Date, y=`GB%`, group=player)) +
  geom_line(aes(colour=player), size=2) +
  ggtitle("Ground Ball Percentage")

We can see Arrieta continually improving, finally blasting past Kershaw.

Arrieta's Second Half

Not sure what we do with this, but here how you do it -

allstarbreak = to_date('Jul 14')
data %>%
  filter(player == "arrieta", Date >= allstarbreak) %>%
  arrange(Date) %>%
  addStatisticsColumns ->
  arrieta2H

Grid O' Stats

Now let's produce some more plots!

It's difficult to reproduce, exactly, the plot stlye in matplotlib. However, we can do an approximation of one of the rows very quickly:

data %>%
  gather(vars, values, rollingERA, `K/9`, AVG, OBP, SLG) %>% 
  ggplot(aes(x=Date, group=player)) +
  geom_line(aes(y=values, colour=player), size=2) +
  facet_wrap(~vars, nrow=1, scales="free")

Now let's do the same thing for more columns -

data %>%
  gather(vars, values, `IP%`, BABIP, `XBH%`, `HR%`, `K%`) %>% 
  ggplot(aes(x=Date, group=player)) +
  geom_line(aes(y=values, colour=player), size=2) +
  facet_wrap(~vars, nrow=1, scales="free")

Season Simulation

What if we replayed the season (sampling randomly from their performances)? Can we tell who is truly the ERA winner?

calculateSeasonStats <- function(season) {
  season %>%
    summarise(
      ERA = sum(ER) / sum(IP) * 9,
      SO = sum(SO),
      H = sum(H),
      `2B` = sum(`2B`),
      `3B` = sum(`3B`),
      HR = sum(HR),
      BB = sum(BB),
      HBP = sum(HBP),
      SF = sum(SF),
      AVG = H / sum(AB),
      OBP = (H + BB + HBP) / (sum(AB) + BB + HBP + SF),
      SLG = (H + 2*`2B` + 3*`3B` + 4*HR) / sum(AB),
      AB = sum(AB),
      BF = sum(BF),
      Pit = sum(Pit),
      Str = sum(Str),
      StL = sum(StL),
      StS = sum(StS)
    ) %>%
    return
}

sampleSeasonWithReplacement <- function(season, runs=1000){
  results = list()
  for(sample_idx in 1:runs) {
    season %>% 
      # By default, sample is 100% of original size.
      sample_frac(replace=T) %>%
      calculateSeasonStats ->
      results[[sample_idx]] 
  }
  df = bind_rows(results)
  return(df)
}

Now that we have some helper functions to sample, we can just execute against each player -

data %>%
  group_by(player) %>%
  do(sampleSeasonWithReplacement(.)) %>%
  ungroup -> 
  simulation

That allows us to plot comparison histograms:

simulation %>% 
  ggplot(aes(x=ERA)) + 
  geom_histogram() + 
  facet_grid(player ~ .) + 
  ggtitle("ERA by Player")

Simulation Results

Now let's use some of the simulation results we have.

We can take a look at the CDF, where you can see the same pattern as in the histograms but more clearly represented.

simulation %>%
  ggplot(aes(x=round(ERA, 2))) +
  stat_ecdf(aes(colour=player), size=2)

We can also look at histograms for most of the statistics -

simulation %>%
  gather(vars, values, ERA, SO, AVG, OBP, SLG) %>%
  ggplot(aes(x=round(values, 2))) +
  geom_histogram(size=2) +
  facet_grid(player~vars, scales="free")

It's also interesting to look at the CDF for much the same view.

simulation %>%
  gather(vars, values, ERA, SO, AVG, OBP, SLG) %>%
  ggplot(aes(x=round(values, 1))) +
  stat_ecdf(aes(colour=player), size=2) +
  facet_wrap(~vars, scales="free", nrow=1)

Pitch f/x

Load Pitch Data

Now let's take a look at pitching data.

files = c("arrieta", "greinke", "kershaw")
pitch_data = list()
for(file in files){
  read_csv(sprintf("data/pitchfx/%s.csv", file)) %>%
    mutate(player = file) ->
    pitch_data[[file]]
}
pitch_data = bind_rows(pitch_data)
head(pitch_data, n=2)
name player_id pitch_type pitch_result atbat_result start_speed z0 x0 pfx_x pfx_z px pz break_angle break_length spin_rate spin_dir zone balls strikes outs play game_date inning inning_topbot tfs tfs_zulu catcher umpire umpire_name stolen_base_attempt stolen_base_success batted_ball_type [EMPTY] angle batted_ball_velocity direction hc_x hc_y pitch_id distance_feet player
Jake Arrieta 453562 SL In play, out(s) Pop Out 90.2 6.294 -2.992 5.78 0.77 0.238 2.296 -19.8 7.5 1150.921 97.998 6 2 0 2 Adam Lind pops out to third baseman Javier Baez in foul territory. 2015-10-02 6 bot 21030 NA 471083 427019 Ted Barrett 0 0 PU NA NA NA NA 77.25 170.2 404 NA arrieta
Jake Arrieta 453562 CU In play, out(s) Groundout 82.5 6.406 -2.972 5.86 -9.36 0.719 1.339 -11.9 13.2 1919.844 32.187 14 1 2 2 Khris Davis grounds out, second baseman Starlin Castro to first baseman Anthony Rizzo. 2015-10-02 1 bot 2815 NA 471083 427019 Ted Barrett 0 0 GB NA 0 67 NA 143.8 160.1 58 0 arrieta

Analyze Pitch Data

We can peek at pitch result -

pitch_data %>% 
  group_by(player, pitch_result) %>% 
  summarise(value=n()) %>% 
  spread(player, value)
pitch_result arrieta greinke kershaw
Ball 1148 1089 981
Ball In Dirt 42 65 101
Called Strike 605 522 559
Foul 612 513 615
Foul (Runner Going) 9 9 10
Foul Bunt 15 14 10
Foul Tip 25 32 28
Hit By Pitch 6 5 5
In play, no out 128 124 128
In play, out(s) 413 441 369
In play, run(s) 39 33 45
Intent Ball 8 2 2
Missed Bunt 5 4 1
Swinging Strike 352 351 465
Swinging Strike (Blocked) 31 35 73

... and at bat results.

pitch_data %>% 
  group_by(player, atbat_result) %>% 
  summarise(value=n()) %>% 
  spread(player, value)
atbat_result arrieta greinke kershaw
Bunt Groundout 6 6 12
Bunt Pop Out 1 NA 4
Double 106 83 90
Double Play 12 4 2
Fan interference NA 4 NA
Field Error 29 28 10
Fielders Choice 5 3 NA
Fielders Choice Out 16 1 1
Flyout 245 317 200
Forceout 66 31 65
Grounded Into DP 52 51 18
Groundout 710 687 583
Hit By Pitch 15 12 21
Home Run 23 51 53
Intent Walk 8 4 4
Lineout 197 250 175
Pop Out 85 143 117
Runner Out 6 12 16
Sac Bunt 13 14 11
Sac Fly 2 6 NA
Single 387 342 373
Strikeout 1165 955 1390
Strikeout - DP 7 6 8
Triple 12 7 3
Walk 270 222 236

We also want to add a few columns for strikes, etc.

ball_vals = c('Ball', 'Ball In Dirt', 'Intent Ball', 'Hit By Pitch')
swing_and_miss = c('Swinging Strike', 'Swinging Strike (Blocked)', 'Missed Bunt')
hit_vals = c('Single', 'Double', 'Triple', 'Home Run')

# Add lookup table for at bat results -> bases equivalency.
at_bat_bases = data.frame(
  atbat_result=c("Single", "Double", "Triple", "Home Run"), 
  total_bases=1:4
)
  
pitch_data %>%
  left_join(at_bat_bases) %>%
  mutate(is_strike = ifelse(pitch_result %in% ball_vals, 0, 1),
         swing_and_miss = ifelse(pitch_result %in% swing_and_miss, 1, 0),
         is_hit = ifelse(pitch_result %in% hit_vals, 1, 0)
         ) ->
  pitch_data
## Joining by: "atbat_result"

## Warning in left_join_impl(x, y, by$x, by$y): joining factor and character
## vector, coercing into character vector

Now let's see who hits harder!

pitch_data %>%
  ggplot(aes(x=batted_ball_velocity)) +
  geom_histogram(aes(fill=player)) +
  facet_grid(. ~ player)

Let's also take a look for a few summary statistics.

pitch_data %>% 
  filter(batted_ball_type != "") %>%
  ggplot(aes(x=batted_ball_velocity)) +
  geom_histogram() +
  facet_grid(player ~ batted_ball_type, scales="free")

Now, what about their pitching speed? We can see the realized distributoin -

pitch_data %>% 
  filter(batted_ball_type != "") %>%
  ggplot(aes(x=batted_ball_velocity)) +
  geom_density(aes(fill=player, alpha=.2))

... but let's try to simulate the difference.

set.seed(49)

simulatePitches = function(pitches, runs=1000){
  pitches %>%
    filter(!is.na(batted_ball_velocity)) %>%
    select(batted_ball_velocity) ->
    draws
  results = list()
  for(i in 1:runs){
    draws %>%
      sample_frac(replace=TRUE) %>%
      summarise(average_velocity = mean(batted_ball_velocity)) ->
      results[[i]]
  }
  results %>%
    bind_rows %>%
    return
}

# Run the simulation
pitch_data %>%
  group_by(player) %>%
  do(simulatePitches(.)) %>%
  ungroup ->
  pitches_simulated
head(pitches_simulated)
player average_velocity
arrieta 84.84
arrieta 85.29
arrieta 84.99
arrieta 84.18
arrieta 85.05
arrieta 85.17

Now that we have some data on simulated pitches, let's take a look!

pitches_simulated %>%
  ggplot(aes(x=average_velocity)) +
  geom_density(aes(fill=player, alpha=.3))

So, how do we know if they're significantly different?

The means for greinke and arrieta are certainly different - greinke is at ~88, whereas arrieta is at ~85.

pitches_simulated %>%
  group_by(player) %>%
  summarise(velocity = mean(average_velocity))
player velocity
arrieta 85
greinke 88.35
kershaw 84.9

We can also run a t-test

v1 = pitches_simulated %>% filter(player=="arrieta") 
v2 = pitches_simulated %>% filter(player=="greinke")

# Run the test
t.test(v1$average_velocity, v2$average_velocity) ->
  t_arrieta_greinke
t_arrieta_greinke
## 
## 	Welch Two Sample t-test
## 
## data:  v1$average_velocity and v2$average_velocity
## t = -220.73, df = 1993.6, p-value < 2.2e-16
## alternative hypothesis: true difference in means is not equal to 0
## 95 percent confidence interval:
##  -3.383607 -3.324010
## sample estimates:
## mean of x mean of y 
##  84.99914  88.35295

We see there's a very low chance (p ~= 0) that these came from the same underlying distribution. So: Greinke gets hit "harder" than the other two players, for whatever reason - perhaps his pitches are easier to hit head on.

What is the relationship between batted ball velocity and batting average against these three?

To replicate - count the number of non-null balls hit back.

pitch_data %>%
  filter(!is.na(batted_ball_velocity)) %>%
  group_by(player) %>%
  summarise(`# of pitches batted` = n())
player # of pitches batted
arrieta 1591
greinke 1598
kershaw 1291

How difficult is each of their particular pitches to hit?

pitch_data %>%
  group_by(player, pitch_type) %>%
  summarise(total = n()) %>%
  ungroup() %>%
  spread(player, total)
pitch_type arrieta greinke kershaw
5 3 8
CH 145 599 18
CU 531 293 616
EP NA 2 NA
FA 13 NA 2
FF 524 1398 1823
FT NA 321 NA
IN 6 2 1
SI 1225 NA NA
SL 989 621 924

Historical Cy Young Results

Now let's take a look at some historical results.

# Load data file and convert share % to a number.
read_csv("data/cyyoung/results.csv") %>%
  mutate(share = as.numeric(gsub("%", "", share)) / 100) ->
  results
results %>%
  group_by(year, league) %>%
  # Note that we're using dense_rank here, which does *not* allow for gaps, but *does* allow for ties.
  # This gives different results than the Python code.
  # We could replicate with row_number() to an extent, but we'd need to order by a third column to get consistent results,
  # In the situation of ties.
  mutate(era_rank = dense_rank(desc(earned_run_avg)),
         wins_rank = dense_rank(desc(W)),
         # Add "winner" flag
         winner = ifelse(rank == 1, 1, 0)
         ) %>%
  ungroup ->
  results

Note that, since the way we're calculating rank is different, we get different results from the iPython notebook -

results %>% 
  group_by(wins_rank) %>% 
  summarise(sum(winner))
wins_rank sum(winner)
1 67
2 21
3 8
4 4
5 5
6 2
7 1
8 0
9 0
10 0 
results %>%
  group_by(wins_rank, era_rank) %>%
  summarise(total=sum(winner)) %>%
  ungroup %>%
  spread(era_rank, total)
wins_rank 1 2 3 4 5 6 7 8 9 10 11 12
1 11 9 10 6 9 6 7 3 3 1 2 NA
2 1 2 5 2 4 4 1 1 1 0 NA NA
3 0 0 0 3 1 0 2 1 1 NA 0 NA
4 0 0 0 2 1 0 0 1 0 0 NA NA
5 0 0 0 0 0 1 1 2 1 0 NA NA
6 0 0 0 0 0 0 1 0 1 0 0 NA
7 NA NA 0 0 0 0 0 0 0 1 0 NA
8 NA 0 NA 0 NA 0 NA 0 0 0 0 NA
9 NA NA NA NA NA NA 0 0 0 0 0 NA
10 NA NA NA NA NA NA NA NA NA NA NA 0