The outfielder problem: The psychology behind catching fly balls [Cognitive Daily]

It's football season in America: The NFL playoffs are about to start, and tonight, the elected / computer-ranked top college team will be determined. What better time than now to think about ... baseball! Baseball players, unlike most football players, must solve one of the most complicated perceptual puzzles in sports: how to predict the path of a moving target obeying the laws of physics, and move to intercept it.

The question of how a baseball player knows where to run in order to catch a fly ball has baffled psychologists for decades. (You might argue that a football receiver faces a similar task, but generally in football, the distances involved are much shorter, and most football players aren't expected to catch passes at all.)

There are three primary possible explanations for how a baseball fielder catches a fly ball:

• Trajectory Projection (TP): The fielder calculates the trajectory of a ball the moment it is hit and simply runs to the spot where it will fall (of course, taking into account wind speed and barometric pressure).
• Optical acceleration cancellation (OAC): The fielder watches the flight of the ball; constantly adjusting her position in response to what she sees. If it appears to be accelerating upward, she moves back. If it seems to be accelerating downward, she moves forward.
• Linear optical trajectory (LOT): The fielder pays attention to the apparent angle formed by the ball, the point on the ground beneath the ball, and home plate, moving to keep this angle constant until she reaches the ball. In other words, she tries to move so that the ball appears to be moving in a straight line rather than a parabola.

In principle, all three of these systems should work. However, TP is probably impossible; our visual system isn't accurate at determining distances beyond about 30 meters, and outfielders stand up to 100 meters away from home plate. The second system, OAC, might not work because the visual system isn't actually very sensitive to acceleration. And the third system, LOT, is problematic because it doesn't predict a unique path for the fielder to take to the ball. Further, the most likely paths a fielder would take to catch a ball wouldn't be much different under OAC and LOT.

But Philip Fink, Patrick Foo, and William Warren figured out a way to experimentally distinguish between all three models. They had 8 skilled male baseball players and 4 skilled female softball players don VR headsets and attempt to catch virtual balls in a large room. The room was big enough that they could freely move 6 meters in each direction. VR was necessary because the researchers made their virtual balls take paths that aren't possible in real life:

The players stood about 35 meters from "home plate" and the balls were hit either 4 meters in front or behind them. They were also offset to either side, but this turned out not to matter for the results. Here's a movie (QuickTime required) showing what a typical player saw in her VR display. And here's a movie showing what the players actually did.

As the image above shows, half the time the balls took their normal trajectory, but half the time they proceeded in a physically-impossible straight line for the second half of their flight. For the TP model, this shouldn't matter -- players should go straight to the landing point in either case. But with a straight-line motion, OAC and LOT predict very different paths. This graph compares one player's actual movements with the OAC model's projections:

The thick lines show the predicted movement if the player was following the OAC model, and the thin lines show the actual movement (tan[alpha] is the acceleration in the change of the angle of the ball relative to the player). As you can see, these patterns match up pretty well. But take a look at this graph:

Here, the thick lines show the predicted movement if the player was following LOT, and the thin lines show the actual movement (again, tan[alpha] is the acceleration in the change of the angle of the ball relative to the player, and tan[beta] is the acceleration in the angle between the ball's position above the ground and home plate). This time, the model does significantly worse after the ball shifts to a straight trajectory.

The researchers say this is compelling evidence that ball players do rely on the apparent acceleration of the ball's movement (OAC) in order to track it down and catch it. You'll notice from the second movie that the player clearly isn't moving in a straight line to catch the ball, so the TP model is also ruled out. Even though people aren't very good at detecting acceleration, apparently we're good enough to catch a fly ball hit 30 to 40 meters (and baseball players routinely shag fly balls hit over 100 meters!).

Fink, P.W., Foo, P.S., & Warren, W.H. (2009). Catching fly balls in virtual reality: A critical test of the outfielder problem Journal of Vision, 9 (13), 1-8 : 10.1167/9.13.14