The Physics of Being Hit by a Pitch

The 2018 season represented the last of 16 seasons of professional baseball for Chase Utley. The “Silver Fox” had become known as “Dad” during his time with the Dodgers. When he announced his retirement, it seems he became “Grandad,” as his teammates presented him with a rocking chair.

Utley will be remembered most for his years with the Phillies, particularly his role in the team’s five straight division titles starting in 2007. During four of those years, he was named an All-Star. It could be argued that despite his more well-known teammates, he led the Phil’s to their 2008 World Series victory.

He will also be known for the “Utley Rule,” which was put into effect after he made a hard slide into Mets shortstop Ruben Tejada during the 2016 Division Series. The collision broke Tejada’s leg. The Utley Rule cleaned up the traditional rough-and-tumble play previously allowed–and even encouraged–around second base.

Utley likely will garner many votes for the Hall of Fame. His case for inclusion was thoroughly discussed by Jay Jaffe, writing for FanGraphs. Jaffe describes the unofficial “Rule of 2000,” which seems to be the minimum number of hits required for position players to garner support from BBWAA voters and enter the Hall. Chase Utley’s total is “only” 1885.

However, I suggest Hall of Fame voters might want to consider the fact that Utley finished eight all-time in hits by pitch. He “took one for the team” 204 times during the regular season. He was “plunked” eight additional times in the postseason and once, for good measure, in the All-star Game. Indeed, Utley’s ability to take first base with a hit by pitch was a serious piece of his offensive approach.

Utley easily clears the Rule of 2000 if his hit-by-pitches were to be treated as hits. However, my expertise in Hall of Fame decision-making is quite limited, so let’s address a question about which I can at least feign some authority: How can you get hit by a pitch and minimize the chances of getting injured?

The answer, as is so often the case for physics questions, is explained by Newton’s Second Law,

Since m (the mass of the ball) is fixed by rule, it isn’t something the players on the field can do much to influence. The key issues are the change in velocity (∆v) of the ball and the time it takes the ball to collide with the batter (∆t). The smaller the change in speed or the longer the collision time, the smaller the force exerted on the batter.

Let’s start with a couple examples of methods for minimizing the change in velocity of the ball, which will then result in smaller forces.

Example 1: Make sure the ball barely grazes you.

Here is an example from the master.

The change in velocity of the ball is essentially zero–it is moving at just about the same velocity after the collision as it was before the collision. Therefore, the force will be small.

Example 2: Be moving away from the ball when it hits you.

Watch Utley’s shoulder in his 200th career hit by pitch.

Notice he moves his shoulder toward the catcher as quickly as he can. As such, the incoming pitch is not moving as quickly toward his shoulder as it would be if his shoulder remained still. The change in the relative velocity of the ball will be smaller, keeping the force down.

Imagine the pitch is like a car speeding down the highway traveling at say 90 mph. If Utley’s shoulder was still, like a stalled car, the moving car would slam into it at 90 mph. If instead, Utley’s shoulder was moving like a car slowed to 40 mph, then the speeding car would only hit with a relative speed of 50 mph.

I actually have watched one of our previous college coaches teach this shoulder-turn technique. I can’t imagine this practice was much fun for the players. It should be noted that this method also increases the collision time, reducing the force.

The primary method for increasing the collision time is the effect of padding. If the ball strikes a spot on the body with little padding, like the fingers or lower arm, the forces can become dangerously high, leading to broken bones. Justin Turner lost a good chunk of the 2018 season to such an injury.

Utley was smart (or stubborn) enough to avoid the following methods that increase the collision time in order to reduce the force. He is simply too “old school” to wear padding as most batters do nowadays.

Example 3: Be sure the ball lands on your batting armor.

This type of armor typically consists of some padding covered with a plastic plate. The plate distributes the force over a larger area, while the padding underneath increases the collision time as it gets compressed, thus lowering the force.

Example 4: Be sure to get hit on the “fleshier” parts of the body.

You can just hear them from the dugout. “That’s using your head!” The collision time is much longer on the…er, fanny, than it is on the shin. The longer collision time reduces the force, although a bruise is still the likely outcome.

I suppose the issue of the “bean ball” needs to be addressed. One might be tempted to think getting hit in the head should be relatively safe considering the batter has a plastic helmet to distribute the force with padding inside to increase the collision time.

In fact, there is almost no damage directly to the head in these collisions. The batters that get beaned don’t bleed, bruise, or get their skulls cracked. In this sense, the helmet does its job. However, inside the skull lies the brain–although hitting coaches might disagree in some cases.

The collision with the helmet causes the brain to slam into the inside of the skull. The resulting “brain bruise” is usually called a concussion. These are very dangerous (much more so than the flesh wounds of other hit-by-pitches), which is why they are often subject to fines and suspensions if done intentionally. I expect even Utley tried to get out of the way of those.

Well, that just about covers the physics of “wearing one.” The writers’ Chase Utley Hall of Fame decision is still five years away.