Baseball is a game of numbers. Ask a diehard fan about batting averages, earned run averages, home run records, stolen base records, or even those little numbers he scribbles when keeping box score, and you're in for a long discussion.
Baseball is numbers to Terry Bahill, as well - but of a different kind. The University of Arizona professor of systems and industrial engineering has used numbers, graphs and mathematical analysis to investigate some of baseball's more intriguing questions, most of which center around that half second between the time a pitcher releases the ball and the moment the batter hits it.
Some of Bahill's conclusions:
The rising fastball is an illusion
There is an ideal bat weight for every player from little league to major league, and many players use a bat that is too heavy for them.
Outlawing aluminum bats in college would produce faster batted ball speeds, endangering pitchers.
Most batters would profit from using an end-loaded bat, but some would not.
The Rising Fastball For years batters swore that some pitchers could throw a rising fastball that would "jump" a half foot as it crossed the plate, making it hop over the bat. But this isn't possible, Bahill says. Even the greatest pitchers can't violate the laws of physics. Once a ball is thrown, it follows a smooth trajectory. Physics simply doesn't allow abrupt jumps in that trajectory.
So what's happening? "The batter is using the wrong mental model," Bahill says.
Batters divide a pitch into thirds. The first third is sensory gathering, the second is computing, and the third is swinging. So a pitcher throws several 90-mph fastballs and the batter develops a mental model and reaction to this speed, Bahill says.
Then the pitcher slips in a 95-mph fastball. During the sensory gathering segment of the pitch, the batter doesn't see anything different. He calculates where the 90-mph fastball would go and swings at that spot. But the 95-mph fastball has a flatter trajectory. It doesn't drop quite as much from the pitcher to plate because it's going faster.
"When the batter starts to swing, he takes his eye off the ball to look at the predicted bat-ball collision point," Bahill says. "When the ball comes back into his view, it is higher than his mental model predicted and he sees it 'jump' higher than where he calculated that it would be."
Ideal bat weight OK, we're talking momentum here. The batter wants to transfer the greatest amount of momentum possible from the bat to the ball. In this case, we can think of momentum being the speed of the bat times its weight.
Now a batter can swing a broomstick very fast, but won't hit home runs. It has a lot of speed, but not much weight. He also could swing an anvil lots of weight but no speed. Somewhere between these two extremes there is an ideal weight times bat-speed that generates the largest amount of momentum. But this ideal bat weight is different for each player, depending on his strength and physiology and how fast he can swing the bat.
"If a player came to our lab and used our bat chooser machine, we could tell him exactly what weight bat to use," Bahill says. "But that's not possible, so we have produced a chart that gives a rough approximation for various groups." This chart and lots of other information about modeling physiological systems to the sport of baseball can be found in "Keep Your Eye on the Ball: Curve Balls, Knuckle Balls and Fallacies about Baseball." The book by Bahill and Robert G. Watts, a professor of mechanical engineering at Tulane University, presents a popularized version of their work, which has appeared in numerous research journals.
Aluminum bats While some have contended that aluminum bats generate higher ball speeds and are therefore more dangerous for pitchers, Bahill returned to his bat chooser data to show that this isn't the case.
Generally, lighter bats are better for most hitters because they offer more control. But for a batter to get the same length in a wooden bat that is available in aluminum, he almost always has to go to a heavier bat. "Wood is about an ounce an inch and to get the length, you have to increase the weight," Bahill says. Although bat speed decreases somewhat with a heavier wooden bat, the increased weight overcomes the decrease in speed and still gives the ball more momentum, which means it's traveling faster toward the pitcher.
End-loaded bats Aluminum bats are made with a lightweight shell and an internal weight that can be placed anywhere along the length of the bat. Some contend that putting the weight all the way at the far end away from the batter's hands generates more home runs.
The idea is that the bat develops greater angular momentum with the weight at the end. It's like standing out on the edge of a merry-go-round instead of in the middle. At the edge your weight is being propelled much faster and you have greater momentum. Similarly, the weight at the end of the bat has greater momentum than if it were distributed evenly throughout the bat.
But there is a tradeoff, bat speeds go down as the weight is moved out to the end.
"For most players if the speed comes down a little, end-loading still helps," Bahill says. "They swing slower, but the bat has more moment of inertia - the speed times weight combination again - and the momentum goes up."
Bahill tested a large number of subjects to collect data for the end-loading experiment, including three players from UA's championship women's softball team. He found that two of these players had such high bat speeds that the drop in speed caused by end-loading actually hurt their hitting. "This is a real phenomenon," Bahill says, "Some very good hitters fall into this category and they can be hurt by an end-loaded bat."
Only through testing can a hitter find out if an end-loaded bat will help or hurt and exactly what weight bat he should use. Unfortunately, there's nowhere to go to be tested. Although some sporting goods manufacturers have looked at Bahill's bat chooser testing apparatus, they have concluded that the market isn't large enough to justify building such devices and installing them in sporting goods stores.
As for major league baseball, Bahill worked briefly with the San Francisco Giants. "We're engineers and scientists, not marketing people," Bahill says. "And we weren't able to convince them that this would be beneficial. There was resistance. The players have been successful using their present bats and there are a lot of myths and tradition built up around hitting. We weren't able to break through that and the players wouldn't accept the program."
Still, Bahill plans to contact three major league teams that come to the Tucson area for spring training to see if they might be interested in testing their hitters on his bat chooser.
He believes he can help them find just the right bats to use in putting up some good numbers to delight baseball fans this season.