Randomness of Pitcher

 The legendary Major League pitcher Warren Spahn once said, “Hitting is timing. Pitching is upsetting timing.” This statement perfectly captures the essence of both pitching and hitting.

A pitch that disrupts a batter’s timing is one that is difficult to react to. So, what kind of pitches are hard to react to? It could be an extremely fast pitch, or a very slow one. But more importantly, it could be a pitch that’s difficult to predict. In this article, I use entropy to simply calculate the randomness of Major League pitchers.

Method 1

Here’s how I calculated randomness:

1. I calculated the entropy of each pitcher’s pitch usage rates by pitch type. Then, I normalized each pitcher’s entropy score between 0 and 1 to obtain a “pitch usage entropy score.” The more pitch types a pitcher uses, and the more evenly they’re distributed, the higher this score becomes.

2. I selected every pair of pitch types a pitcher throws (for n pitch types, there are nC2 combinations), calculated the absolute difference in average velocity between each pair, and averaged those values. This score was also normalized between 0 and 1. The larger the velocity differences, the higher the score.

3. I added the two scores together to calculate each pitcher’s overall randomness score.

The sample consisted of 107 pitchers who qualified for the innings limit in the 2024 Major League Baseball season. The results are as follows.

The pitcher with the highest randomness score was BlueJays pitcher Chris Bassitt. He received consistently high scores in both pitch usage entropy and average velocity difference.

In 2024, Bassitt threw eight different pitch types. Among them, his sinker and cutter were thrown 41% and 20% of the time, respectively, while his curveball accounted for 14%. The remaining five pitch types each had a usage rate of 7% or lower. This uneven distribution explains why his entropy score wasn’t even higher, despite the number of pitch types he used.

Seth Lugo and Dylan Cease, who ranked fourth and fifth, received the top scores in pitch usage entropy and velocity difference, respectively.

Lugo threw nine pitch types, the most among pitchers included in the analysis. His most frequently used pitch was the four-seam fastball at 24%, while his least used was the splitter at 3%.

Cease had the largest average velocity gap between any two pitch types. His fastest pitch in 2024 was the sinker, which averaged 98.1 mph, but it was only thrown twice. It’s likely that these pitches were misclassified four-seam fastballs. Even so, Cease’s four-seam fastball averaged 96.9 mph, while his changeup — which he threw only 28 times — averaged just 69.7 mph. The difference between these two pitches was 27.2 mph. That’s about 5.4 mph more than the second-largest velocity gap, which belonged to Patrick Corbin, whose sinker-curveball combination had a difference of 21.8 mph (91.5 vs. 69.7 mph).

This highlights a flaw in the method: Cease’s changeup was thrown only 28 times, that means most hitters likely didn’t expect it. Therefore, it’s difficult to argue that the large velocity gap between his four-seamer and changeup significantly disrupted timing.

To address this issue, I slightly revised the method for calculating randomness.

Method 2

The revised calculation aimed to reflect the following principles:

• The more pitch types a pitcher uses, and the more evenly distributed they are, the greater the randomness.

• Pitch pairs with high usage rates should have large velocity gaps to maximize unpredictability.

I formed every possible pair of pitch types a pitcher throws, calculated their joint entropy, and multiplied it by the absolute velocity difference between the pair. This yielded a weighted score for each pitch pair, accounting for both pitch usage and velocity gap. The sum of all pairwise scores became the pitcher’s new randomness score.

Despite the revised calculation method, the rankings from 1st to 4th remained unchanged. When both pitch usage and velocity are taken into account, Chris Bassitt is arguably the pitcher whose next pitch is the hardest to anticipate in terms of timing.

There was a change at 5th place. Dylan Cease was replaced by Ranger Suárez of the Philadelphia Phillies. The five pitch types he threw ranged from 12% to 30% in usage rate. His slowest pitch was the curveball, averaging 74.4 mph, and his fastest was the four-seam fastball, averaging 91.9 mph.

Finally, the pitch combination with the highest Randomness Score, along with the usage rates and average velocities of each pitch in the pair, is presented below.

Conclusion

This calculation only considered pitch velocity and usage rate. While I contemplated adding vertical and horizontal movement as variables, I concluded that doing so would ultimately introduce the concept of pitch tunneling into the randomness metric. When focusing purely on usage rate and timing, I believe that considering velocity alone is sufficient.

In the future, I plan to incorporate pitch movement into the calculation. In that case, pitch combinations that break in opposite directions will receive higher scores.