Categorizing Pitches in Baseball

How is pitch type detected today?

There are three key features of every pitch to watch for:

Velocity - the speed of the pitch
Movement - the general movement of the pitch
Break - the shift in direction

…and by asking the pitcher what types he throws.

Source: Baseball pitches illustrated by Lokesh Dhakar

What types of pitches are there?

Fastballs

Four-seam

Two-seam

Cutter

Sinker

Breaking balls

Curveball

Slider

Slurve

Screwball

Offspeed

Changeup

Palmball

Circle change

Splitter

There’s another couple of pitches that don’t quite fall into any of those categories: eephus, knuckle, fork, gyro. Source: Baseball pitches illustrated by Lokesh Dhakar

How many pitch types exist?

Code

pitch.types.df <- data.all |>
  left_join(pitchtypes) |>
  mutate(pitch=factor(pitch)) |>
  group_by(pitch,category) |>
  count() |> 
  arrange(desc(n)) 

pitch.types.df |>
ggplot(aes(x=reorder(pitch,-n),y=n)) +
  geom_bar(stat="identity",fill="#999999") +
  geom_text(aes(label=pitch,y=0),angle=90,nudge_y = 5000,hjust=0)+
  labs(x="Pitch Type",
       y="Number of Pitches") +
  scale_y_continuous(labels=scales::label_comma()) +
  ggthemes::theme_hc() +
  theme(axis.ticks.x = element_blank(),
        axis.text.x = element_blank())

What data do we have to work with?

Variables that I use from the dataset:

Pitcher ID (pitcherId)
Pitch type (pitchType, pitch, category)

Release velocity (releaseVelocity)
Velocity along the X axis of the field at the first measurement (vx0, vy0, vz0)
Acceleration of the ball (ax, ay, az)
Spin rate (spinRate)
Spin direction (spinDir)

Distance from the horizontal center of the plate as the ball crosses the front plane of the plate (px)
Height above the ground as the ball crosses the front plane of the plate (pz)
Distance from the center of the plate at the first measurement (x0, y0, z0)

How many clusters should I use?

pitch.data.cv <- vfold_cv(pitch.data, v=5)
km.stats.spec <- k_means(mode="partition",engine="stats",num_clusters=tune())
pitch.data.recipe <- recipe(~ .,
                            data = pitch.data) |>
  step_rm(pitcherId, pitchType, pitch, category)
km.workflow <- workflow(pitch.data.recipe, km.stats.spec)
cluster.grid <- grid_regular(num_clusters(range=c(4,15)),
                             levels=12)
km.results <- tune_cluster(
  km.workflow,
  resamples=pitch.data.cv,
  grid=cluster.grid,
  control=control_grid(save_pred=TRUE, extract=identity),
  metrics=cluster_metric_set(sse_within_total, sse_total, sse_ratio)
)
km.performance <- km.results |> collect_metrics()
km.performance |>
  filter(.metric=="sse_ratio") |>
  ggplot(aes(x=num_clusters, y=mean)) +
  geom_point() +
  geom_line() +
  ggthemes::theme_hc() +
  labs(x="Number of Clusters",
       y="Mean WSS/TSS ratio over 5 folds") +
  scale_x_continuous(breaks=4:15)

Clustering pitches together

Code

n_clusts <- 10
km.spec.n <- k_means(mode="partition", engine="stats", num_clusters = n_clusts)

km.fit <- km.spec.n |>
  fit(~ . -pitcherId -pitchType -pitch -category, data=pitch.data)

km.fit |> tidy() |>  
  select(cluster, size, releaseVelocity, spinRate, spinDir, px, pz, x0, z0, vx0, vy0, vz0, ax, ay, az) |>
  knitr::kable(digits=2,format.args = list(big.mark = ",",scientific = FALSE)) |>
  kableExtra::kable_styling(latex_options = "scale_down")

cluster	size	releaseVelocity	spinRate	spinDir	px	pz	x0	z0	vx0	vy0	vz0	ax	ay	az
1	253,185	90.56	2,156.25	189.05	-0.07	2.41	-0.70	5.87	2.35	-132.52	-5.38	-3.85	28.81	-18.65
2	250,592	89.57	1,981.08	190.69	-0.13	2.41	-0.90	5.86	2.80	-131.10	-4.75	-4.36	28.00	-21.01
3	235,132	84.37	1,263.99	157.67	-0.04	2.19	-0.99	5.92	2.12	-123.57	-3.16	0.87	24.32	-28.40
4	239,909	83.56	865.60	161.01	0.02	2.05	-0.76	5.92	1.71	-122.38	-3.09	1.29	23.55	-30.08
5	70,505	92.46	2,933.46	166.03	0.09	2.31	0.53	5.86	-2.16	-135.13	-7.12	5.36	31.59	-12.25
6	259,554	86.12	1,569.13	194.63	-0.18	2.29	-0.95	5.87	2.62	-126.11	-3.43	-3.37	25.66	-26.43
7	223,821	91.44	2,336.79	190.16	-0.01	2.39	-0.61	5.88	2.35	-133.76	-6.03	-4.10	29.62	-16.41
8	227,071	88.11	1,801.24	190.41	-0.17	2.36	-1.04	5.85	3.02	-129.00	-4.05	-4.27	27.02	-23.77
9	208,841	91.77	2,563.43	174.45	0.06	2.36	0.10	5.88	-0.33	-134.20	-6.51	1.27	30.24	-14.62
10	175,253	83.34	430.82	157.31	0.05	1.93	-0.61	5.91	1.48	-122.04	-3.09	0.89	23.57	-31.27

How did the model perform?

Code

dists |>
  group_by(category, pitchType,.cluster_pred) |>
  count() |>
  ggplot(aes(x=pitchType,
             y=.cluster_pred,
             fill=.cluster_pred,
             alpha=n,
             label=scales::label_number(accuracy=1,scale_cut = cut_short_scale())(n),
             group=category)) +
  geom_tile() +
  geom_text(aes(color=ifelse(n<15000,"white","black"))) +
  labs(x="Pitch Type",
       y="") +
  scale_fill_discrete(type="viridis") +
  scale_x_discrete(limits=rev) +
  scale_color_identity() +
  facet_grid(category~., scales="free", switch="y", space="free_y") +
  coord_flip() +
  guides(fill="none",alpha="none") +
  ggthemes::theme_hc() +
  theme(strip.placement="outside",
        strip.background = element_blank(),
        panel.grid.major.y = element_blank())

What about those pitches that don’t really fit?

Code

outliers <- dists |>
  group_by(.cluster_pred) |>
  mutate(outlier = ifelse(dist_from_centroid > quantile(dist_from_centroid, 0.75)+1.5*IQR(dist_from_centroid),"#DC3220","#212529")) |>
  mutate(outlier = ifelse(dist_from_centroid < quantile(dist_from_centroid, 0.25)-1.5*IQR(dist_from_centroid),"#DC3220",outlier)) 

outliers |>
  ggplot(aes(x=.cluster_pred,y=dist_from_centroid)) +
  geom_boxplot(outlier.shape=NA) +
  geom_jitter(data=outliers |> filter(outlier=="#DC3220"), aes(color=outlier), width=.15, alpha=.1) +
  labs(y="Distance from Centroid",
       x="") +
  scale_color_identity() +
  guides(color="none") +
  ggthemes::theme_hc()

What do those outliers look like?

Code

outliers |>
  filter(.cluster_pred=="Cluster 1") |>
  group_by(category,pitchType,outlier) |>
  count() |> group_by(outlier) |>
  mutate(pct=n/sum(n),
         pct=ifelse(outlier=="#212529",-1*pct,pct)) |>
  ggplot(aes(x=pitchType,y=pct,fill=outlier)) +
  geom_col() +
  facet_grid(category~., scales="free", switch="y", space="free_y") +
  scale_y_continuous(breaks = c(-1,-.5,0,.5,1),
                     limits = c(-1,1),
                     labels=c("100%","50%","0%","50%","100%")) +
  scale_fill_identity() +
  coord_flip() +
  labs(x="Pitch Type",
       y="",
       title="Proportion of Pitch Types assigned to Cluster 1") +
  ggthemes::theme_hc() +
  theme(strip.placement="outside",
        strip.background = element_blank())

Code

outliers |>
  filter(.cluster_pred=="Cluster 5") |>
  group_by(category,pitchType,outlier) |>
  count() |> group_by(outlier) |>
  mutate(pct=n/sum(n),
         pct=ifelse(outlier=="#212529",-1*pct,pct)) |>
  ggplot(aes(x=pitchType,y=pct,fill=outlier)) +
  geom_col() +
  facet_grid(category~., scales="free", switch="y", space="free_y") +
  scale_y_continuous(breaks = c(-1,-.5,0,.5,1),
                     limits = c(-1,1),
                     labels=c("100%","50%","0%","50%","100%")) +
  scale_fill_identity() +
  coord_flip() +
  labs(x="Pitch Type",
       y="",
       title="Proportion of Pitch Types assigned to Cluster 5") +
  ggthemes::theme_hc() +
  theme(strip.placement="outside",
        strip.background = element_blank())

Code

outliers |>
  filter(.cluster_pred=="Cluster 10") |>
  group_by(category,pitchType,outlier) |>
  count() |> group_by(outlier) |>
  mutate(pct=n/sum(n),
         pct=ifelse(outlier=="#212529",-1*pct,pct)) |>
  ggplot(aes(x=pitchType,y=pct,fill=outlier)) +
  geom_col() +
  facet_grid(category~., scales="free", switch="y", space="free_y") +
  scale_y_continuous(breaks = c(-1,-.5,0,.5,1),
                     limits = c(-1,1),
                     labels=c("100%","50%","0%","50%","100%")) +
  scale_fill_identity() +
  coord_flip() +
  labs(x="Pitch Type",
       y="",
       title="Proportion of Pitch Types assigned to Cluster 10") +
  ggthemes::theme_hc() +
  theme(strip.placement="outside",
        strip.background = element_blank())

Thank you

Christopher Teixeira

christopherteixeira.com

chris@christopherteixeira.com

in/christopherteixeira

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