Figuring 'The Physics of Basketball' Can studying the laws of physics help you be a better basketball player? It might help you find the best angle for your jump shot. U.S. Naval Academy professor John Fontanella, author of The Physics of Basketball, offers his insights.

Figuring 'The Physics of Basketball'

Figuring 'The Physics of Basketball'

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Can studying the laws of physics help you be a better basketball player? It might help you find the best angle for your jump shot. U.S. Naval Academy professor John Fontanella, author of The Physics of Basketball, offers his insights.


This hour it's Sports Friday, we might dub this show on SCIENCE FRIDAY, because later in the hour we're going to talk about the opening day of baseball. We'll get into a little bit of that strange atmospheric hexagon that's on Saturn. But first the Final Four.

Who do you like in college basketball this weekend: Florida, UCLA, Ohio State, Georgetown? I say forget about who has the hot hand or the old rivalries. Now it all comes down to who has the laws of physics on their side, and who understands how to use those laws the best. We'll be talking about physics in basketball and everything a player needs to know about Newton and Magnus and things their coach never told them. The science of sports may explain why some people are so much better at shooting foul shots. Why is that that these big guys just can't seem to do it, you know, Wilt Chamberlain, people like that? There is a reason. We're going to talk about it and about any other aspect of the game that you think science can solve. Our number: 1-800-989-8255, 1-800-989-TALK. The science of sports and basketball.

John Fontanella is a former college basketball player himself. He's now a professor of physics at the United States Naval Academy in Annapolis and author of the new book "The Physics of Basketball," out this year from Johns Hopkins University Press. He joins us by phone from his office. Welcome to the program, Dr. Fontanella.

Dr. JOHN FONTANELLA (Author, "The Physics of Basketball"): Oh, thank you, Ira. Thank you for having me on.

FLATOW: You were a pretty good player yourself at one point, I understand.

Dr. FONTANELLA: Well, I do still hold the single game and single season scoring records at Westminster College, and in fact Earl Monroe and I were on the same All-American team, except that he was drafted by the Baltimore Bullets and I was drafted by Uncle Sam.

FLATOW: So Earl the Pearl went one way and you went the other.

(Soundbite of laughter)

Dr. FONTANELLA: Well, yes.

FLATOW: Well, you're happy where you are now, I'm sure.

Dr. FONTANELLA: Oh, it's wonderful here, yes.

FLATOW: You say that many of today's best basketball players focus on what looks good rather than what is good. Tell us why you say that.

Dr. FONTANELLA: Yes, well, there's - there are an awful lot of fundamentals that are lacking. I hate to say it. People these days love to shoot the three-pointer and slam dunk but seem to have forgotten about everything in-between.

FLATOW: Mm-hmm. Well, let's talk about some of those fundamentals and how physics is involved in basketball. Let's just - let me just take a random fact out of your book and something that you cover in depth, and that is the right way to shoot a basket, the right way - let's talk about the foul line. Why are some people so poor at shooting fouls?

Dr. FONTANELLA: Well, in my opinion it really is a matter of practice, but actually directed practice. In the book I do describe that there is a correct angle, correct launch angle for shooting the foul shot. After extensive video analysis, and I did some modeling, mathematical modeling, the only way I could rationalize those two was if - that the best shooters shoot at the angle where the speed of the ball at the basket is the slowest, is a minimum, and that gives rise to the softest shot. And the math tells us exactly what that angle should be.

FLATOW: What angle is that?

Dr. FONTANELLA: Well, for a six-footer, a typical six-footer at the foul line, that would be 51 degrees, which is a very strange angle. For people like Shaq, the taller, I give him an extra foot or two in height, we're talking 49 degrees. Now obviously Shaq doesn't do that.

FLATOW: No, that's something he should be practicing more.

Dr. FONTANELLA: Exactly, so that's kind of the point here. In the off-season these are the things they really need a little help from physics, I think.

FLATOW: Yeah, you also mention that the ball should be launched at the slowest speed possible to get in.

Dr. FONTANELLA: Well, that was the previous theory.

FLATOW: Mm-hmm.

Dr. FONTANELLA: If you launch - oh, I'm sorry - launched at the previous speed at the basket.

FLATOW: Right.

Dr. FONTANELLA: Before this book came along, it was launch with the smallest speed, so - and so there is a difference there, of about three degrees, actually.

FLATOW: So it should reach the basket at the slowest speed it can, when it gets there.

Dr. FONTANELLA: Exactly, because this way it has least energy, it'll bounce out - it decreases the probably that it'll bounce out. You really want the slowest speed into - at the basket because you want the ball to spend more time around the basket; there's a greater probability of going in.

FLATOW: 1-800-989-8255 is our number. Why not - you know, you also talk about how big the basket is compared to the ball and how at different angles the ball sees the basket as a different size. And you say you don't want to shoot it at certain angles because it really will never get in at those angles.

Dr. FONTANELLA: Well, certainly, yes. Actually, below 33.3 degrees, what I call an angle of approach, where the ball would be going toward the basket at an angle 33 degrees below the horizontal, it literally can't fit through.


Dr. FONTANELLA: So it literally has to have enough arc on it to get greater than 33.3 degrees.

FLATOW: Mm-hmm.

Dr. FONTANELLA: And the theoretical in it of course is if it came straight down, which is great for people who slam dunk, but for the little guys like me, you've got to - the problem with that, of course, is you'd really have to shoot it very, very fast. They just - it would have to be going just too fast if you wanted it to come straight down.

FLATOW: Now, do you want to put a spin on the ball when you shoot it?

Dr. FONTANELLA: Well, yes, you do. Interestingly, the physics says you want - you really want to put the other spin, this spin force called the Magnus force. You would get more angle that way, but there are overwhelming factors. See, all the shooting is an optimization problem.

FLATOW: Mm-hmm.

Dr. FONTANELLA: And the real key, the one that's most consistent, with proper biomechanics anyway, is the back spin. All the good shooters do that. And that has another advantage because when a ball with back spin hits the basket, it loses more energy, so we're back to the minimizing speed thing again. So you do want to get some back spin on the ball.

FLATOW: You also say that coaches should use more video analysis of the shots, that they don't do enough of that.

Dr. FONTANELLA: Well, what they don't do is the mathematical analysis. They all do these days. They have shooting camps, and the coaches that I know that do that, they have a look at it and they look at it qualitatively.

FLATOW: Mm-hmm.

Dr. FONTANELLA: But what I propose and presented in the book is a technique for quantitative video analysis; literally do the math, we can tell you exactly what angle the person is shooting at.

FLATOW: Mm-hmm. Let's go to Bob in Castor Valley, California. Hi, Bob.

BOB (Caller): Oh, hi. So you - I just was on the phone, and I'm just catching the end of that. So yes, there's some guys down in Sunnyvale that have a machine for that. I don't know if you've seen that or not. But that's not what I want to talk about, the video analysis. I am a math teacher and a basketball coach. I want to use shooting free throws to introduce parabolic arcs in a algebra class, and I'm trying to figure how to turn that into an activity after they shoot the free throws, if there's anything I can do as a follow-up.

Dr. FONTANELLA: Yes, what you'll find almost immediately - you have to be a little be careful because if you do this video analysis what you'll find is it's not exactly parabolic. That was a bit of a shock to me because I was absolutely certain that the - that when I started this project, that gravity would dominate everything. And it turns out that it's really not all that parabolic...

BOB: Really?

Dr. FONTANELLA: it's very difficult to get...

BOB: How can it not be parabolic? What's...

Dr. FONTANELLA: Well, you have - it's what I call the Physics Final Four. In addition to the gravity, which gives you parabola, you have the buoyant force, and that's a bit strange that it's as strong as it is. But that does give parabolic - that all - all that does is reduce the acceleration of gravity, so that's parabolic. But the real killer of course is the drag force.

FLATOW: The wind, yeah.

Dr. FONTANELLA: And the drag force completely destroys the parabolic nature. In fact, if you got a basketball traveling 10 meters per second, about 20 miles per hour - that's a little fast - but it turns out the drag force is 15 percent of the gravitational force, and it doesn't have any parabolic nature to it at all. It completely destroys it. If you cut it back to - a foul shot goes about five meters per second, so since the drag force goes as the square, you decrease that 15 percent (unintelligible) so it comes down to about five percent or so.

And then there's - the funny one is the spin, which everybody told me wasn't important until I started looking at things carefully. And there's a real nice video on the NPR Web site showing the effect of spin. And at 10 meters per second, the effect of spin is 10 - or is five percent - I'm sorry - five percent of the gravitational force. And the spin, of course, totally destroys parabolic nature, also...

BOB: (unintelligible)

Dr. FONTANELLA: these things are all much larger than I expected.

BOB: That's surprising. I didn't think those were significant. I thought mostly it was just gravity.

Dr. FONTANELLA: Yeah, nether did I when I started the project.

(Soundbite of laughter)

FLATOW: Quite interesting.

BOB: I assume you have papers on this.

FLATOW: Read his book.

Dr. FONTANELLA: Well, it's in the book.

BOB: In the book.

FLATOW: "Physics of Basketball," John J. Fontanella we're talking to this hour. Thanks for calling 1-800-989-8255. Yeah, so you even as a basketball player and a physicist were surprised by these results. Is there a basketball player out now who you think is the epitome of what you try to teach, or what you explain in the book?

Dr. FONTANELLA: The good shooters in the pros, that'd be Dirk Nowitzki, just a really - just a beautiful thing to watch. And my favorite player in the NCAAs is Taurean Green. May not be as pure a shooter, but he does all sorts of things - so many things so well that he's dominant. The fellow - Jonathan Wallace, for Georgetown, I think is a little bit better shooter, but I don't think he has quite - well, has quite the range as does Taurean.

FLATOW: Well, let's see if I can get a quick question in. Hi, welcome to SCIENCE FRIDAY. Whoops, let's try it again. Let's see if I can get one in here. Kathleen(ph) in Tucson, hi.

KATHLEEN (Caller): Hi there.

FLATOW: Hi there.

KATHLEEN: Hi, I learned when I was playing high school basketball that shooting from the foul line was also an opportunity for a brief rest, to take advantage of that and to maybe change your technique and shoot from the chest maybe, rather than overhead. And I'm wondering how you balance that with the physics and the correct angle of shooting the ball.

Dr. FONTANELLA: It's - that's some very good points, and I'd really love to get the name of your coach because I really like what they taught you. That was exactly the technique that I used when I was in college. In fact that's dealt with in detail in the book. There were two of us who it was foul shots we analyzed. The first was Mike Kiery(ph), a former Navy great, and he shoots more of the traditional way. His foul shot is exactly the same as his jump shot, except he doesn't jump. And mine is exactly what you were describing, where you shoot from the chest. Now I actually was the National Foul-shooting Champion in 1965, I guess, with a 92.2 percent - now that's NEIA - and so the answer is that you really can justify it perfectly well. I go into all the details of why I think that's a good thing to do.

You don't rest when you get to the foul line, but it is a change. So that's really the key. You really can't rest because you have to be tuned up for - to get that ball right up over the rim, but the - it is indeed a change because you're out of the flow of the game, you're slow. And in fact in order to avoid that just a little bit, I used to jump at the foul line a few times before I shot just partly to remind me that I was there, get it loosened up a little bit but...

FLATOW: Mm-hmm.

Dr. FONTANELLA: really wasn't - I wouldn't have said - I wouldn't have called it a rest.

FLATOW: All right, we're going to come back and talk more with John Fontanella, author of "The Physics of Basketball," take some more of your questions about how to maximize your game on this Final Four weekend of the NCAA Championships, so stay with us. We'll be right back with your calls. I'm Ira Flatow.

(Soundbite of music)


(Soundbite of music)

FLATOW: I'm Ira Flatow. You're listening to TALK OF THE NATION: SCIENCE FRIDAY.

We're talking this hour about basketball and physics with my guest John Fontanella, professor of physics at the U.S. Naval Academy in Annapolis, author of the book "The Physics of Basketball." If you want to know everything there is about the physics of basketball, give Dr. Fontanella's book a read. Our number: 1-800-989-8255. Let's see if we can get another phone call here. Let's go to David in Reno. Hi, David.

DAVID (Caller): Yeah, how you doing?

FLATOW: Hi there.

DAVID: Yeah, I had a question. I notice that back in the '50s, the style was to kind of throw a granny shot from the free throw, underhanded, and that was very successful. I'd like to know what the physics on that versus...

FLATOW: Yeah, didn't Wilt do it that way, too, Dr. Fontanella?

Dr. FONTANELLA: He did, yes, and the last player to actually do it, or to do it seriously in the NBA, was Rick Barry, and he was certainly very successful. Well, interestingly, the window for that kind of shot - I shouldn't say the window - but the physics says that it is actually a bit more difficult...

FLATOW: Really?

Dr. FONTANELLA: ...believe it or not. Yes, it does say it's a bit more difficult, but again, we come back to the spin situation. I'm not certain, but I think that the spin is a bit greater, so I think that was a large factor in why the ball is a little - or has a little bit - has a decent probability at least of going on. Yeah, there were very successful people, but I think the overhand shot at the foul line is, from a physics standpoint, is a higher probability shot as long as one shoots at the correct angle.

FLATOW: You don't think the ball arrives any slower that way.

Dr. FONTANELLA: Let me think about it. No.


Dr. FONTANELLA: I don't really think so, though I probably got to make some calculations to check that out. That's an excellent question.

FLATOW: That's what - when I used to shoot the granny shot like that, that's what I always thought. Gee, look, how slow it gets up there, and it does exactly like that.


FLATOW: It bounces around the rim a little bit and just stays there and bounces out in my case, but...

Dr. FONTANELLA: Oh, yeah.

FLATOW: other cases. OK, 1-800-989-8255. Let's go to Wiley(ph) in Kingston, North Carolina. Hi, Wiley.

WILEY (Caller): Yes, hi are you today.

FLATOW: Mm-hmm.

WILEY: I'd like to ask your guest in his research if he has found an optimal position for the fingers on the ball, spreading versus being close together...

FLATOW: Oh, good question.

WILEY: ...and whether it's relative to anatomy...


WILEY: ...of the individual?

Dr. FONTANELLA: That's really an excellent question. I'm going to have to drop back to experience on that, OK...

(Soundbite of laughter)

Dr. FONTANELLA: ...because I really don't - have don't the science of that, but that's certainly a very, very interesting question. Frankly, I would have said a medium spreading of the fingers, and then the real question is where does it come off?

WILEY: Right.

Dr. FONTANELLA: And I've always had the ball come off between the third and fourth fingers.

WILEY: Right.

Dr. FONTANELLA: Right, that's - I think that's it. And I don't think you want them close together because you're going to have a rigid system, that's going to make it tougher. So in my opinion, that's the right way to do it, but I, frankly, I'm not sure what the physics is. I'll have to write that down as an excellent question.

WILEY: Thanks. The reason - if I could make a quick comment.


WILEY: I came to really shooting basketball later in life, put a goal up outside and started using it for exercise in my later years. And I found, for me at least - I had some weird looking fingers to begin with, they're kind of crooked - that the further apart they are, they seem to be a better grip on the ball and plus a better - it seems to be less spin coming off for me, and it gives me better control. So I was just wondering about that.

FLATOW: Whatever works.

WILEY: Whatever works, you're right, absolutely.

(Soundbite of laughter)

WILEY: OK, thanks a lot.

FLATOW: Thanks a lot. Well, what about this new basketball they tried out this year?

Dr. FONTANELLA: Well, that was a real disaster. In fact I got a good one about that. I bought one of them, I took it over to the gym, and the guys at the pickup game wouldn't use it.

FLATOW: What was it made out of? What was so different about it?

Dr. FONTANELLA: Well, it was this micro fiber, and left to itself, that wasn't so bad. Though when it got particularly wet, it did indeed get very, very slick. Under the circumstances as advertised, it did absorb moisture very nicely - or not absorb it, it really just dissipated it.

FLATOW: Right.

Dr. FONTANELLA: But what they did was put very deep lettering on it, and not only did they make it very deep, but they put the lettering close together on the panels. So the ball, number one, wasn't spherical, and what's even worse, it wasn't symmetrical. It was a total disaster actually, yeah.

FLATOW: Players revolted, didn't they?

Dr. FONTANELLA: Oh, yeah, they certainly did, except for the fact that it didn't bounce as high. So here we go again...

(Soundbite of laughter)

Dr. FONTANELLA: ...the shooting percentages were starting to go up just a bit because when you fired them up, the ball - it was just like shooting a dead ball.

FLATOW: Right.

Dr. FONTANELLA: And, yeah, I shot one up in another game, and it - yeah, I swear that it only bounced about three inches above the hoop after it hit it, so.

(Soundbite of laughter)

FLATOW: Jim in San Antonio, hi, welcome to SCIENCE FRIDAY.

JIM (Caller): Thank you. I was just curious, and I know this is not an anomaly just at our pro-basketball team here in San Antonio, but what is it about someone who can do so well shooting a three-pointer, but can't make a free throw to save their life? And I'm not talking about just Bruce Bowen.

(Soundbite of laughter)

FLATOW: OK, maybe we...

JIM: Is it physics or is it psychological? Is it angle? Is it practice?

Dr. FONTANELLA: The psychology of shooting a foul shot is very - is a very, very big factor.

JIM: Pressure.

Dr. FONTANELLA: Yeah, there's a great article by Mark Roth of the Pittsburgh Post-Gazette where he talks about - there's a fellow at Pitt by the name of Aaron Gray who has those problems. So the number one factor is psychological, but there's always the factor of practice from the free-throw line, and I think it's a combination of those two, frankly.

FLATOW: Mm-hmm.

JIM: Well, I know that a lot of teams even hire specialists for free throws.

Dr. FONTANELLA: Oh, yes, the...

JIM: And even with all that, it just - I don't...


JIM: I know there's more angle the further out you get and, you know, you were talking about how the ball needs to be at its slowest point as it's dropping.

Dr. FONTANELLA: Exactly.

JIM: And is it that a lot of times they're still shooting from the free-throw line with that same force, they're trying to shoot the same shot?

Dr. FONTANELLA: You know, it certainly could be, because this is another thing that I talk about in the book. The angle, the proper launch angle for a three-pointer is a lot lower. This really kind of boggled my mind a bit...

JIM: (unintelligible) there's more with distance, certainly.

Dr. FONTANELLA:'s a lot lower than it is at the foul line.


Dr. FONTANELLA: It goes down to like 45 degrees...


Dr. FONTANELLA: ...and - oh, by the way, I wanted to say about this - I hate to bring it up since you're in San Antonio - but the Dallas Mavericks...

(Soundbite of laughter)

Dr. FONTANELLA: ...are shooting 80.8 percent of free throws as a team. And they do have this coach, they do have a free-throw shooting coach. So, you know, 80.8 percent is, to me, that's where everybody should be.

JIM: Well, we'll see what happens in the playoffs.

Dr. FONTANELLA: Absolutely.

(Soundbite of laughter)

Dr. FONTANELLA: Best of luck to you.

JIM: All right, thanks.

FLATOW: 1-800-989-8255. Who are you picking this weekend?

Dr. FONTANELLA: This weekend - oh, I'm - I've got to go with Florida, I think.

FLATOW: Are they going to go all the way in your book?

Dr. FONTANELLA: Yeah, I - well, I - it depends on a lot of things and somewhat how the games are called. I hate to say that, but if the games are called according to the book, I think they'll go all the way, but we'll see. It's really going to be interesting. My goodness, there's a tremendous amount of talent in the tournament this year.

FLATOW: The - you have an excellent set of three shots of three different stages of shooting a jump shot...


FLATOW: ...and three different players.


FLATOW: And then you show the final part is like they wave good-bye, wrist flick at the end there.


FLATOW: How important is that part, in getting that right?

Dr. FONTANELLA: Well, without that you don't have the proper form.

FLATOW: Mm-hmm.

Dr. FONTANELLA: So it's kind of key. I mean if you're going to fire up a shot, you really need - and in a way, you might as well - you want to focus on the end, because if you get the end right, almost certainly you've got most of the rest of the shot right.

FLATOW: Mm-hmm, does the basketball change characteristics as the game goes on and the floor heats up, everything heats up, and the air heats up inside the basketball?

Dr. FONTANELLA: Well, probably not a lot. Probably not a lot, though I did a quick experiment which I talk about in the book where I dribbled vigorously, and I found that I was able to raise the temperature of the ball by about two degrees just from bouncing. But that was a pretty extreme circumstance, so I don't think it does that much. Oh, there is the factor that the leather - yeah, so I take that back. If they don't swap the ball in and out, if the ball gets a little bit wet, the confusion(ph) friction of leather, believe it or not, increases as the amount of moisture increases. And that was - it was exactly the opposite the case with that new NBA basketball, by the way.

FLATOW: Mm-hmm, you know, sometimes you also see a backboard shatter, usually after a giant slam dunk and they hang on the rim. Is that really a sign of a powerful player or something wrong with the backboard?

(Soundbite of laughter)

Dr. FONTANELLA: Well, yeah, not really at all. It doesn't matter how much force is applied, it's really how the force is applied, the key being that the thing is made out of tempered glass, and tempered glass really only shatters when you perturb the edge, when you have access to the edge. I mean, for example, the first backboard shattered was in 1946 by Chuck Connors, the old "Rifleman."

FLATOW: Oh, yeah.

Dr. FONTANELLA: Yeah, yeah, that was the very first one.

FLATOW: He was the first to do that, huh?

Dr. FONTANELLA: And it was shattered, but it was the ball that did it.

FLATOW: Really?

Dr. FONTANELLA: It wasn't Chuck. He had nothing to do with it. He just fired up just a little lazy 20-footer and the backboard shed. And the reason was they left - they left out rubber bushing. And the bolt just hit the edge - the edge of the glass and the thing shattered.

FLATOW: I got one more question left and that is, is it better to shoot off the glass or to go for the net when you're shooting.

Mr. FONTANELLA: It depends on where you are. It depends on where you are. If you're in close, in around the paint and, you know, just a few feet around -there's overwhelming evidence that you should shoot off the glass.

You get further out you definitely want - don't want to do that. It has to do with the speeds involved.

FLATOW: All right.


FLATOW: I'll have to watch for that in the paint this year.

Mr. FONTANELLA: Yes. And there was one other factor that I did want to throw in here. It's a question, too, of where you shoot from. You know, I think the physics says you really want to shoot from the vicinity of the key, because that way the backboard can help you.

And this has really been born out in this tournament so far. I haven't seen one good shot come from the side of the wings yet.

FLATOW: Well John Fontanella, I want to thank you for taking time to be with us. And good luck to you this weekend.

Mr. FONTANELLA: Well thank you very much, Ira.

FLATOW: Hope you've got the grid that you're looking for.

Mr. FONTANELLA: Thank you.

FLATOW: John Fontanella, former college basketball player himself, holder of free shooting - the foul line record, which I wasn't aware of - professor of physics at the U.S. Naval Academy and author of the new book, "The Physics of Basketball." If you want to learn everything you wanted to know about the science of basketball I think it's right in there.

We're going to take a short break and come back with switching gears.

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