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
I remember working on this problem as an undergraduate RA for Michael McBeath. I ran around a baseball field catching balls with a portable eye-tracking unit. More embarrassing than wearing the rig around campus was watching the video with the research team where everyone can see where my eyes wandered during regular activities. Virtual Reality does provide the experimenter a lot more control over ball movements, which was a problem I remember us having.
This is very cool, and it also demonstrates an interesting aspect of intelligence.
'Jocks' are usually portrayed in movies etc as thick-head with limited intellect, as opposed to 'nerds' who are super smart. However, if you think about it, the processing power needed to observe a ball in the distance, calculate its flight, make the necessary adjustments for wind etc, move your body to where and when it is going to land, and then actually catch the ball, are far greater than that required to do complex mathematical calculations or play chess - the simplest computer can do that.
Maybe the jocks are the smarter ones.
For whatever it's worth ... I recall thinking about this a bit when I was a Little Leaguer playing the outfield, trying to figure out what was different on fly balls that were easy to track versus ones that were harder.
I concluded that both the sound of the bat making contact and the jump of the bat off the ball were significant, in addition to my actual tracking of the ball in flight. It seemed to me that my initial break on the ball was based on that instantaneous information, after which I used the visual information to close in for the catch. That is, the fielder also integrates sensory information on how well the ball is struck in addition to its flight path.
The most difficult catches were the ones in which for some reason I couldn't get a good read on the ball as it came off the bat. I then had to respond solely to the flight information. It was as if that initial information on the jump off the bat allowed me to limit the possible range of flight paths.
And I'm always impressed with an outfielder who can turn his or her back to home plate and run to the place where the ball is headed without tracking the ball visually until they are closing in on the catch. Absolutely amazing!!
Wille Mays' most famous catch:
Good fielders also take some of their cues from sound i.e. "the crack of the bat", and "situational awareness", i.e. the ball-strike count, where the pitcher is locating the ball, late inning vs early inning at bat and of course the score of the game.
Visual cues can also throw off a fielders perception - you can see at times that a hitter will take a full swing (aka a home-run swing), which will cause a fielder to break back on the ball on cantact, but the hitter can miss-hit the ball, leading to a bloop hit in front of the fielder.
BTW - Mandas - You bring up a good point about perception vs reality for "jocks" - but my daugter was a 3-year softball varsity starter and is now a chemical engineer, and my son plays baseball and takes all Honors and AP classes in HS.
And I am always amazed watching kids play that know how to play. Poetry in motion.
"'Jocks' are usually portrayed in movies etc as thick-head with limited intellect, as opposed to 'nerds' who are super smart. However, if you think about it, the processing power needed to observe a ball in the distance, calculate its flight, make the necessary adjustments for wind etc, move your body to where and when it is going to land, and then actually catch the ball, are far greater than that required to do complex mathematical calculations or play chess - the simplest computer can do that.
Maybe the jocks are the smarter ones."
That would make birds and frogs smarter still. Not a very useful criteria of smarts.
On a more germane topic, this was an interesting finding, but it's likely a bit more complicated than that. We use different estimation methods at different distances; once the ball is closer - or the moving object is larger - we use tau-margin estimation (use the change in apparent size), and really close up we do use stereoscopic vision as well. And of course we rely a good deal on previous experience on what that ball "should" do in a given situation.
I think one possibility was overlooked and that is recalling similar "fly balls" from previous experience. By high school level, most outfielders would have a nice internal database of fly balls and be able to approximate where they will land. This is not to say that they still need to fine tune once the get to the desired location.
Do these results rule out the possibility of using a combination of the methods? Doesn't it seem likely that the fielder's brain makes an early estimate that is continuously refined, which might mean that as the distance changes the method used to determine the path of the ball changes?
Be very interested if some of you could take a look at this youtube video of cricket catches: http://www.youtube.com/watch?v=05klsa3M08A
Having never played, but admired baseball, I'm curious what comments you may have on these catches.
I wasn't very interested in baseball or stuff like that, but now i see the physics in catching a fly ball! I knew about all other physics, but i needed some extra knowledge, so thanks. (but Dont take my thanks too seriously, i'm still just in grade 5.)
The best center fielder I ever saw was Steve Finley, who played for all the NL west teams. He would watch the ball leave the bat, put his head down and run to where he anticipated the ball to land, look up and readjust is location, and (without fail) catch the ball. I know a lot of coaches teach their players to follow that strategy, but few players can.
I would be interested to find out just how much extra information the fielder is getting from his surroundings. Some have mentioned the sound of the bat, or perhaps, for example, the reactions of the batter, other fielders, and base runners are visible in the peripheral vision of the fielder catching the ball. I wonder if the fielder's path toward a fly ball in a game would be different from the path taken in an open field toward the same fly ball thrown by a machine.
Wonder about the situation where we are the moving object such as landing a small aircraft or helicopter, we used to pick a spot and go for that...seems OAC might be at work there. : )
For what it is worth the way I catch fly balls.
I played baseball thru High School and then recreational soft ball for twenty years. Being very slow and not have good hands I almost always was in the outfield. I concluded I must make up for my lack of foot speed by getting a very good jump on the ball. The best way I discover to do this was to check the wind speed and direction as the batter comes to the plate. Watch the pitch leave the pitcher hand and then how the batter begins to swing. These observations give me a rough idea of where the ball is going to wind up before it is actually stuck. I then begin moving to that spot but I keep watching the swing and see the bat speed, see where it hits the bat, listen to the sound it makes and most importantly observe the spin of the ball. (I am surprised no one has talked about spin because the spin determines the amount the ball will slice) (TP) This gives me enough information to know the neighborhood where the ball will land. Watching the flight of the ball as much a possible will allows me to keep refining where the ball will land as I move until I am able to determine the spot where the ball comes down. (OAC) If possible I stop one step behind this spot. Standing back does two things. It allows me to still catch the ball if it carries and to have momentum behind my throws. I step forward and catch the ball about shoulder high and directly in front of my throwing arm. Catching the ball with both hands and allowing the impact of the ball hitting the glove to push the arm back behind the shoulder to the point I begin a throw. Now the ball is caught and I have my arm cocked ready to throw.
I do not believe I ever use the LOT method when catching a fly ball.
My first thought was "My GOD, how big are the flies over there!"
This is a study of how the eye and mind coordinate to project the flight of the ball. To me as a kid it was an inherent skill, I knew where that ball was going to go and never thought about it. You just ran to the spot as fast as you could or as fast as you needed to. This was a study to show how the mind does that. If you're standing in left with a right handed batter there isn't much cheating to be done.
Re: Cricket. Boswell once wrote about taking a British friend to an Orioles game, and discovering that the feat that amazed him wasn't the pitching or the hitting or the fielding - cricket players threw and hit and caught. It was the double plays.
Mike Cameron (who recently signed with the stat-friendly Boston Red Sox) claims to use the TP method:
The "baseball-chess" example actually contradicts your point. My TI graphing calculator can find the exact solution to any trajectory problem in a matter of seconds. It only requires basic trigonometry. A human, as good as his or her catching skills may be, can't begin to match the accuracy of even a very basic computer. By contrast, computers cannot always find the exact solution to a chess move, even if given several minutes to do so. They only make the best guess they can. They think of so many possible moves that a chess computer can beat almost anyone. However, the best grandmasters can typically win or draw against a computer. So by the analogy you gave, nerds can rival the best computers, whereas jocks canât even beat the simplest ones.
The important thing is that all humans are more intelligent than computers. The only thing that the machines have on us (so far) is their ability to perform arithmetic incredibly fast and store huge amounts of detailed data. Comparing human intelligence to machine intelligence is, as Janne said, "not a very useful criteria of smarts."
Nonetheless, your point is well taken. Jocks are not necessarily less intelligent than nerds. They are just not as technically practiced as nerds are. Likewise, a nerd is not as physically practiced as a jock. Each focuses on honing their preferred skill sets. Indeed, the labels are not mutually exclusive.