Tennis Tennis


Predictions, predictions

Posted: Monday December 03, 2001 2:23 PM

Sports Illustrated senior writer Jon Wertheim will answer your tennis questions every Monday. Click here to send a question.

If tennis had a Player of the Week award, the latest honoree would be Nicolas Escude, who won two singles matches to help France pull off a shocking Davis Cup upset of Australia. ... The Backfiring Gamble of the Week (sponsored by Enron) goes to John Fitzgerald. The Aussie captain replaced the doubles team of Wayne Arthurs and Todd Woodbridge (the best doubles player of the past 20 years) with Lleyton Hewitt and Pat Rafter, neither of whom sports a top-100 doubles ranking. First, the Aussies lost to Cedric Pioline and crafty Fabrice Santoro, who was outstanding. (World No. 1 Hewitt, incidentally, was far and away the weakest player on the court.) Then, Rafter revealed that his bum arm would prevent him from playing singles the following day. Ball game. ... Speaking of Rafter, a little birdie -- albeit a well-connected one -- told me Sunday morning that we shouldn't write his tennis obit just yet: "Between losing in Australia, losing in the Wimbledon final and now losing in Davis Cup, I don't see him going out that way." ... If my math is right, no team in the Davis Cup finals has lost the doubles match and come back to win the tie since 1977. ...

From the sublime to the ridiculous: Monica Seles waxed Anna Kournikova in an exhibition last week in Denver. Luke Jensen, also on hand to make some nice cake, blamed Kournikova's spotty play on the altitude. Kournikova couldn't be reached for comment as she blew off the media afterward. ... Speaking of Seles, who turned 28 last week, she'll play Martina Navratilova in an exhibition (anyone else sense a theme here?) at a Connecticut casino next weekend. Said Navratilova, now -- gulp -- 45 years old: "I'm very excited to be playing tennis with Monica Seles. Playing against top players is something I really love to do. The last time Monica and I played was for her comeback, so maybe this match signals my comeback. No. I'm just kidding." ... Keep an eye out for Deuce, a new ATP magazine, in the upcoming months. ... Several readers passed along this item about Serena Williams that ran in The Washington Post last week. I have no idea about the veracity, but here it is.

Stay tuned next week for the Fourth Annual Baggie Awards ...

FIRST, as promised, some predictions for 2002. In the interest of full disclosure/embarrassment, I've humbly posted my whiffs, I mean, picks for 2001.

Wins first career title

Men: Mikhail Youzhny
Women: Elena Dementieva
2001 picks: Guillermo Coria and Anna Kournikova

Wins first career Grand Slam

Men: Andy Roddick
Women: Kim Clijsters
2001 picks: Magnus Norman and no one.

Comeback player of the year

Men: Norman
Women: Mary Pierce
2001 picks: Marcelo Rios and Pierce

Lives up to the hype

Men: Roddick
Women: Daja Bedanova
2001 picks: Roger Federer and Lina Krasnoroutskaya

Continues to be all hype

Men: Todd Reid
Women: Ashley Harkleroad
2001 picks: Mark Philippoussis and Alexandra Stevenson

Most likely to retire

Men: Andre Agassi
Women: Arantxa Sánchez-Vicario
2001 picks: Pat Rafter and Sánchez-Vicario

Most likely to make a splash

Men: Marko Ancic
Women: Angelique Widjaja
2001 picks: Roddick and Maria Emilia Salerni

Finishes the year ranked No. 1

Men: Juan Carlos Ferrero
Women: Venus Williams
2001 picks: Marat Safin and Venus Williams

Were you surprised at the choice of grass as the surface for the Davis Cup? I thought it was the worst choice Australia could have made, especially since Nicolas Escude had beaten Lleyton Hewitt at Wimbledon. If the matches had been played on anything, even clay, Australia would have won. What are your thoughts?
—J. Gudmunsson, Iceland

If we're going to play Monday Morning, what, Serve-and-Volleyer, we can definitely second-guess the choice of surface. First of all, that was some of the nastiest grass I've ever seen. A set into the first match, it looked like the dog run in Central Park. The players would have gotten better bounces playing on gravel. Anyway, the thought behind choosing grass was that it was Rafter's strongest surface and that Hewitt is capable of winning on anything. We know, obviously, what came to pass. If the tie had been on clay? Interesting hypo. I say Hewitt would have beaten both Escude and Sebastien Grosjean, while Rafter and/or Arthurs would have lost their singles matches, leaving the doubles match as the decisive point. The Aussies would have been better off leaving well enough alone and playing on the regular synthetic surface of Rod Laver Arena. By the way, I believe this is our inaugural Mailbag submission from Björk country. So thanks, J. And enjoy the upcoming Icelandic summer. I hear it falls on a Thursday this year.

Re: jumping over the net, you may want to look into this. My current tennis pro has told us the story (or urban legend) of a young female player who did this at the conclusion of a match, caught her feet, flipped over, hit her head and died. I can't find any real evidence of this on the Web, but I don't have access to your research tools. Lexis-Nexis, anyone?
—Klaas Kwant, Grand Rapids, Michigan

I took your advice and made a date with Lexis-Nexis, the single greatest invention since the Diaper Genie. Alas, I found nothing, nor was there any reference to fatality via tennis net in the Sports Illustrated library. (We actually have a file of clippings called "Tennis -- Oddities.") The National Center for Catastrophic Sports Injury Research cites one indirect high school fatality in women's tennis in 1987-88. I have no idea if jumping over the net is "direct" or "indirect," and the voice mail I left the center went unreturned. Though this constitutes my lone research exercise for 2001, it wasn't exhaustive. If any of you know of the incident in question, fire away.

Here's a fun question. Which five announcers from other sports would you like to see broadcast tennis. How about it?
—Jennifer DiRocca, Boston

This question was meant for fun, but, in truth, it's not a bad idea. As the New York Observer put it recently, tennis announcers can tend to sound like the "Delicious Dish" hosts on Saturday Night Live, soft-balling former players who are about as hip as Jordache jeans. There was a rumor last summer that the folks at Turner were seriously trying to convince Charles Barkley to do Wimbledon. It obviously didn't happen. Which is too bad, because it would have done wonders attracting general sports fans to tennis. Anyway, here are my five talking heads:

1) Bill (Grateful Red) Walton: " Gustavo Kuerten losing nine of his last 10 matches ... that's HORRIBLE!"

2) Dennis Miller: "Last time I saw an overhead botched that badly I was watching Myrna Loy and Pericles get it on in a panzershrank headed to Antietam."

3) Walt (Clyde) Frazier: "There's Yevgeny Kafelnikov showin' audacity and perspicacity, tankin' and bankin'."

4) Keith Jackson: "Hewitt reminds me of cowpoke on the prairie trying lasso the ... and it's a drrrrrrrrrrrop shottttttttttttttt."

5) Marv Albert: The real Marv. Not the lame impersonator who showed up in the booth at Wimbledon last summer.

I just finished your book Venus Envy. You wrote a bit about Debbie Graham, who has retired. Can you tell us what she has been doing after tennis?
—Ian Katz, Key Biscayne, Fla.

From the horse's mouth: "I did an Internet gig right after I retired. I still kept my foot in the door in the tennis world, running Southern California's Area Training Clinic for the best juniors in SoCal. This is run by the USTA. When my company went under after a year, I continued coaching on the side. I do work some work for the USTA. I also do consulting for Wilson Sporting Goods in regards to marketing tennis rackets. I also sit on the Board of Directors of the U.S. Olympic Committee; I represent tennis for the U.S. I am privileged to sit next to the likes of Henry Kissinger and other former Cabinet members. I am involved with some TV shows involving tennis. I can't disclose too much on that yet. It is in the works. So basically, you can say I am really busy. I am getting the opportunity to dip here and there and do what makes me happy. I am thinking about going back to business school next year at USC."

People forever are accusing you of Thomas Johansson worship, but I think Pat Rafter is the one player you bow to. You constantly put him in the same category as Andre Agassi and Pete Sampras, yet he has done nothing to deserve it. Of this generation, Yevgeny Kafelnikov and Jim Courier are Sampras' and Agassi's contemporaries, not Rafter. He has only won 11 titles and two Slams; by comparison, Kafelnikov has almost 30 titles with two different Slams, plus an Olympic gold medal. I just don't see how Rafter compares. In 1997 and '98 he, like a lot of other people, prospered because of Agassi's absence; now that Agassi is back, Rafter's fortunes have turned decidedly.
—Jason Gould, Columbus, Ohio

Congratulations on being the first person ever to use the words Thomas, Johansson and worship in succession. (I plead innocent to all charges.) I readily concede that I think Rafter is (warning: cliché alert) a credit to the sport and wish more players had his serve-and-volley sensibilities. But please tell me where, when and under what circumstances I put him in the same corral as Agassi and Sampras? While he's been among the better players of the '90s, no way is Rafter in the same league as Pete or Andre. On the other hand, I think he is (if that's the right tense?) a cut above Kafelnikov, despite their winning the same number of Slams. Rafter has made the semis of all four Slams, has had Davis Cup success, plays an aesthetically appealing game and is/was as good a sportsman as the sport has known. You also have to give bonus points to a guy who started his career playing challengers and qualies for a few years before breaking through. In Rafter's case. his career is more than the sum of its parts.

This question arises in the wake of Michael Jordan's third coming: Of the following five retired thirtysomethings, who would have the best chance of making another go at it on the ATP Tour: Stefan Edberg, Boris Becker, Jim Courier, Petr Korda or Aaron Krickstein?
—Greg Daud, Fishkill, N.Y.

I wouldn't hold your breath waiting for any to return to the fold. I think that after a lengthy hiatus, it's easier to get back in shape for basketball than for tennis. Plus, in the NBA a player with a guaranteed contract is on the team. If he shoots, say, 30 percent from the field and his team is abysmal -- just hypothetically, of course -- he still has a job next week. In tennis, a player making a comeback would have to grope for wild cards and then have to win matches before getting a respectable ranking. This is a convoluted way of saying that, procedurally, it's tougher to return to tennis than other sport. However, if I had to pick one of the five you mentioned, I'd say Korda. Don't ask me why.

I've noticed that you have used some Simpsons references in the 'Bag. So how about a top five list of the best Simpsons episodes. How's that for a tough question?
—Jorge Caussade, San Juan, Puerto Rico

Can't pass this one up.

1) Milhouse falls in love/ Homer gets a vocabulary builder
2) Sideshow Bob Cape Fear takeoff
3) The spoof of Streeetcar Named Desire
4) Springfield gets a monorail (Trivia: written by Conan O'Brien )
5) Homer's gay friend, John Waters.

Unfortunately, the tennis episode "starring" Sampras, Agassi and the Williams sisters ranks among the lamest.

FINALLY, with respect to our previous discussions about the physics of tennis and how it compares to other sports, I'm adapting and reprinting the following with permission from the newsletter Daily Tennis. This was written by Robert Waltz. It's long but worth the payoff.

Have a good week, everyone.

Sports Illustrated senior writer Jon Wertheim, author of Venus Envy: A Sensational Season Inside the Women's Tennis Tour, is a regular contributor to Click here to send him a question or comment.

Tennis physics

We don't claim that a player with a barely secondary-school education can handle advanced physics. But most basic physical concepts require only the mathematics one learns in the first six years of school. And they are the basis of the whole sport of tennis. We have seen, in the reactions to items in our publications, how many people don't understand these subjects -- even though people like Vic Braden have been studying them for years. It really isn't that hard.

What follows is a lecture, but there are hardly any equations and you won't need anything more complicated than a five-function calculator (add, subtract, multiply, divide and square root). Much as physicists hate to admit it -- after all, one of the ways we keep score is the number of buttons on our calculators -- physics can be taught at the grade-school level.

Take an issue we raised last week: The speed with which one can hit a groundstroke. This is, in fact, an extraordinarily complicated problem, because of air resistance. Air resistance varies according to the velocity of a ball -- hit it hard, it slows down a lot; hit it softly, it hardly slows at all. So when you play catch with the kid across the street, the ball has just about the same speed when you throw it and when he catches it. Hit a tennis ball with full force, though, and it will shed much more than half its velocity before it gets across the court. Consider this: A tennis court is 78 feet (about 24 meters) long. On the men's side these days, you routinely see serves in the 200 kilometers-per-hour range. That's 55 meters per second. In other words, such a serve, if there were no air resistance, would travel the entire length of the court (down the center T) in .44 seconds. If the ball actually moved through the court that fast, no one would ever touch it. But players like Andre Agassi do return such serves, often hitting winners. Obviously, the ball has slowed dramatically.

But while air resistance makes a huge difference in the real world (and it is a great credit to the human brain that it can, in effect, solve this partial differential equation and hit a return that keeps the ball in the court), the basic facts can all be derived from the simplest of formulas with no need whatsoever for calculus. The answers won't be right, but they'll be the right type of answers.

Let's start with the problem of a ball going over the net. What we want to know is, How fast can it be moving? Let's look at the geometry of the court, seen from above:

|\        |
| \       |
|  \      |
|     \   |
|      \  |
|       \ |

The distance from A to D (the length of the court) is set at 78 feet, or about 23.75 meters. The distance from D to E is 27 feet, or 8.25 meters. At B, the net is 3.5 feet high (107 cm); at C, 3.0 feet high (91 cm).

So how fast can a ball go through the court? We have to make some assumptions here. First, the ball is going straight through the court -- not moving up or down -- as it crosses the net. This will generally be close to true for balls which barely clear the net; it's not true for high balls.

If the ball just clears the net and lands as close to the baseline as possible, how fast can it be moving? This is actually a relatively simple problem. The "general" formula for distance travelled by a moving object, ignoring air resistance, is given by the distance formula -- d = .5at2 + vt +d(0) -- which looks complicated, but most of it goes away. We don't care about the d(0) term, and we just said that the ball is not moving up or down as it crosses the net. So vt is also 0. And a is also known; it's 9.8 meters (or 32 feet) per second. (We're going to use metric units, though, because every physicist does these days.) That leaves us with the simple equation d = (.5)(9.8)t2, where d is measured in meters and t in seconds.

So if the ball crosses the net at C (i.e., a cross-court shot), where the net is .91 meters high, we get to solve:

.91 = 4.9t2


.19 = t2


t = .43 seconds.

This result is fairly close to correct no matter how much air resistance there is because the ball isn't moving up and down very fast, and so air resistance and spin don't have that much effect.

If we perform the same calculation for a down-the-line shot, where the ball crosses the net at B, where the net is 107 cm. high, we find the answer to be: t = .47 seconds.

So no matter where the ball crosses the net, if it just clears it, it must bounce within half a second. (Note: Hit the ball higher over the net and it will take longer to bounce. This is why defensive lobs work; hitting the ball higher means the ball takes longer to land, giving you time to get back into position. But a lob, of course, isn't moving very fast, and your opponent has plenty of time to get to it. In general, the lower the point at which the ball crosses the net, the faster it is moving and the harder it is for your opponent to reach.)

Knowing when the ball must land in turn allows us to compute the maximum possible speed of the ball. For a cross-court shot, where the ball goes from C to E, the Pythagorean theorem lets us show that the distance from C to E is about 12.25 meters. From the number above, we know that the ball covers this distance in .43 seconds, so our average speed across the court will be 12.25/.43 = 28.5 meters per second. That, sparing you the tedium of the math, is 102.5 kilometers per hour, or 64 miles per hour. We are not making this up.

Of course, the ball can, and will, be moving faster when the returner first strikes it; he can put more speed on the ball and let the air take the speed off. Plus, if he hits the ball above the ground, he can allow it to have some slight downward motion as it crosses the net, which allows it a slightly greater speed through the court. But you're still looking at an average effective speed on the order of 150 kilometers per hour, or 100 miles per hour. If the ball lands short of the corner; goes down the line or at any angle other than corner to corner; or is allowed a little height to clear the net, it will have to move more slowly.

If you put a radar gun on a groundstroke, it will likely register something higher than this. That's because the radar gun measures the velocity off the racket, before air resistance has had time to bite. We've heard of groundstrokes hit in the 200 km/h range, just like a fairly big serve. But because air resistance increases as speed increases, the ball quickly slows to a more reasonable speed.

Now, 100 mph is pretty gol durn fast. It will get the ball across the court in 2/3 of a second. (And if you think about it, most balls don't go through the court, baseline to baseline, cross court, that fast.) But it is a limit. And it's a limit which, as the radar gun shows, most players can approach.

That's for groundstrokes. The key point for groundstrokes is that they are hit below net level -- or, at the very least, at a level which does not have a sight line to the far side of the court. Picture an imaginary line from the baseline to the net, like this (the height is exaggerated):

      .......      |

Any ball not struck above this approximate line (it's approximate because the shape is actually what mathematicians call a "manifold," depending on where you want to hit the ball and a whole bunch of other things) has to be hit up, and with reduced velocity, if it is to land in the court.

The serve is a completely different matter. It's hit above that line -- but it has to land much, much shorter.

We won't do the math on this one -- for one thing, since the server is hitting more nearly down on the ball, air resistance becomes a much greater factor in our time-till-landing calculations. But a key point emerges: The higher you hit the ball, the greater the velocity you can put on it. (This is why volleys are generally history: the volleyer can hit them as fast as his muscles allow.) So, on the serve, taller players do have an advantage. Much more of an advantage than they have on the groundstroke, where the shot is limited by geometry.

There are some interesting footnotes here about the serve. The big push today is to produce the fastest possible serve. This may not always be smart.

The trick here is how the ball bounces. Basically, a bouncing ball follows a V-shaped path: drop it from a sharp angle, like this, and it will bounce at a sharp angle:

*              *
  *          *
    *      *
      *  *

Fire it at a shallower angle, though, and it will bounce lower:

*                      *
    *              *
        *      *

To hit the serve as hard as possible, you must hit it as high as possible. But that means that it comes in for the bounce at a sharper angle, and bounces higher -- probably right into the returner's wheelhouse, especially if you're on a hard court. (We would contend, incidentally, that this is why grass is faster than hard courts: It's not that the ball goes through the court faster than on grass; indeed, because dirt is softer than DecoTurf, it goes across the court more slowly. But the ball bounces lower on grass, and so is harder to return.) If you can hit a lower, flatter ball, you may well get an easier return, even if the serve is slower, simply because the returner has to hit up at a higher angle.

Physics tells us the most about the flight of the ball, but it also tells us something about the players. For example, it tells us why smaller players are generally regarded as fast. It isn't that way in other sports; indeed, runners are often above average in height.

The reason is that speed in tennis isn't the same as speed in a straight race. It's the ability to get somewhere from a standing start -- the ability to change direction. This makes the most important element in "tennis speed" not actual speed but acceleration -- how fast you can get started toward the ball.

And Newton's Second Law tells us that Force equals Mass times Acceleration (F=ma). Or, to write this in terms of acceleration, Acceleration equals Force divided by Mass (a=F/m). What does this mean? It means that, the heavier you are, the more force you have to apply to achieve the same acceleration.

It's at this point that we invoke a rule called the "square-cube law." Basically, this law says that, as you make a person (or anything) bigger, it gets heavier faster than it gets taller. By a lot.

The reason is that mass (or weight) increases with the cube (third power) of the length -- that is, you multiply the value by itself, and by itself again, when you increase the length. Think of this in terms of a an actual cube: A cube that's one unit long by one unit wide by one unit high has a volume of one unit. But a cube two units along a side has a volume of 2 x 2 x 2 = 8. Make it three units on a side, and it's 3 x 3 x 3 = 27 units on a side. (You can prove this using a child's set of blocks. A single block is a cube one "block" big. But you need eight blocks to make a cube two blocks on a side.) As you can see, the volume is increasing a lot faster than the length. And how heavy something is depends on its volume. So if you take two people of similar builds, but one is 10 percent taller than the other (i.e., has a height 1.1 times the other), then that person's weight will be 1.1 x 1.1 x 1.1 = 1.33 times as much. Our taller player is only one tenth taller, but weighs a third more. It's true that his muscles are bigger -- but the force exerted by muscles, we are told, increases as the square of the length (hence square-cube law; get it?). So someone who is 10 percent taller can exert 1.1 x 1.1 = 1.21 times as much force, but weighs a third more. His weight has gone up faster than his ability to exert force. So he can't accelerate as fast. It all varies from person to person, but taller players will be slower on average. And very likely more injury-prone (since, again, they're hauling around more weight -- and operating at the end of longer levers).

Taller players may also have more heat problems, though this is more speculative and depends more on individual differences. Like muscle force, surface area increases with the square of length. So, as you get taller, your surface area -- and hence the area that can radiate heat -- doesn't increase as fast as your weight. Tall players should theoretically overheat more easily (lest you think this is a pure advantage to short players, they freeze faster in cold weather).

The compensation for tall players, of course, is that they can hit harder. This is another case of physics: How hard you can hit the ball of course depends on how fast you're moving your racket. And those taller players are holding the racket at the end of longer arms. The longer the arm, the faster the racket is moving. Try an experiment: Put your elbow against your side, and swing your arm back and forth. Put it straight out from our side, and then forward in front of your body, and measure how far your hand moves. If you're a normal person, the distance will probably be about 15-20 inches, or not much more than half a meter.

Now hold out your arm straight out from your shoulder, and move your hand through the same angle. Again, measure how far your hand has moves. It's about twice as far.

Assuming everyone swings a racket at about the same angular velocity (that is, swings it through the same angle in the same amount of time), the players with longer arms -- and, of course, longer rackets -- will be able to hit the ball harder. This is why longbody rackets are such an advantage.

We could go on. The point is, even a little physics can help you plan your strategy. And if you want more, there is always Vic Braden. But this is something the tour could easily help players with. Most colleges have a course along the lines of Physics for Poets; the professors have had to learn (sometimes reluctantly) how to teach students with almost no math. It wouldn't take much to create a tennis physics course.


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