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The following are excerpts from Bob Larson's Tennis International Newsletter, published weekly by TennisONE. For more Larson tennis news products, go to: www.tennisnews.com

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Rankings Updates

Maybe it's the fact that there were two big Challengers. Maybe it's just the fact that one of them was in the U. S. (the other was in China). Whatever the explanation, the WTA had a half-dozen Top 100 players in action last week, starting with Melinda Czink -- who, however, had points to defend and fell from #74 to #79. An even bigger blow was suffered by Julia Vakulenko, who lost first round in Florida and fell from #82 to #94. We did see one player break into the Top 100: Marta Marrero went from #109 to #98. As we noted Monday, Tatiana Panova also played -- and lost in the quarterfinal. But at least she's back, and moved from #119 to #114.

This year's Big Surprise doubles team, Ting Li and Tian Tian Sun, didn't use their Top 50 status as an excuse not to play in Changsha. Having already won three WTA titles and at least two high-level Challengers, they earned title #6 of the year with a win over countrywomen Zi Yan and Jie Zheng (the latter was also the singles finalist, losing to Shuai Peng). That's small enough points, though, that Li and Sun stay at co-#48. Yan and Zheng stay co-#74. There was, in fact, almost no movement in the doubles rankings; the top player to actually move was Janet Lee, who rose from #53 to #52, with Alina Jidkova falling from #52 to #54 (rather ironic, given that Jidkova earned three times as many points as Lee, but she was defending points).

The two $50K Challengers will not be the last events to go on the record in 2003, but they mark the end of significant events. We probably won't see any more changes in the Top 100 this year.

The big news on the men's side is that Johansson is now Top 100. Only that's not Thomas, who is still waiting for a comeback. It's Joachim Johansson, who has been having a very good post-season. A big Challenger result this week gained him 19 places, and put him in the Top 100, at #95. Johansson is the only Top 100 player to gain more than one ranking spot. Though we did see one player take a dramatic dive: John van Lottum fell from #80 to #92 (and his fall caused most of the other moves in the Top 100). The only other Top 100 player to move more than one spot was Rafael Nadal, who slipped from #47 to #49.

Hand It Over, Part II

Earlier this week, we looked at the list of tournament repeat winners. This was actually a feature we'd used a year before, updated to reflect results from 2003.

Last year, when we looked at the list, though, we looked mostly at the players who owned events. This year, as a different twist, let's look at the numbers themselves.

First let's briefly review our data. The ATP has 43 different events which date back 14 years (or more). The following list shows those events, the number of different winners, and the number of times the biggest winner has won:
Event.........Distinct Winners....Biggest Adelaide....................11..........2 Amsterdam (Hilversum).......11..........2 Auckland....................14..........1 Australian Open..............8..........4 Barcelona...................13..........2 Basel.......................13..........2 Bastad......................10..........4 Canadian Open...............12..........3 Casablanca..................12..........2 Cincinnati..................10..........3 Estoril.....................12..........2 Gstaad.......................8..........3 Hamburg.....................12..........3 Indian Wells.................9..........3 Indianapolis................12..........3 Kitzbuhel...................11..........3 London (Queen's)............11..........3 Long Island.................11..........2 Los Angeles..................9..........3 Lyon........................11..........3 Masters Cup..................8..........5 Memphis.....................12..........2 Miami........................7..........6 Monte Carlo..................9..........3 Moscow.......................8..........5 Munich......................13..........2 Newport.....................13..........2 Palermo.....................13..........2 Paris.......................11..........2 Roland Garros...............10..........3 Rome........................11..........3 Rotterdam...................12..........2 's-Hertogenbosch (Rosmale...10..........3 San Jose (San Francisco).....8..........5 Stockholm...................10..........3 Stuttgart (outdoor).........12..........2 Sydney......................11..........2 Tokyo.......................12..........3 Umag.........................9..........4 U. S. Open...................7..........5 Vienna......................12..........2 Washington, D. C.............9..........5 Wimbledon....................8..........7

That gives us some interesting data right there. We can look at the number of times the biggest winner has won. One event -- only one -- has had a seven time winner: Wimbledon. (If you can't name him, maybe it's time to ask yourself why you're even reading this.) One other event -- Miami -- has had a six time winner. (You probably can name him, too.) Five events -- Masters Cup, Moscow, San Jose, the U. S. Open, and Washington D.C. -- have had a five-time winner. Three events -- the Australian Open, Bastad, and Umag -- have had four-time winners. No fewer than sixteen events have had at least one three-time winner. Sixteen more have been limited to a two-time winner. And only one event -- Auckland -- has had no repeat winners.

But let's try something else: Let's try slicing the data first by surfaces. It turns out that our 43 stable events include approximately 16 clay events, four grass events, 14 hardcourt events, and nine indoor events (carpet and indoor hardcourt). (We must say "approximately" because of course events change surfaces from time to time, as the Masters Cup did this year. We treated it as an indoor event even though the 2003 version was played on hardcourts; it's been mostly an indoor event historically.)

Let's count the distinct winners by surfaces. Taking grass as the easiest example to show what we mean, our four stable grass events are Queen's, Newport, 's-Hertogenbosch, and Wimbledon. Queen's has had 11 distinct winners in this time, Newport 13, Wimbledon eight, and 's-Hertogenbosch 10. That's a total of 42. (Note that that doesn't actually mean 42 different winners spread across these events; Hewitt, e.g., has won Queen's, 's-Hertogenbosch, and Wimbledon at one time or another. What we are totalling is not actual distinct winners but distinct "winner-at-events.") That means that the typical long-lived grass event has had 10.5 distinct winners (42 divided by four is 10.5).

Computing this for all four surfaces gives us this:

Surface......Winners....Events....Winners/Event Clay...........170........16...........10.6 Grass...........42.........4...........10.5 Hard...........142........14...........10.1 Indoor..........92.........9...........10.2

Thus we see that we get just about the same winners-at-events numbers for all four surfaces. The gap between the highest figure (clay) and the lowest (hardcourt) is only five percent. The complete implications of this are not immediately obvious.

More interesting is if we sort the results by tournament tier: Optional, Masters, and Slam plus Masters Cup. Pursuing this calculation, we find:

Tier......Winners....Events....Winners/Event Optional.....333........29............11.5 Masters.......81.........8............10.1 Slams.........41.........5.............8.2

This time, we have a real and statistically significant gap. Remember that the maximum possible value for winners at an event is 14 -- and, at optional events, the average is 11.5. That makes repeaters few and far between. They're more common at the Masters, but only slightly so. But at that Slams, the average Slam winner has averaged almost two Slams during this period. Slam winners are much, much more likely to repeat. It may be true that, on the ATP, any player can beat anyone else on a given day. But if it's a Slam, some guys are a lot more likely to be the "any player" than others.

Clijsters Out of Olympics -- Maybe

This is a hard story to report, because it's "official" but hardly final. A statement on the web site of Kim Clijsters (which has supplied some surprisingly inflammatory statements in the past, supposedly inspired not by Kim Clijsters but by her father Leo) says that she won't be playing the Olympics because of a clothing dispute. There had been rumors of this before, but now it's supposedly True and Real and Official. Clijsters wears Fila apparel, and the Belgian Olympic Committee has agreed to have its team members wear Adidas apparel, and ne'er the twain shall be seen on the same body....

The problem is, while the Clijsters report says that the Belgian Olympic committee will not budge, other sources say that they are working desperately on a compromise, and that high Belgian officials have even become involved, and that the Clijsters camp is entirely unwilling to compromise. So there is a certain air of a negotiating ploy about the whole thing. Given that the Olympics are still more than half a year away, obviously this "final" word may not prove to be final.

Vector, Vector, Who's Got the Vector, Part II

Earlier, we looked at the year-end rankings for the men, and looked at their rankings "vectors" -- that is, not just the players' rankings, but whether they were rising or falling.

Obviously, being equal-opportunity number fanatics, we need to do the women also.

You'll be happy to know that we have no intention of going over all the math again. We're going to use essentially the same formula: Average of the rate of change since January 1, May 1, September 1, divided by the player's current ranking. We do have to make a few small changes, though, due to the way our databases are organized. (Yes, we keep completely different databases of men's and women's rankings. This is inherent in the way the men and women do things: The women actually publish full rankings data -- points added, next off, etc. The men just publish Entry totals.) What we did was take all women who were Top 100 on any of the four dates (January 1, May 1, September 1, year-end), except that we eliminated three players who were still ranked on January 1 but retired: Martina Hingis (#10 on January 1, retired but allowed to fall off the rankings), Arantxa Sanchez-Vicario (#53 on January 1, and removed from the rankings shortly after), and Sandrine Testud (#38 on January 1, and like Hingis allowed to fall off the rankings). We also used a slightly different approximating method: Instead of saying players ranked below #200 were ranked at #200, we've assumed that players ranked below #150 were ranked #175. It makes very little difference in the results, and it saved a lot of work.

As a result, we have 130 players to examine, with the most dramatic change being suffered by Anne Kremer, who was out most of the year with a wrist injury. She started the year ranked #25, but played only three events, and won only one match, and ended the year at #389. Ironically, that doesn't make her the player with the worst downward vector -- though only because of the "clamping" at 175 described above; she fell fast early in the year, and then, due to the clamping, slowed down.

In the table below, we show year-end rankings as they actually are, but keep in mind that we actually used the value "175" for Kremer, Svensson, Muller, Kournikova, Arn, Roesch, Diaz-Oliva, Kulikovskaya (whose ranking, incidentally, is in error; note that she was shown on the November 11 ranking list with 190.45 points, which of course is impossible), Taylor, Bedanova, Wartusch, and Neffa-de los Rios.

Rank.Name...............Jan1.May1.Sep1..End..Vector ..1..Henin-hardenne, Ju....5....4....3....1....3.00 ..2..Clijsters, Kim........4....2....1....2....0.17 ..3..Williams, Serena......1....1....2....3...-0.56 ..4..Mauresmo, Amelie......6....7....6....4....0.58 ..5..Davenport, Lindsay...12....5....4....5....0.40 ..6..Capriati, Jennifer....3....6....7....6...-0.11 ..7..Myskina, Anastasia...11...11...10....7....0.52 ..8..Dementieva, Elena....19...13...11....8....0.79 ..9..Rubin, Chanda........13....8....8....9....0.07 .10..Sugiyama, Ai.........24...17...15...10....0.87 .11..Williams, Venus.......2....3....5...11...-0.70 .12..Petrova, Nadia......112...95...19...12....5.28 .13..Zvonareva, Vera......45...28...14...13....1.23 .14..Suarez, Paola........27...29...25...14....0.93 .15..Dokic, Jelena.........9...10...23...15...-0.07 .16..Smashnova-Pistoles...16...21...17...16....0.13 .17..Shaughnessy, Megha...30...19...21...17....0.37 .18..Martinez, Conchita...34...25...13...18....0.33 .19..Hantuchova, Daniel....8....9....9...19...-0.54 .20..Schiavone, Frances...41...34...32...20....0.78 .21..Bovina, Elena........26...16...18...21...-0.05 .22..Serna, Magui.........50...40...27...22....0.77 .23..Schnyder, Patty......15...20...22...23...-0.17 .24..Farina Elia, Silvi...17...24...20...24...-0.15 .25..Coetzer, Amanda......21...18...16...25...-0.27 .26..Daniilidou, Eleni....22...15...26...26...-0.19 .27..Krasnoroutskaya, L..175...54...28...27....2.17 .28..Raymond, Lisa........29...22...30...28...-0.04 .29..Dechy, Nathalie......20...23...24...29...-0.23 .30..Maleeva, Magdalena...14...14...12...30...-0.56 .31..Pisnik, Tina.........47...60...50...31....0.69 .32..Sharapova, Maria....175..175...54...32....3.21 .33..Pierce, Mary.........52...42...64...33....0.60 .34..Tanasugarn, Tamari...28...32...39...34...-0.03 .35..Molik, Alicia........94...47...44...35....0.76 .36..Kuznetsova, Svetla...43...36...29...36....0.00 .37..Likhovtseva, Elena...42...30...36...37...-0.03 .38..Zuluaga, Fabiola.....75...69...37...38....0.59 .39..Srebotnik, Katarin...36...37...34...39...-0.09 .40..Mandula, Petra.......90...72...45...40....0.73 .41..Loit, Emilie.........58...53...49...41....0.30 .42..Sanchez Lorenzo, M..111...87...53...42....0.99 .43..Chladkova, Denisa....63...39...41...43....0.11 .44..Vento-Kabchi, Mari..175..139...84...44....2.02 .45..Asagoe, Shinobu......96...83...55...45....0.73 .46..Granville, Laura.....49...33...47...46...-0.07 .47..Weingartner, Marle...97...79...60...47....0.67 .48..Barna, Anca..........62...57...65...48....0.28 .49..Obata, Saori........126..104...75...49....1.07 .50..Tulyaganova, Iroda...55...41...43...50...-0.07 .51..Harkleroad, Ashley..113...56...52...51....0.44 .52..Black, Cara..........56...68...40...52....0.05 .53..Pratt, Nicole........48...45...57...53...-0.06 .54..Safina, Dinara.......68...70...71...54....0.29 .55..Ruano Pascual, Vir...65...38...62...55....0.00 .56..Gagliardi, Emmanue...61...81...61...56....0.21 .57..Bartoli, Marion.....104...62...46...57....0.24 .58..Matevzic, Maja.......51...50...38...58....-0.2 .59..Sprem, Karolina.....175..175...66...59....1.35 .60..Seles, Monica.........7...12...31...60...-0.72 .61..Frazier, Amy.........39...43...42...61...-0.32 .62..Koukalova, Klara....117...73...63...62....0.36 .63..Morigami, Akiko.....143...93...76...63....0.65 .64..Cervanova, Ludmila..103...85...73...64....0.36 .65..Cohen-Aloro, Steph..175...91...67...65....0.71 .66..Mikaelian, Marie-G...44...35...35...66...-0.42 .67..Kostanic, Jelena.....70..106...82...67....0.28 .68..Parra, Arantxa......175..175...89...68....1.15 .69..Pennetta, Flavia.....95...64...58...69....0.05 .70..Grande, Rita.........46...48...59...70...-0.27 .71..Medina Garrigues, ..116..175..101...71....0.84 .72..Razzano, Virginie....76...55...56...72...-0.13 .73..Vakulenko, Julia....132..122...94...73....0.59 .74..Callens, Els.........67...66...80...74...-0.04 .75..Reeves, Samantha....108..123...85...75....0.40 .76..Sequera, Milagros...115..120..117...76....0.54 .77..Cho, Yoon Jeong......83...46...51...77...-0.22 .78..Brandi, Kristina....175..175..112...78....0.97 .79..Schett, Barbara......40...51...69...79...-0.32 .80..Perebiynis, Tatian..119..124...83...80....0.36 .81..Schaul, Claudine....133..117..100...81....0.44 .82..Stevenson, Alexand...18...26...33...82...-0.69 .83..Czink, Melinda......175..175...93...83....0.78 .84..Garbin, Tathiana.....71...86..110...84....0.06 .85..Jankovic, Jelena....175..132..135...85....0.73 .86..Kurhajcova, Lubomi..110..112..104...86....0.26 .87..Ondraskova, Zuzana..129..109...99...87....0.29 .88..Kleinova, Sandra....137..135..109...88....0.44 .89..Sucha, Martina.......64..121..121...89....0.15 .90..Fernandez, Clarisa...31...27...77...90...-0.50 .91..Nagyova, Henrieta....59...59..118...91...-0.14 .92..Kapros, Aniko.......107..119..129...92....0.29 .93..Talaja, Silvija......74...96...70...93...-0.14 .94..Zheng, Jie..........175..150..134...94....0.63 .95..Widjaja, Angelique...72...63...68...95...-0.29 .96..Leon Garcia, Gala...130..137...97...96....0.26 .97..Jidkova, Alina.......85..101..107...97....0.01 .98..Craybas, Jill........57...65...74...98...-0.33 .99..Camerin, Maria Ele..123..111...92...99....0.10 100..Foretz, Stephanie....80...99...79..100...-0.14 101..Randriantefy, Dall...93...84...81..101...-0.15 102..Casanova, Myriam.....54...49...72..102...-0.43 103..Cargill, Ansley.....122...94...90..103...-0.01 104..Serra Zanetti, Adr...60..143..111..104....0.01 105..Martinez Granados,...98...88..102..105...-0.09 106..Torrens Valero, Cr...79...75..105..106...-0.19 107..Serra Zanetti, Ant...92...80...87..107...-0.19 109..Marrero, Marta.......87...77..103..109...-0.18 112..Drake, Maureen.......99..110..120..112...-0.02 118..Rittner, Barbara.....66...89...96..118...-0.29 119..Panova, Tatiana......23...31...48..119...-0.71 121..Poutchek, Tatiana...100..107..128..121...-0.08 123..Irvin, Marissa.......77...98..108..123...-0.23 125..Husarova, Janette....33...61...78..125...-0.54 128..Fislova, Eva........145..131...98..128...-0.03 131..Majoli, Iva..........32...52...91..131...-0.55 140..Benesova, Iveta......82...71...86..140...-0.43 145..Tu, Meilen...........73..105..175..145...-0.19 151..Neffa-de Los Rios,...88..100..127..151...-0.30 154..Wartusch, Patricia...84...76..175..154...-0.27 156..Bedanova, Daja.......37...44...88..156...-0.64 159..Taylor, Sarah........86...74...95..159...-0.47 164..Kulikovskaya, Evge..102...97..131..164...-0.33 188..Diaz-Oliva, Marian...89...90..175..188...-0.33 210..Roesch, Angelika.....81...82..148..210...-0.41 299..Arn, Greta...........91..175..175..299...-0.16 305..Kournikova, Anna.....35...67..146..305...-0.53 327..Muller, Martina......69..114..175..327...-0.32 364..Svensson, Asa........78...92..175..364...-0.34 389..Kremer, Anne.........25...58..175..389...-0.51

If we look at the ten players with the best upward motion, it is probably no surprise to find Nadia Petrova at the top of the list (though she hasn't risen quite as fast as Andy Roddick on the men's side), with Maria Sharapova a distant second and barely ahead of Justine Henin-Hardenne.

Rank.Name...............Jan1.May1.Sep1..End..Vector .12..Petrova, Nadia......112...95...19...12....5.28 .32..Sharapova, Maria....175..175...54...32....3.21 ..1..Henin-Hardenne, Ju....5....4....3....1....3.00 .27..Krasnoroutskaya, L..175...54...28...27....2.17 .44..Vento-Kabchi, Mari..175..139...84...44....2.02 .59..Sprem, Karolina.....175..175...66...59....1.35 .13..Zvonareva, Vera......45...28...14...13....1.23 .68..Parra, Arantxa......175..175...89...68....1.15 .49..Obata, Saori........126..104...75...49....1.07 .42..Sanchez Lorenzo, M..111...87...53...42....0.99

Looking at the ten biggest losers, it shows us something of how bad the injuries have been this year that long-injured Anne Kremer and Anna Kournikova don't even make the list (Kournikova is eleventh-worst and Kremer twelfth, though again, both saw their falls limited by clamping). Of the ten, Monica Seles, Tatiana Panova, Venus Williams, and Serena Williams were all injured for much of the year -- in the case of Panova, she went out before Roland Garros and never came back; Seles didn't play after Roland Garros; the Sisters didn't play after Wimbledon. The worst of it is, they were all hurt in the second half of the year, meaning that, even if they come back healthy, they may well continue to fall before they start to rise. Janette Husarova played most of the year, but wasn't healthy; Stevenson wasn't right during the indoor season, which represented most of her points. People spent all year worrying about Hantuchova, though she didn't miss any time. Bedanova and Majoli didn't play after the U. S. Open, though they had ruined their years long before that. That means that Magdalena Maleeva was our only 100%-fit Top Ten loser -- and she managed a title this year and posted her best doubles results ever, so her year wasn't all loss....

Rank.Name...............Jan1.May1.Sep1..End..Vector 125..Husarova, Janette....33...61...78..125...-0.54 .19..Hantuchova, Daniel....8....9....9...19...-0.54 131..Majoli, Iva..........32...52...91..131...-0.55 .30..Maleeva, Magdalena...14...14...12...30...-0.56 ..3..Williams, Serena......1....1....2....3...-0.56 156..Bedanova, Daja.......37...44...88..156...-0.64 .82..Stevenson, Alexand...18...26...33...82...-0.69 .11..Williams, Venus.......2....3....5...11...-0.70 119..Panova, Tatiana......23...31...48..119...-0.71 .60..Seles, Monica.........7...12...31...60...-0.72

Davis Cup: Check the Rules

It's an interesting speculation: If the host Davis Cup team wants to play on, say, wet cement, should it be allowed? To put it another way, at what point is a weird surface too weird?

We certainly wouldn't put grass in the "too weird" category (though the Spaniards might). On the other hand, the Davis Cup final wasn't really played on a grass court. It was played on a sod court (temporary grass, not laid on dirt), and that's not really the same thing. Grass is renowned for its off bounces, but this had seams to give the ball just that little extra dose of goofiness.

And the Spaniards were none too happy anyway after the Australians opened things up by playing the wrong Spanish National Anthem.

Juan Carlos Ferrero came surprisingly close to earning revenge for all that. Twice he was up a set on Lleyton Hewitt. Unfortunately, he was up after the first and third sets, not, say, the fourth or the fifth. Hewitt made his pro comeback, and put Australia in the lead, 3-6 6-3 3-6 7-6 6-2.

At that moment, it looked as if the tie might be settled on Saturday. Carlos Moya wasn't too happy with that prospect; flying halfway around the world to go home empty was an uninviting prospect. Plus opponent Mark Philippoussis didn't seem right when things started. His serve wasn't quite its usual self, and though he blamed it on nerves, it's worth noting that he had real problems with his shoulder in his second match. Moya, meanwhile, was serving well and getting in a surprising number of returns against Philippoussis. It wasn't until the third set that the Australian finally started getting some bombs in, and he managed to win the set -- but Moya came back hard in the fourth, and levelled the tie at 1-1 with a 6-4 6-4 4-6 7-6 win.

Saturday started out better for Spain: They played the right national anthem. But that was all that went right. Doubles was Spain's weakest point anyway, and Australia is one of the best nations in the world in that department. And Alex Corretja, the guy Spain usually relies upon in doubles, has been in terrible form this year, and while he'd recovered a bit at the end of 2003, he came into the doubles with a bum shoulder. And he'd played only one previous doubles match with partner Feliciano Lopez (none of the Spaniards plays doubles much; not a huge surprise given that clay is their native surface, which hardly encourages net play). It was Lopez who was playing his first Davis Cup match, but it was Corretja who suffered the first break in each of the first two sets (game four and game three, respectively). Wayne Arthurs and Todd Woodbridge did their duty 6-3 6-1 6-3, and Australia was one win away.

They didn't even need to play Sunday's second match to get it. Philippoussis, who faced Ferrero, definitely had shoulder problems this time, but the crowd urged him on, and he held together through a three-hour clincher 7-5 6-3 1-6 2-6 6-0 despite having the shoulder worked on in the final set. He said afterward that his shoulder felt numb, and he couldn't have gone on except for the fans. Fortunately, he has more than a month to recover.

With Australia having clinched Davis Cup title #28, they didn't even play the final singles match. No doubt the Spanish wanted out of there as soon as possible.

Vector, Vector, Who's Got the Vector

Being a journalist -- even a tennis journalist -- has its complications. When you get reader feedback, it's almost always negative ("so-and-so has a fine backhand, you !!!!"). So it's hard to know what people like.

But we did get one positive comment about our mention, some weeks ago, of rankings vectors -- that is, a ranking that tells you whether a player is on the rise or falling. An ordinary ranking is a scalar -- it measures what you've done over the last twelve months, and who cares if it all happened in the last month or ten months ago? A rankings vector tells you where you are and which direction you're going: "#30 and rising slowly." "#12 and staying steady." "#70 and falling fast."

But while such assessments are easy to make in rough outline (a player like Nadia Petrova is clearly rising; a player like Marat Safin obviously falling), a proper calculation is much more complicated. Let's take a specific case to show what we mean. Specifically, let's look at Rafael Nadal. And let's examine four data points: January 1, May 1, September 1, and year-end. His rankings at those times:

January 1: #235
May 1: #93
September 1: #45
Year-end (November 17): #47

We can graph this, to make things clearer; the big + signs represent Nadal's rankings on the four dates listed.:

300 -   -   -   - |   :   :   : | |   :   :   : 250 +   -   -   -   +++ :   :   : + |   :   :   : 200 -   -   -   - |   :   :   : | |   :   :   : 150 -   -   -   - |   :   :   : | |   +   :   : 100 -   - +++ -   :   -   : |   +   :   : | |   :   +   + 50 -   -   - +++ - +++ |   :   +   + | |   :   :   : 0 +--|--|--|--|--|--|--|--|--|--|--|--|--|   JAN   MAR   MAY   JUL   SEP   NOV

Obviously Nadal has improved fast. Obviously he is levelling off. So what exactly do we make of all this? Is his vector "up," based on his whole year, or "level," based on his last few months?

There is no actual answer; each answer is valid depending on how you define things. We have to define a model. There are many, many choices. And while you probably just want us to pick one, at least some explanation is probably required so you know what you're getting. You can skip this section and skip ahead to the section labelled The Results -- we are, perforce, going to talk math a little -- but ideally you should read it so you'll know what we're handing you. We'll try to make this as painless as possible.

It's important to understand that any method to assess ranking movement, like the rankings themselves, is based on the past. What we are doing is not predicting the future. The rankings don't predict the future. They describe what the player has already done. Ranking vectors describe the past, too, but in more detail: Not just how a player has done, but how he's been moving in the rankings. And, since there are many ways to do this (all equally valid, or equally invalid), we need to describe how.

To illustrate why we can't predict the future: if we just took the above information, and took the slope of Nadal's numbers from the start to the end of year one, we show that he started at #235 and ended at #47. In other words, he gained 188 spots during the year. Add on another year at that rate, and he'd end 2004 at -- negative #141.

Oops.

Clearly we can't just take starting and ending rankings and calculate from there. We want to say which players are on their way up, which are heading down, which are staying level. But players do even that in different ways. Some climb steadily. Some rise or fall in spurts. Nadal's curve looks, based on the above, like an exponential decay, settling down somewhere around #40. But it might be a parabola (heading back out to infinity), or he might just have hit a temporary rough patch. We don't know the answer, and even if we did, a model that fits Nadal probably wouldn't fit Andy Roddick's steady rise, and Alex Corretja's sudden fall and recent recovery, and everything else the players do.

Another approach we must reject is the usual one for "fitting" four points: a cubic equation, that is, an equation of the form

  3 2 f(x) = ax + bx + cx + d.

This is even worse at predicting than the last one. If we arbitrarily set January 1, 2003 as date "0," make May 1 equal "1", September 1 be date "2," and the year-end be date "3," and apply all this to Nadal, then this gives us four equations, corresponding to x=0, 1, 2, and 3:

235 = d
93 = a + b + c + d
45 = 8a + 4b + 2c + d
47 = 27a + 9b + 3c + d

Which gives us values of a=-7.33333, b=69, c=-203.6666667. By which numbers, Nadal would be at #55 next May 1, at #25 next September 1 -- and at #-87 at the end of next year. Two years from now, he would have a negative ranking of #-1355! Cubic equations simply go out of control too fast. They are excellent for approximating within the period specified (e.g. the above formula says Nadal "should" have been #59 after Wimbledon, and he was in fact #61), but beyond the range is no good.

So we aren't even going to try to predict mathematically. Any method we use will fit some players and not others. We're going to do something very simple instead. We're going to take just the four points specified -- January 1, May 1, September 1, year-end. We're going to calculate three slopes: January 1 to year-end, May 1 to year-end, and September 1 to year-end. And then we're going to average those three numbers. This means that recent results have more weight, but not overwhelming weight. We then divide by the final ranking to normalize the results.

To put this in symbols, if J is the January rankings, M the May ranking, S the September ranking, and Y the year-end ranking, then our vector V is defined by

(J-Y)+(M-Y)+(S-Y)   (J+M+S-3Y) V = ----------------- = ---------- 3Y 3Y

Taking Nadal as an example, his one-year slope is 235-47 = 188. His eight-month slope is 93-47 = 46. But his four-month slope is 45-47 = -2. In other words, his ranking rose quickly over the year, less quickly over eight months, and actually fell over the last part of the year. Adding all these up, we get an average of 232/3 = 77.3 That means he's going up, and fairly quickly.

But we have to measure that against where he started. If you're #2, and gain one spot, it's huge. If you're #99, and gain one spot, it's just noise. What matters is how much you move with respect to your ranking. Hence we divide by the player's final ranking. In Nadal's case, e.g., that means we divide 77.3 by his current #47 ranking. That gives us a ratio of 1.65. And that is our "vector." Nadal's ranking is #47. His direction is upward at a rate of 1.65. That's a dimensionless number; it's not 1.65 "per month" or some such thing. It's just 1.65, relative to the values posted by other players.

The Results

The results of the above calculations are, obviously, positive or negative numbers, with positive numbers being good (a player who is rising); the higher this number, the better a player is doing. A number larger than one (for that matter, a number larger than about .4) means a fast-rising player. Negative numbers indicate players who are, on the whole, falling; a number smaller than -0.4 means a guy who is in a fair bit of trouble.

To keep this list within some sort of bounds, we will look only at players who either ended up in the Top 100 at year-end or were in the Top 80 at some time this year, and who were actually active during the year (that still leaves us with 119 players). We're also going to "clamp" the rankings: Any player ranked below #200 in a given ranking period will have his ranking treated as #200.

That gives us this list, in ranking order. Remember, positive numbers in the "Vector" column are good, negative bad, and the larger the positive number, the better.

Note how many of the final Top Ten have positive numbers, and large ones.

Rank.Name...............Jan1.May1.Sep1..End..Vector ..1..Roddick, Andy........10....6....4....1....5.67 ..2..Federer, Roger........6....5....2....2....1.17 ..3..Ferrero, Juan Carl....4....3....3....3....0.11 ..4..Agassi, Andre.........2....1....1....4...-0.67 ..5..Coria, Guillermo.....45...16....5....5....3.40 ..6..Schuettler, Rainer...33...13....8....6....2.00 ..7..Moya, Carlos..........5....4....7....7...-0.24 ..8..Nalbandian, David....12...12...13....8....0.54 ..9..Philippoussis, Mar...80...62...20....9....5.00 .10..Grosjean, Sebastie...17...14....9...10....0.33 .11..Srichaphan, Parado...16...10...11...11....0.12 .12..Massu, Nicolas.......56...89...42...12....4.19 .13..Novak, Jiri...........7....9...10...13...-0.33 .14..El Aynaoui, Younes...22...17...21...14....0.43 .15..Henman, Tim...........8...31...33...15....0.60 .16..Kuerten, Gustavo.....37...15...14...16....0.38 .17..Hewitt, Lleyton.......1....2....6...17...-0.82 .18..Schalken, Sjeng......20...11...12...18...-0.20 .19..Verkerk, Martin......86...68...16...19....1.98 .20..Fish, Mardy..........84...53...26...20....1.72 .21..Robredo, Tommy.......30...20...17...21....0.06 .22..Mantilla, Felix......55...47...22...22....0.88 .23..Mirnyi, Max..........43...33...18...23....0.36 .24..Calleri, Agustin.....50...28...19...24....0.35 .25..Costa, Albert.........9....8...24...25...-0.45 .26..Ferreira, Wayne......39...27...23...26....0.14 .27..Zabaleta, Mariano....53...36...27...27....0.43 .28..Lopez, Feliciano.....62...56...29...28....0.75 .29..Spadea,Vincent.......67...32...31...29....0.49 .30..Ginepri, Robby......100...49...40...30....1.10 .31..Bjorkman, Jonas......48...71...44...31....0.75 .32..Clement, Arnaud......38...37...32...32....0.11 .33..Dent, Taylor.........57...39...73...33....0.71 .34..Gaudio, Gaston.......21...29...30...34...-0.22 .35..Gonzalez, Fernando...18...21...15...35...-0.49 .36..Nieminen, Jarkko.....40...35...39...36....0.06 .37..Blake, James.........28...23...35...37...-0.23 .38..Chela, Juan Ignaci...23...34...41...38...-0.14 .39..Sargsian, Sargis....103...75...52...39....0.97 .40..Kucera, Karol........83...50...37...40....0.42 .41..Kafelnikov, Yevgen...27...25...28...41...-0.35 .42..Ljubicic, Ivan.......49...46...43...42....0.10 .43..Youzhny, Mikhail.....32...30...36...43...-0.24 .44..Davydenko, Nikolay...81...41...38...44....0.21 .45..Saretta, Flavio......92...80...49...45....0.64 .46..Stepanek, Radek......63...51...46...46....0.16 .47..Nadal,Rafael........200...93...45...47....1.40 .48..Volandri,Filippo....154...92...47...48....1.03 .49..Rochus, Olivier......64...60...48...49....0.17 .50..Sanchez, David.......60...48...55...50....0.09 .51..Gambill, Jan-Micha...42...40...50...51...-0.14 .52..Arazi, Hicham........90...96...65...52....0.61 .53..Lee, Hyung-Taik......87...54...69...53....0.32 .54..Koubek, Stefan.......54...63...68...54....0.14 .55..Martin, Alberto......61...65...63...55....0.15 .56..Malisse, Xavier......25...26...67...56...-0.30 .57..Lapentti, Nicolas....29...42...57...57...-0.25 .58..Kiefer, Nicolas......72...73...62...58....0.19 .59..Soderling, Robin....176..158...99...59....1.45 .60..Sluiter,Raemon.......71...66...54...60....0.06 .61..Hrbaty, Dominik......51...58...53...61...-0.11 .62..Santoro, Fabrice.....35...52...58...62...-0.22 .63..Carraz,Gregory......138..130..100...63....0.95 .64..Ancic, Mario.........89...77...74...64....0.25 .65..Beck, Karol.........125...74...71...65....0.38 .66..Vicente, Fernando....58...57...61...66...-0.11 .67..Horna, Luis..........85...78...76...67....0.19 .68..Sanguinetti, David...46...84...86...68....0.06 .69..Martin, Todd.........47...95...93...69....0.14 .70..Hanescu,Victor......170..147...84...70....0.91 .71..Ferrer, David........59...59...59...71...-0.17 .72..Pavel, Andrei........26...38..103...72...-0.23 .73..Labadze, Irakli......93..104..105...73....0.38 .74..Karlovic, Ivo.......175..200..109...74....1.18 .75..van Lottum,John.....115..102...83...75....0.33 .76..Burgsmuller, Lars....76..100...85...76....0.14 .77..Safin, Marat..........3....7...25...77...-0.85 .78..Dupuis, Anthony......70...86...64...78...-0.06 .79..Melzer, Jurgen.......91...88...81...79....0.10 .80..Ramirez Hidalgo,Ru..145..146...70...80....0.50 .81..Montanes, Albert.....78...91...87...81....0.05 .82..Moodie,Wesley.......200..153...95...82....0.82 .83..Mathieu, Paul-Henr...36...44...56...83...-0.45 .84..Vahaly, Brian.......102...72...78...84....0.00 .85..Rochus,Christophe...146..134...89...85....0.45 .86..Portas, Albert.......88...85...88...86....0.01 .87..Saulnier, Cyril.....161..124..101...87....0.48 .88..Behrend, Tomas......142..101...79...88....0.22 .89..Ascione,Thierry.....200..200..116...89....0.93 .90..Andreev,Igor........200..200..122...90....0.93 .91..Hernandez,Oscar.....200..195..113...91....0.86 .92..Popp,Alexander......117..163..107...92....0.40 .93..Gasquet,Richard.....166..114..124...93....0.45 .94..Mahut,Nicolas.......200..200..114...94....0.82 .95..Enqvist, Thomas......44...90..143...95...-0.03 .96..Lisnard,Jean-Rene...104...99...94...96....0.03 .97..Bogomolov Jr., Ale..198..122..117...97....0.50 .98..Tursonov,Dmitry.....200..200..174...98....0.95 .99..Blanco,Galo.........133..126..110...99....0.24 100..Corretja, Alex.......19...18..102..100...-0.54 101..Acasuso, Jose........41...45...75..101...-0.47 104..Mutis, Olivier.......94...79...80..104...-0.19 105..Rios, Marcelo........24...43...51..105...-0.63 108..Boutter, Julien......77...69...96..108...-0.25 112..Escude, Nicolas......34...61...60..112...-0.54 114..Carlsen, Kenneth.....65...67...72..114...-0.40 116..Arthurs, Wayne.......52...55..118..116...-0.35 118..Rusedski, Greg.......31...70...90..118...-0.46 119..Vinciguerra, Andre..181..109...92..119....0.07 120..Squillari, Franco....79...94...97..120...-0.25 123..Norman, Magnus......107...82...77..123...-0.28 127..Voltchkov, Vladimi...73...64...66..127...-0.47 129..Kratochvil, Michel...69...81..150..129...-0.22 154..Voinea, Adrian.......68...87..135..154...-0.37 210..Sa, Andre............66...83..155..200...-0.49 213..Meligeni, Fernando...74..107..153..200...-0.44 262..Ulihrach, Bohdan.....75..108..188..200...-0.38 274..Canas, Guillermo.....15...22..200..200...-0.60 434..Pless, Kristian......82..105..133..200...-0.47

Searching the list for our ten biggest upward movers (or, correctly, our ten players with the largest upward vectors; they are not our biggest movers in terms of places gained), they are:

Rank.Name...............Jan1.May1.Sep1..End..Vector ..1..Roddick, Andy........10....6....4....1....5.67 ..9..Philippoussis, Mar...80...62...20....9....5.00 .12..Massu, Nicolas.......56...89...42...12....4.19 ..5..Coria, Guillermo.....45...16....5....5....3.40 ..6..Schuettler, Rainer...33...13....8....6....2.00 .19..Verkerk, Martin......86...68...16...19....1.98 .20..Fish, Mardy..........84...53...26...20....1.72 .59..Soderling, Robin....176..158...99...59....1.45 .47..Nadal,Rafael........200...93...45...47....1.40 .74..Karlovic, Ivo.......175..200..109...74....1.18

Obviously Roddick can't move above #1, but he can strengthen his position -- and, indeed, that seems fairly likely, given how little he has to defend between the Australian Open and Paris. A lot of those other guys, like Schuettler and Philippoussis, are probably at the ends of their runs also. But Soderling and Nadal and perhaps even Fish still have some room to rise, and Karlovic, who finally will get to play regularly on the ATP, has a big opportunity.

Our ten biggest ground-losers are:

Rank.Name...............Jan1.May1.Sep1..End..Vector 127..Voltchkov, Vladimi...73...64...66..127...-0.47 101..Acasuso, Jose........41...45...75..101...-0.47 .35..Gonzalez, Fernando...18...21...15...35...-0.49 210..Sa, Andre............66...83..155..200...-0.49 100..Corretja, Alex.......19...18..102..100...-0.54 112..Escude, Nicolas......34...61...60..112...-0.54 274..Canas, Guillermo.....15...22..200..200...-0.60 105..Rios, Marcelo........24...43...51..105...-0.63 ..4..Agassi, Andre.........2....1....1....4...-0.67 .17..Hewitt, Lleyton.......1....2....6...17...-0.82 .77..Safin, Marat..........3....7...25...77...-0.85

There are, of course, a lot of injuries in there -- Safin, Canas, Escude; we'd expect them to spring back. The others -- well, we'll just have to wait and see.

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