The Physics of Splash Hits

While watching the National League Championship Series tonight and this week, did you notice on the right-field wall at AT&T Park a small scoreboard with the number 68 illuminated? Since it is between innings and they are showing that silly Dodge Dart commercial again, let me explain.

Beyond the wall is a small piece of San Francisco Bay called “McCovey Cove” named after the Giants’ Hall of Fame slugger, Willie McCovey. Home runs hit by the Giants into the bay are dubbed “Splash Hits.” Since the ballpark opened in 2000, there have been just 68.

The San Francisco Giants web site lists them all. As you might imagine, the list is dominated by Barry Bonds, with 35. Pablo Sandoval is a distant second, with seven.

Wait a second…there have only been 68 splash hits in the 15 seasons since AT&T Park has opened!?! Why so few? It is only 309 feet down the right-field line, which is on the short side for major league parks. Part of the answer is an outfield fence dubbed the “Willie Mays Wall,” due to its purported height of 24 feet (in case you’re not familiar, ’24’ was his jersey number).

The wall is 29 feet wide. Then there is a 24-foot walkway between the stadium and McCovey Cove. Now we are up to 362 feet. The wall and walkway are not perpendicular to the foul line, so that adds another four feet. Now we are looking at about 366 feet for a splash hit landing along the foul line.

As the Willie Mays Wall moves outward toward center field, the distances increase. The table below shows the distance needed for a splash hit at various angles from the right field line. By the time you are 10˚ off the foul line, you are looking at about a 404 foot blast.

Distance Needed for Splash Hit

Angle (˚)	Distance (ft)
0	367
5	383
10	404
15	431
20	466

Looking at the 28 splash hits since 2006 on ESPN Home Run Tracker, we find the average distance is coincidentally 405 feet. All but two of these shots they rank as ND, for “no doubt.” According to the glossary, ND means “the ball cleared the fence by at least 20 vertical feet and landed at least 50 feet past the fence. These are the really deep blasts.” They also indicate that all but two would have left any park in the big leagues.

Is the rarity of splash hits solely due to the limited number of very long homers? Since 2006, the Giants have hit 469 round-trippers at AT&T. They averaged 393 feet, though only 28 resulted in splash hits. That’s almost exactly six percent.

The last 500 homers hit in 2014 in all ballparks by all teams might be a representative sample for comparison. They averaged 395 feet, almost the same as the Giants in their home park. Examining the landing location using the overlay tool at ESPN Home Run Tracker showed that 24 of these would have been splash hits. That amounts to 4.8 percent.

These numbers make it look like splash hits aren’t especially rare at AT&T. In fact, there seems to an excess of them. It doesn’t take much looking around to find a potential culprit. According to Mike Fast’s blog Fast Balls, AT&T Park is the windiest in the majors. This, despite the efforts of designers to avoid the arctic blasts of its notorious predecessor Candlestick Park.

The table below summarizes the wind direction and speed for all 81 games at AT&T in 2014. The average wind speed overall is 11.8mph. The wind blows out to center field 83 percent of the time, and it also averages 11.8 mph. Note that only rarely does the wind blow out toward McCovey Cove – just 12 percent of the time.

AT&T Park Wind direction and speed, 2014

Wind Direction	No. of games	Pct	Avg. Wind Speed
Overall	81		11.8
Out to RF	10	12%	11.1
Out to CF	67	83%	11.8
Out to LF	3	4%	14.7
R to L	1	1%	12.0

Now, let’s use Baseball-Reference to look at the wind on days when splash hits happened. The results are in the table below. The average wind speed is a bit higher, but more significantly the wind direction is much different. The wind is three times more likely to be blowing out toward the cove.

AT&T Park Wind direction and speed, Splash Hit Games

Wind Direction	No. of Splash Hits	Pct	Avg. Wind Speed
Overall	66		13.0
Out to RF	27	41%	12.3
Out to CF	20	30%	14.5
Out to LF	8	12%	15.5
R to L	5	8%	10.2
L to R	2	3%	8.0
In from LF	3	5%	13.7
In from CF	1	2%	7.0

Since we now have some suspicion that the wind can explain the excess of splash hits, let’s take a minute to be sure we understand the physics of the flight of a baseball in the wind.

Figure 1 shows three forces acting on a ball in flight. They are shown as the red arrows. The velocity is represented by the blue arrow, while the backspin on the ball is indicated by the circular green arrow.

The gravitational force, or weight, pulls the ball downward. Air resistance or drag acts opposite the velocity of the ball. Drag, as the name implies, slows the ball down. The drag grows as the square of the speed of the ball through the air.

The other force exerted by the air is the Magnus force or lift. It is always perpendicular to the velocity and is in the direction of the spinning motion of the front of the ball as it moves through the air. Due to the spin, the front of the ball in figure 1 is moving mostly upward and slightly backward, matching the direction of the lift. Magnus force depends upon the speed of the ball through the air to the first power and the rate at which the ball is spinning.

When the wind moves along with the ball, both the lift and the drag will decrease, because the speed the ball moves with respect to the air drops. Let’s say at some point during the flight, the ball is moving at 60 mph and the wind is moving along with the ball at 12 mph – 20 percent of the speed of the ball.

Since the lift depends upon the speed of the ball with respect to the wind, it will also drop 20 percent. However, the drag depends upon the square of the speed of the ball with respect to the wind, so it will drop by 40 percent. This steep reduction in drag accounts for the longer distance for a homer hit with the wind at its back.

Let’s apply this to a typical splash hit. We’ll use the 405-foot smash on May 12, 2014 struck by Tyler Colvin in a wind of 12 mph out to right field. Let’s watch:

Not bad for his first homer in a Giants uniform, huh? Now, a quick but complicated calculation (which, lucky for you I’m leaving out) gives the results shown below.

Test Results

Wind Direction	Wind Speed	Distance	Splash Hit
No wind	0 mph	363′	no
Out to RF	12 mph	405′	yes
Out to CF	12 mph	388′	no
Out to LF	12 mph	357′	no

All these hits would have resulted in a homer, but only the one hit with the wind is a splash hit. The wind added the additional 42 feet to clear the seats and the sidewalk. A wind out to center field would have added only 25 feet, while a wind toward left actually reduces the distance by six feet.

Now that we’ve mastered the physics of homers in the wind, back to the game!