Pruning Trees

MLB Data

Author

Byeong-Hak Choe

Published

March 25, 2026

Modified

April 13, 2026

Overview

In this lab, you will use decision trees to study two baseball-related prediction problems using Major League Baseball data.

You will do two tasks:

  1. Build a regression tree to predict w_oba using batting statistics.
  2. Build a classification tree to predict whether a batted ball becomes a home run.

Setup for Decision Trees

library(tidyverse)
library(skimr)
library(janitor)
library(broom)
library(ggthemes)
library(rmarkdown)

library(rpart)
library(rpart.plot)
library(vip)
library(pdp)

theme_set(
  theme_bw() +
    theme(
      legend.position = "bottom",
      strip.background = element_rect(fill = "lightgray"),
      axis.title.x = element_text(size = rel(1.1)),
      axis.title.y = element_text(size = rel(1.1))
    )
)

scale_colour_discrete <- function(...) scale_color_colorblind(...)
scale_fill_discrete <- function(...) scale_fill_colorblind(...)

Part 1. Regression Tree with MLB Batting Data

Batting data

mlb_data <- read_csv(
  "http://bcdanl.github.io/data/mlb_fg_batting_2022.csv"
) |>
  clean_names() |>
  mutate(across(bb_percent:k_percent, readr::parse_number))

mlb_data |> 
  paged_table()

What the variables mean

  • w_oba: weighted on-base average, a summary measure of offensive performance
  • bb_percent: walk percentage
  • k_percent: strikeout percentage
  • iso: isolated power
  • avg: batting average
  • obp: on-base percentage
  • slg: slugging percentage
  • war: wins above replacement

Step 2. Explore the variables

mlb_data |>
  select(w_oba, bb_percent, k_percent, iso) |>
  skimr::skim()
Data summary
Name select(mlb_data, w_oba, b…
Number of rows 157
Number of columns 4
_______________________
Column type frequency:
numeric 4
________________________
Group variables None

Variable type: numeric

skim_variable n_missing complete_rate mean sd p0 p25 p50 p75 p100 hist
w_oba 0 1 0.33 0.04 0.25 0.31 0.33 0.35 0.44 ▃▇▇▃▁
bb_percent 0 1 8.80 2.97 3.50 6.50 8.60 11.00 20.30 ▆▇▆▁▁
k_percent 0 1 20.47 5.89 8.10 16.10 19.90 24.80 36.10 ▃▇▇▅▁
iso 0 1 0.17 0.06 0.05 0.12 0.17 0.20 0.35 ▃▇▇▂▁ 
mlb_data |>
  ggplot(aes(x = iso, y = w_oba)) +
  geom_point(alpha = 0.6) +
  labs(
    title = "wOBA and ISO",
    x = "ISO",
    y = "wOBA"
  )

Task 1

Write 2 to 3 sentences describing the relationship between iso and w_oba. What pattern do you see in the scatterplot?

Answer:

There is a clear positive relationship between iso and w_oba. Players with higher isolated power tend to have higher offensive production overall, so the cloud of points slopes upward. The pattern is not perfectly linear, but stronger power clearly tends to be associated with a larger w_oba.

Step 3. Fit an initial regression tree

We will begin with a simple decision tree using three predictors.

mlb_tree_1 <- rpart(
  w_oba ~ bb_percent + k_percent + iso,
  data = mlb_data,
  method = "anova"
)

mlb_tree_1
n= 157 

node), split, n, deviance, yval
      * denotes terminal node

 1) root 157 0.215948200 0.3291338  
   2) iso< 0.2055 123 0.113126200 0.3175691  
     4) iso< 0.1035 16 0.016633000 0.2837500 *
     5) iso>=0.1035 107 0.075457050 0.3226262  
      10) bb_percent< 8.75 65 0.039689380 0.3146154  
        20) k_percent>=27.15 9 0.001585556 0.2902222 *
        21) k_percent< 27.15 56 0.031887930 0.3185357  
          42) iso< 0.152 27 0.010937850 0.3089259 *
          43) iso>=0.152 29 0.016135240 0.3274828  
            86) k_percent>=21.85 17 0.008568235 0.3194706 *
            87) k_percent< 21.85 12 0.004929667 0.3388333 *
      11) bb_percent>=8.75 42 0.025140980 0.3350238  
        22) k_percent>=23.45 11 0.002378909 0.3129091 *
        23) k_percent< 23.45 31 0.015473480 0.3428710  
          46) iso< 0.159 15 0.006778000 0.3320000 *
          47) iso>=0.159 16 0.005260937 0.3530625 *
   3) iso>=0.2055 34 0.026860970 0.3709706  
     6) iso< 0.2595 23 0.009236609 0.3608696 *
     7) iso>=0.2595 11 0.010370910 0.3920909 *
rpart.plot(mlb_tree_1)

Task 2

Answer the following in complete sentences:

  1. Which variable appears at the first split?
  2. What does that suggest about the predictor’s importance in this tree?
  3. Choose one terminal node and explain what its predicted value means.

Answer:

  1. The first split is on iso.
  2. This suggests that iso is the most important predictor near the top of this tree because it gives the largest reduction in impurity at the first decision point.
  3. For example, if a terminal node predicts a w_oba around 0.37, that means players whose statistics place them in that region of the tree are predicted to have an average w_oba of about 0.37.

Step 4. Grow a larger tree

Now let the algorithm grow a much more flexible tree.

mlb_tree_full <- rpart(
  w_oba ~ bb_percent + k_percent + iso,
  data = mlb_data,
  method = "anova",
  control = rpart.control(cp = 0, xval = 10)
)

mlb_tree_full
n= 157 

node), split, n, deviance, yval
      * denotes terminal node

 1) root 157 0.215948200 0.3291338  
   2) iso< 0.2055 123 0.113126200 0.3175691  
     4) iso< 0.1035 16 0.016633000 0.2837500 *
     5) iso>=0.1035 107 0.075457050 0.3226262  
      10) bb_percent< 8.75 65 0.039689380 0.3146154  
        20) k_percent>=27.15 9 0.001585556 0.2902222 *
        21) k_percent< 27.15 56 0.031887930 0.3185357  
          42) iso< 0.152 27 0.010937850 0.3089259  
            84) k_percent>=18.5 10 0.003274000 0.3020000 *
            85) k_percent< 18.5 17 0.006902000 0.3130000 *
          43) iso>=0.152 29 0.016135240 0.3274828  
            86) k_percent>=21.85 17 0.008568235 0.3194706 *
            87) k_percent< 21.85 12 0.004929667 0.3388333 *
      11) bb_percent>=8.75 42 0.025140980 0.3350238  
        22) k_percent>=23.45 11 0.002378909 0.3129091 *
        23) k_percent< 23.45 31 0.015473480 0.3428710  
          46) iso< 0.159 15 0.006778000 0.3320000 *
          47) iso>=0.159 16 0.005260937 0.3530625 *
   3) iso>=0.2055 34 0.026860970 0.3709706  
     6) iso< 0.2595 23 0.009236609 0.3608696  
      12) k_percent>=18.8 13 0.004075077 0.3523846 *
      13) k_percent< 18.8 10 0.003008900 0.3719000 *
     7) iso>=0.2595 11 0.010370910 0.3920909 *
rpart.plot(mlb_tree_full)

plotcp(mlb_tree_full)

Task 3

Answer the following:

  1. Compared with the first tree, is this tree more or less complex?
  2. Why might a very large tree be a problem for out-of-sample prediction?
  3. Looking at plotcp(), what kind of tree are we usually trying to choose: the biggest tree, the smallest tree, or a tree that balances fit and complexity?

Answer:

  1. This tree is more complex than the first tree because it has more splits and more terminal nodes.
  2. A very large tree can overfit the training data by capturing noise or very specific local patterns that do not generalize well to new observations.
  3. We usually want a tree that balances fit and complexity rather than simply choosing the biggest or smallest tree.

Step 5. Fine-tune tree growth before pruning

Before pruning, try a few different tree-growth settings. This is a simple form of hyperparameter tuning. The goal is to see how choices like minsplit and maxdepth affect the size of the tree and the cross-validated error.

reg_tuning_grid <- tribble(
  ~minsplit, ~maxdepth,
  20,        4,
  20,        6,
  30,        4,
  30,        6,
  40,        4,
  40,        6
)

reg_tuning_results <- reg_tuning_grid

fit_list <- vector("list", nrow(reg_tuning_results))
cp_table_list <- vector("list", nrow(reg_tuning_results))
min_xerror_vec <- numeric(nrow(reg_tuning_results))
best_cp_vec <- numeric(nrow(reg_tuning_results))
nsplit_at_best_cp_vec <- numeric(nrow(reg_tuning_results))

for (i in seq_len(nrow(reg_tuning_results))) {
  
  fit_list[[i]] <- rpart(
    w_oba ~ bb_percent + k_percent + iso,
    data = mlb_data,
    method = "anova",
    control = rpart.control(
      cp = 0,
      xval = 10,
      minsplit = reg_tuning_results$minsplit[i],
      maxdepth = reg_tuning_results$maxdepth[i]
    )
  )
  
  cp_table_list[[i]] <- as_tibble(fit_list[[i]]$cptable)
  
  min_xerror_vec[i] <- min(cp_table_list[[i]]$xerror)
  
  best_cp_vec[i] <- cp_table_list[[i]] |>
    slice_min(xerror, n = 1) |>
    pull(CP)
  
  nsplit_at_best_cp_vec[i] <- cp_table_list[[i]] |>
    filter(CP == best_cp_vec[i]) |>
    slice(1) |>
    pull(nsplit)
}

reg_tuning_results <- reg_tuning_results |>
  mutate(
    fit = fit_list,
    cp_table = cp_table_list,
    min_xerror = min_xerror_vec,
    best_cp = best_cp_vec,
    nsplit_at_best_cp = nsplit_at_best_cp_vec
  ) |>
  select(minsplit, maxdepth, min_xerror, best_cp, nsplit_at_best_cp)

reg_tuning_results |> 
  paged_table()

Task 4

Answer the following:

  1. Which combination of minsplit and maxdepth gives the smallest cross-validated error?
  2. Does a deeper tree always give the best xerror?
  3. Based on this table, which setting would you carry forward to pruning, and why?

Answer:

  1. In this setup, minsplit = 20 and maxdepth = 6 tends to give the smallest cross-validated error.
  2. No. A deeper tree does not always give the best xerror because extra depth can improve fit in-sample while hurting generalization.
  3. I would carry forward minsplit = 20 and maxdepth = 6 because it gives the best or near-best cross-validated performance while still being reasonably interpretable.

Step 6. Find the best complexity parameter for your tuned tree

Use the hyperparameter setting you prefer from Step 5. In the example below, we use minsplit = 20 and maxdepth = 6. You may change these values if your preferred setting is different.

mlb_tree_tuned <- rpart(
  w_oba ~ bb_percent + k_percent + iso,
  data = mlb_data,
  method = "anova",
  control = rpart.control(cp = 0, xval = 10, minsplit = 30, maxdepth = 6)
)

plotcp(mlb_tree_tuned)

cp_table <- as_tibble(mlb_tree_tuned$cptable)

cp_table |> 
  paged_table()
best_cp <- cp_table |>
  slice_min(xerror, n = 1) |>
  pull(CP)

best_cp
[1] 0

Task 5

What does the xerror column represent? Why do we often use it when choosing the pruning parameter?

Answer:

The xerror column reports the cross-validated prediction error relative to the root node benchmark. We use it to choose the pruning parameter because it gives a better sense of out-of-sample performance than training error alone.

Step 7. Prune the tuned tree

mlb_tree_pruned <- prune(mlb_tree_tuned, cp = best_cp)

mlb_tree_pruned
n= 157 

node), split, n, deviance, yval
      * denotes terminal node

 1) root 157 0.215948200 0.3291338  
   2) iso< 0.2055 123 0.113126200 0.3175691  
     4) iso< 0.1035 16 0.016633000 0.2837500 *
     5) iso>=0.1035 107 0.075457050 0.3226262  
      10) bb_percent< 8.75 65 0.039689380 0.3146154  
        20) k_percent>=26.55 10 0.004590000 0.2960000 *
        21) k_percent< 26.55 55 0.031004000 0.3180000  
          42) iso< 0.152 27 0.010937850 0.3089259 *
          43) iso>=0.152 28 0.015699250 0.3267500 *
      11) bb_percent>=8.75 42 0.025140980 0.3350238  
        22) k_percent>=23.45 11 0.002378909 0.3129091 *
        23) k_percent< 23.45 31 0.015473480 0.3428710  
          46) iso< 0.159 15 0.006778000 0.3320000 *
          47) iso>=0.159 16 0.005260937 0.3530625 *
   3) iso>=0.2055 34 0.026860970 0.3709706  
     6) iso< 0.2595 23 0.009236609 0.3608696 *
     7) iso>=0.2595 11 0.010370910 0.3920909 *
rpart.plot(mlb_tree_pruned)

print(mlb_tree_tuned$cptable, digits = 10)
             CP nsplit    rel error       xerror          xstd
1 0.35175593513      0 1.0000000000 1.0247010103 0.11422594301
2 0.09741279039      1 0.6482440649 0.6881039267 0.06849768789
3 0.04920942319      2 0.5508312745 0.6767565392 0.07901199586
4 0.03375153638      3 0.5016218513 0.6469185346 0.07623617988
5 0.03358885650      4 0.4678703149 0.6468806080 0.07611077547
6 0.01959331708      5 0.4342814584 0.6415395239 0.07541331004
7 0.01590449243      7 0.3950948242 0.6336073936 0.07527289719
8 0.00000000000      8 0.3791903318 0.6214235319 0.07169012554
print(mlb_tree_full$cptable, digits = 10)
               CP nsplit    rel error       xerror          xstd
1  0.351755935125      0 1.0000000000 1.0034335772 0.11224471440
2  0.097412790388      1 0.6482440649 0.6804862766 0.06673476282
3  0.049209423195      2 0.5508312745 0.6839363504 0.07707515460
4  0.033751536385      3 0.5016218513 0.6753597271 0.07626021573
5  0.033588856500      4 0.4678703149 0.6694411278 0.07434778713
6  0.028784221147      5 0.4342814584 0.6694411278 0.07434778713
7  0.022296252245      6 0.4054972373 0.6359749830 0.06673738691
8  0.015904492433      7 0.3832009850 0.6296295617 0.06664772048
9  0.012212834038      8 0.3672964926 0.6487070022 0.06725423256
10 0.009968278788      9 0.3550836585 0.6560410825 0.06765635252
11 0.003527938104     10 0.3451153798 0.6338444973 0.06918226896
12 0.000000000000     11 0.3415874417 0.6106143144 0.06730844609

Task 6

Compare the tuned unpruned tree and the pruned tree.

Write 2 to 4 sentences addressing these questions:

  • What became simpler after pruning?
  • Why can a pruned tree sometimes predict better on new data even if it fits the training data less closely?
  • Did your earlier hyperparameter choices seem to matter for the final pruned result?

Answer:

After pruning, the tree has fewer splits and fewer terminal nodes, so the model is easier to explain. A pruned tree can predict better on new data because it removes weaker splits that may mainly capture noise in the training sample. The earlier hyperparameter choices still matter because they affect the size and shape of the tree before pruning, which changes what pruning is able to keep or remove.



Part 2. Classification Tree with MLB Batted-Ball Data

Batted-ball data

batted_ball_data <- read_csv(
  "http://bcdanl.github.io/data/mlb_batted_balls_2022.csv"
) |>
  mutate(is_hr = as.factor(events == "home_run")) |>
  filter(
    !is.na(launch_angle),
    !is.na(launch_speed),
    !is.na(is_hr)
  )

batted_ball_data |> 
  paged_table()
batted_ball_data |> 
  count(is_hr)
# A tibble: 2 × 2
  is_hr     n
  <fct> <int>
1 FALSE  6702
2 TRUE    333

Visualize the classification problem

batted_ball_data |>
  ggplot(aes(x = launch_speed, y = launch_angle, color = is_hr)) +
  geom_point(alpha = 0.35) +
  labs(
    title = "Home Runs vs. Other Batted Balls",
    x = "Launch speed",
    y = "Launch angle",
    color = "Home run?"
  )

Under construction

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