Pitch movement and whiffs

pitcherstring

Invented pitcher name

pitch_typestring

FF four-seam, SI sinker, SL slider, CH changeup, CU curveball, FC cutter

release_speednumber · mph

Speed out of the hand

hb_innumber · in

Horizontal break, arm side positive

ivb_innumber · in

Induced vertical break (movement against gravity alone)

plate_xnumber · ft

Horizontal location at the plate, catcher's view, 0 is the middle

plate_znumber · ft

Height at the plate

swinginteger · 0/1

The batter swung

whiffinteger · 0/1

The batter swung and missed

Simulated for practice. Simulated for practice by AthlyticZ (agents/sim_data.py, seed 20261109). License CC BY 4.0. Generated from a documented model with realistic distributions; every name is invented.

1. Easy

   Build each pitcher's arsenal: usage, average velocity, horizontal break and induced vertical break for every pitch type.

   Hint

   Group by pitcher and pitch type, aggregate, then turn counts into shares within each pitcher with a grouped transform.

   Worked solution

   import pandas as pd
   
   p = pd.read_csv("data/pitch_movement.csv")
   arsenal = (p.groupby(["pitcher", "pitch_type"], as_index=False)
                .agg(n=("hb_in", "size"), velo=("release_speed", "mean"), hb=("hb_in", "mean"), ivb=("ivb_in", "mean"))
                .assign(usage=lambda d: d.n / d.groupby("pitcher").n.transform("sum"))
                .round(2))
   print(arsenal.head(10).to_string(index=False))

   Output, from running this code on the dataset when the page was built

   pitcher pitch_type   n  velo    hb    ivb  usage
   Caden Okonkwo-Reyes         CH 112 84.48 14.54   7.35   0.17
   Caden Okonkwo-Reyes         FF 270 94.94  9.45  14.39   0.40
   Caden Okonkwo-Reyes         SI 123 91.98 15.87   9.86   0.18
   Caden Okonkwo-Reyes         SL 165 86.98 -5.92   1.74   0.25
       Felix Dunmarrow         CH 100 84.96 13.59   5.84   0.17
       Felix Dunmarrow         CU  74 78.57 -9.14 -12.68   0.13
       Felix Dunmarrow         FF 254 94.55  6.47  16.90   0.43
       Felix Dunmarrow         SL 158 84.94 -5.39  -0.29   0.27
     Isaac Vantongeren         CH 131 84.65 13.71   5.95   0.21
     Isaac Vantongeren         FF 325 92.92  4.38  14.10   0.51

2. Medium

   Which two pitchers throw the most similar slider? Standardize velocity and the two breaks across all sliders, and find the closest pair of pitcher averages.

   Hint

   Average each pitcher's sliders, z-score the three columns, then compute all pairwise distances with scipy.spatial.distance.pdist and take the smallest.

   Worked solution

   import numpy as np
   import pandas as pd
   from scipy.spatial.distance import pdist, squareform
   
   p = pd.read_csv("data/pitch_movement.csv").query("pitch_type == 'SL'")
   avg = p.groupby("pitcher")[["release_speed", "hb_in", "ivb_in"]].mean()
   z = (avg - avg.mean()) / avg.std()
   d = pd.DataFrame(squareform(pdist(z)), index=avg.index, columns=avg.index)
   np.fill_diagonal(d.values, np.inf)
   a, b = np.unravel_index(np.argmin(d.values), d.shape)
   print(f"most similar sliders: {d.index[a]} and {d.columns[b]}, distance {d.values[a, b]:.2f}")
   print(avg.loc[[d.index[a], d.columns[b]]].round(1).to_string())

   Output, from running this code on the dataset when the page was built

   most similar sliders: Caden Okonkwo-Reyes and Luis Vantongeren, distance 0.91
                        release_speed  hb_in  ivb_in
   pitcher                                          
   Caden Okonkwo-Reyes           87.0   -5.9     1.7
   Luis Vantongeren              86.8   -4.8     2.2

3. Hard

   Model whiffs: on swings only, fit a logistic regression of whiff on pitch type, velocity, both breaks and location. Hold out 30 percent and compare the log loss with a model that knows only the overall whiff rate.

   Hint

   One-hot the pitch type, describe location with an in-zone flag and how far below two feet the pitch was, and use scikit-learn's train_test_split and log_loss.

   Worked solution

   import numpy as np
   import pandas as pd
   from sklearn.linear_model import LogisticRegression
   from sklearn.metrics import log_loss
   from sklearn.model_selection import train_test_split
   
   s = pd.read_csv("data/pitch_movement.csv").query("swing == 1")
   X = pd.get_dummies(s.pitch_type, prefix="pt").assign(
       velo=s.release_speed, hb=s.hb_in, ivb=s.ivb_in,
       in_zone=(s.plate_x.abs() <= 0.83) & s.plate_z.between(1.5, 3.5), below=(2.0 - s.plate_z).clip(lower=0)).astype(float)
   Xtr, Xte, ytr, yte = train_test_split(X, s.whiff, test_size=0.3, random_state=11, stratify=s.whiff)
   m = LogisticRegression(max_iter=2000).fit((Xtr - Xtr.mean()) / Xtr.std(), ytr)
   p_model = m.predict_proba((Xte - Xtr.mean()) / Xtr.std())[:, 1]
   p_base = np.full(len(yte), ytr.mean())
   print(f"held-out log loss: model {log_loss(yte, p_model):.4f}, overall rate {log_loss(yte, p_base):.4f}")

   Output, from running this code on the dataset when the page was built

   held-out log loss: model 0.6002, overall rate 0.6031