Predicting outcomes at Slams is a game for the adventurous. No individual can observe more than a fraction of a tournament's action. Not even tennis insiders can foresee the random uncertainties that give all sport a critical dimension. Here, our analysis and predictions for U.S. Open 2013 rely heavily on several numerical indicators, developed largely empirically from the recent historical record. Still, we reserve a final role for subjective judgment, i.e., guesswork.
 
THE PRELIMINARIES -- CANADA AND CINCINNATI
 
Members of the long-time Big Four in men's tennis captured the first three Slams of 2013 -- Novak Djokovic won in Melbourne, Rafael Nadal won in Paris, Andy Murray in London. Meanwhile the leader of the Four for many years, Roger Federer, at age 32 slipped behind as his official ranking drifted downward.
 
Tops in the official men's rankings through all of 2013 to date has been Djokovic. But it was Andy Murray who, by winning Wimbledon 2013, became our unofficial immediate king-of-the-hill, our Il Primo of men's pro tennis, replacing the Garros winner, Nadal. Murray, however, lost his second match at the August tournament in Montreal, victim of the talented Ernests Gulbis.
 
The Canadian event nevertheless produced a superb semi-final, pitting Novak Djokovic and Rafael Nadal, both of them healthy and strong in unleashing their magnificent weaponry. The quality and ferocity of their three-setter, played on a cool Saturday evening, almost defies description. Nadal was generally the heavier and more aggressive striker, determined to force himself on his opponent without letup. Rafa won the first set upon Novak's slower start, lost the second set closely, then prevailed at the finish in a third-set tiebreaker. Rafa's triumph led to an easy win in the next-day's final, Rafa managing to return Raonic's potent serves and otherwise dominating.
 
The cast then moved to Cincinnati for the next week's action. All members of the Big Four reached the round of eight. But on a bewildering quarter-final Friday, first Murray lost to Berdych, and then Djokovic lost to John Isner. The latter affair produced an unusual ending after Isner had used his dominating serve and forceful forehand to keep the score close. But in the final moments, Djokovic displayed an uncharacteristic breakdown of confidence, plunking several shot attempts, none of them forceful, miserably into net or out of court.
 
Nadal and Federer met each other that same evening, where the winner would be the only Big Four member to reach the semis. Roger played aggressively, trying to dominate in points and avoiding Nadal's wonderful attacking forehand. The first set was Roger's, who showed some of the spectacular tactics and execution often produced by Roger in decisive moments during his glory years. After the first set, however, Roger's brilliance appeared only sporadically, and Rafa's heavy back-court striking, backed by Rafa's wonderful court coverage, turned matters on the scoreboard.
 
John Isner produced another stunning victory in the semis, taking advantage of del Potro's fade when the tall Argentine needed only to hold serve to collect the victory. Having avoided defeat, John thereafter perplexed the favorite with some remarkable defenses, occasional offensive thrusts including net sallies, along with his best serving of the day. It was a sharp loss for del Potro.
 
Isner applied the same medicine in his final-round meeting with Nadal. It made trouble for Rafa, but not enough to stop Rafa from prevailing in two tiebreak sets.
 
For several years there has been a distinctive Second Four, bringing speculation as to which member would be the one eventually to penetrate the Big Four. David Ferrer had done so temporarily during Rafa's absence from play and now again entered that select group amid Federer's recent quiescence. At age 31 and height only 5-9, David was widely admired for his determination and wonderful all-court game. But by winning Citi Open in Washington, D.C. and in strong showings in Canada and Cincinnati, all on hard courts, it was Juan Martin del Potro who seemed an even stronger candidate ultimately to claim the vacancy. As to the remaining Second Four members, Tomas Berdych seems co-equal with del Potro in power and movement on hard courts, while Jo-Wilfried Tsonga is currently sidelined with knee problems.
 
U.S. OPEN INDICATORS -- MEN'S SINGLES
 
The scores of the top sixteen players within each indicator are normalized to reach a total of 100.
 
Basic Indicator
 
Here, we tally player results from the past 15 months, weighted according to how well each event has predicted results at past U.S. Opens. Here are the leaders:
 
1. Djokovic, 21.3
2. Murray, 17.6
3. Nadal, 13.9
4. Federer, 8.8
 
Quality-Win Quotient, QWQ
 
1. Nadal, 66.7
2. Djokovic, 13.3
3. Murray, 8.3
4. del Potro, 2.9
 
Nadal's large lead in QWQ reflects his four wins over other Big Four members in 2013, the same number as Djokovic, Murray, and Federer combined. He also leads firmly in his ten wins over members of the Second Four plus seven against members of the Next Eight. His high margin in our calculation also results from his low number of total losses to all opponents during the period -- i.e., only three, fewer than half as many as the next-best among the contenders, Murray, whose losses total seven.
 
Tomas Berdych, who is fifth in this calculation, equals Nadal in his four wins against Big Four members but is far behind in other quality wins and has many more total losses.
 
Hard-Court Index, HCX
 
1. Djokovic, 16.7
2. Nadal, 14.4
3. Murray, 13.9
4. Federer, 10.3
 
The above scores combine two separate calculations:
 
(1). Career won/lost percentage in hard-court matches, weighted slightly for recency and in favor of Slams. Federer leads, showing an 83.7% winning record. Djokovic is a close second, at 82.8%. Murray is third, at 79.1%.
 
(2). Ranking points earned on hard courts in 2013. Djokovic leads here, reflecting his 2000-point victory at the hard-court Slam in Australia. Nadal won Indian Wells, Canada, and Cincinnati, all 1,000-pointers, his only hard-court events of the year. Murray was second at Melbourne and he won the hard-court 1,000-pointer in Miami.
 
Composite of Indicators
 
Djokovic thus leads in Basic Indicator and HCX and is second in QWQ. Nadal leads in QWQ, is second in HCX, and is third in Basic. It is, however, Nadal, not Djokovic, who leads in our Composite of Indicators, reflecting Rafa's strong margin in QWQ.
 
Here are the leaders in Composite, obtained by averaging the scores from the three prime indicators.
 
1. Nadal, 30.0
2. Djokovic, 17.1
3. Murray, 13.0
4. del Potro, 6.7
5. Federer, 6.6
6. Berdych, 5.3
 
David Ferrer is seventh in Composite, reflecting that clay, not hard, is David's best surface.
 
Our top six are clearly split at the middle, including a closely-grouped second threesome, seen above. All members are taller than six feet, and all are in prime-age range, 24-27, save Roger, at 32.
 
THE DRAW -- THE LUCKY AND THE UNLUCKY
 
The Open's seedings were reached from the official rankings as of August 19, which measured player performance over the preceding twelve months. Big Four members Djokovic, Nadal, and Murray were seeded in that order. Fourth-seeded was David Ferrer.
 
The tournament draw, August 22, affected the prospects of every player, but was especially interesting in selecting the lucky and unlucky among the tournament favorites:
 
(1). The draw bracketed Andy Murray, the strongest player outside the top two, to face Djokovic rather than Nadal in the prospective semis. Nadal thus became the lucky one, not having to face either Murray or Djokovic on his path to the final.
 
(2). Of the second four in the seedings (Berdych, del Potro, Federer, Gasquet), the lucky one drawing the least-dangerous higher-ranked opponent in the quarters, (i.e., Ferrer), was Richard Gasquet.
 
(3). Of those seeded #9-#16, unfortunate were those drawn to face one of the top-rated three in the fourth round; the unlucky ones were Fognini, Almagro, and Isner. Also ill-fortuned were Gasquet and Nadal -- the players among the top eight seeds drawn against Raonic and Isner, the most dangerous lower-ranked fourth-round opponents according to our Composite.
 
(4). Also unlucky was Stan Wawrinka -- the player among the top sixteen seeds drawn to face the most dangerous lower-ranked opponent (Kevin Anderson) in the third round.
 
(5). Perhaps unluckiest of all were those unseeded players drawn to face one of the Big Three in the first or second round.
 
The upper half of the draw appeared much the stronger, containing the #1, #3, #5, and #6 seeds (vs. #2, #4, #7, and #8 in the lower half).
 
THE PREDICTIONS
 
Top Quarter -- Djokovic, del Potro, Haas, and Fognini. Except that Tommy Haas could threaten a slightly injured del Potro, and also that Djokovic will early face Grigor Dimitrov, who beat Novak at Madrid this year, a showdown between Djokovic and del Potro seems inevitable. Djokovic won six of their last seven matches, including a five-setter at Wimbledon 2013, and has the strong edge in our indicators. In the quarters: Djokovic over del Potro.
 
Second Quarter -- Murray, Berdych, Wawrinka, Almagro. This too is a strong quarter, also including Kevin Anderson, but Murray and Berdych seem predestined for a quarter-final meeting. All our indicators favor Murray, but the head-to-head edge belongs to Tomas, who may be more inclined to be the aggressor. The verdict is unclear, and Murray's summer since Wimbledon has been less than glorious. But we'll stay with the indicators and the tournament's defending champ. Murray over Berdych.
 
Third Quarter -- Ferrer, Gasquet, Raonic, Janowicz. Our indicators slightly favor Raonic to defeat Gasquet in the fourth round, where Raonic was the winner in their only previous meeting, at Cincinnati 2012. Meanwhile Ferrer should defeat Janowicz, having done so in ending Jerzy's marvelous run at Paris Indoors 2012. Ferrer holds an even clearer head-to-edge over Raonic, and is moderately favored in our indicators. Ferrer over Raonic.
 
Bottom Quarter -- Nadal, Federer, Nishikori, Isner. Roger's power and aggressiveness should overcome Nishikori, and Rafa's ability to answer Isner's unusual tactics was shown in their recent Cincinnati final. Rafa also overcame a strong run by Federer in the Cincinnati semis. Best-of-five sets make Roger's chances yet weaker. Our indicators agree. Nadal over Federer.
 
Semi-final -- Djokovic vs. Murray. These two are close in age, talent, and determination, both already claimants to greatness. Djokovic is ahead in all three of our prime indicators though not overwhelmingly. He defeated Andy at Ausralian Open 2013 in four sets, but Andy won at Wimbledon in straights. Neither excelled at Cincinnati recently, but Djokovic was the more successful at Monreal one week earlier. Djokovic over Murray.
 
Semi-final -- Nadal vs. Ferrer. No match with Ferrer can be taken lightly, but Rafa leads powerfully in our indicators and has won their last nine head-to-head meetings, a majority in straight sets. His bigger game must prevail. Nadal over Ferrer.
 
Final -- Djokovic vs. Nadal. Novak Djokovic holds the edge in two of our indicators, Basic and HCX. Nadal's larger advantage in QWQ puts him ahead in Composite, but Rafa's QWQ margin is probably undercut by the direct head-to-head record. Nadal leads career-wise with 21 wins against Novak's 15. But Rafa was an early maturer, and the picture becomes indistinct in recent years. Starting in 2011, Djokovic has won five of their six meetings on nonclay courts, losing in three close sets at Montreal, described earlier here. Swayed by Rafa's likely easier road to the final, and envisioning a long and severely contested match, the choice is Nadal over Djokovic.
 
Recapping the predictions:
 
Champion: Nadal
Runner-up: Djokovic
3rd-4th places: Murray, Ferrer
5th-8th places: Berdych, del Potro, Raonic, Federer
Nation winning most matches: Spain.
 
Spain's males should collect the most match wins at the Open. Led by Nadal and five other seeded players in singles, and with Granollers and M. Lopez likely to do well in doubles, the Armada should return to first place at the Open after a two-year absence. U.S.A. should finish second behind the Bryans in their quest for the Calendar Year Grand Slam. France should earn third place.
 
THE WOMEN'S PRELIMINARIES
 
The dominance of Serena Williams in recent months had been nearly complete, marred by an unexpected loss to Sabine Lisicki at Wimbledon. Marion Bartoli won that treasured crown, but Marion, 28, later announced her retirement from the pro wars, citing accumulated wear and tear on her body.
 
Serena triumphed in Toronto without losing a set. The other Big Three members did not compete -- Sharapova out with injury, Azarenka withdrawing just prior to the start. Unseeded Sorana Cirstea, 23, advanced by defeating Kvitova and Li, but could not match Serena's big game in the final match.
 
In early-round action the next week in Cincinnati, Sloane Stephens, 20, unexpectedly defeated Maria Sharapova. Maria's stream of errors seemed attributable to rust, but more significant was the strong and steady play of Stephens following an inept first set. Once comfortable in the setting, Sloane showed good mobility along with smoothly generated -- i.e. "easy" -- power that was almost as potent as Maria's. Most impressive was the rising American's ability to outlast her opponent without error in heavy-duty, extended exchanges.
 
The Cincinnati final pitted Serena Williams and Victoria Azarenka, the tournament's top two seeds. It was an up-and-down affair for both players, Victoria starting horribly and then recovering, Serena's languid spells alternating with occasional ones of fire. Throughout, Serena was unable to exploit her usually-dominating first serve, seldom attaining higher velocities and producing few aces. Serena's interest in coming to forecourt was weaker than Victoria's, though Serena was almost always successful when she did so. Serena mounted a characteristic surge toward the finish but ultimately lost in a thrilling third-set tiebreaker, Serena's first serve having almost entirely vanished.
 
Serena had become our La Prima by winning in Toronto, but Victoria captured that honor in Cincinnati in regal fashion -- by defeating the incumbent in a head-to-head final-round meeting.
 
INDICATORS
 
Despite her loss in Cincinnati, Serena Williams leads strongly in our three prime indicators. (Maria Sharapova, having withdrawn from the Open with shoulder trouble, is included in the calculations but is omitted from the listings of rank shown below, where she would otherwise rank third in most cases.)
 
Basic Indicator
 
1. S. Williams, 27.0
2. Azarenka, 18.6
3. A. Radwanska, 9.5
4. Li Na, 6.7
 
QWQ
 
1. S. Williams, 50.1
2. Azarenka, 17.0
3. A. Radwanska, 8.1
4. Li Na, 4.7
 
HCX
 
1. S. Williams, 19.2
2. Azarenka, 13.7
3. A. Radwanska, 12.0
4. Li Na, 8.6
 
Composite
 
1. S. Williams, 32.1
2. Azarenka, 16.4
3. A. Radwanska, 9.9
4. Li Na, 6.7
5. Petra Kvitova, 3.5
 
Serena is first across the board here, her edge over Azarenka reduced moderately by the outcome in Cincinnati. The top four are the same in all three prime indicators.
 
THE DRAW
 
Upon Sharapova's withdrawal, the top-seeded four became Serena, Azarenka, Radwanska, and Errani. Errani seemed out of place, as she ranked only thirteenth in our Composite of Indictors.
 
(1). Of the top-seeded four, lucky was Azarenka, drawn to face Errani rather than Radwanska in the semis. Unlucky among the top group was Agnieszka Radwanska, whose likely quarter-final opponent would be Li, clearly the strongest of the second foursome.
 
(2). Of the next-seeded four (Li, Wozniacki, Kvitova, Kerber), Wozniacki seemed the luckiest, drawn against Errani in the quarter-final round. Li Na was also probably happy, drawing Radwanska instead of Serena or Azarenka.
 
(3). Of those seeded #9-#16, probably most unlucky were Sloane Stephens and Ana Ivanovic, drawn to face Serena and Azarenka, respectively, in the fourth round. Probably best positioned among this group was Maria Kirilenko, drawn to face Errani in that round.
 
PREDICTIONS
 
Top Quarter -- Serena Williams, Kerber, Flipkens, Stephens. Sloane Stephens's improbable win over Serena at Australian Open 2013 was followed by an abrupt loss to Azarenka in the next round. Sloane had good runs at Wimbledon and Garros, and defeated Sharapova at Cincinnati, described earlier. But a fourth-round victory by Sloane over Serena here defies nearly all other evidence. Serena, if she attacks with resolve, should comfortably defeat both Sloane and then Kerber, the narrow choice over Flipkens. In the Quarters: Serena over Kerber.
 
Second Quarter --Agnieszka Radwanska, Li Na, Jankovic, Lisicki. This is an interesting quarter, also including Makarova, Robson, and Cirstea. Seventh-seeded Jelena Jankovic had a fine run at Cincinnati, finally beaten by Azarenka in a split-set semi. Still, the power of Li Na should prevail in the fourth round, even as Agnieszka shows the strength of her all-court magic in stopping Lisicki. Following our indicators, Radwanska over Li.
 
Third Quarter -- Errani, Wozniacki, Vinci, Kirilenko. It has been a trying time for Caroline Wozniacki, struggling to develop a mature, more powerful game out of the skills that took her to the top of the rankings in 2010 and 2011. She neverthess holds a respectable Composite indicator in our scheme, outranking all of those in her quarter here. Vinci will be difficult in the fourth round, then most likely Errani in the quarters. A loss in two close sets to Azarenka at Cincinnati shows that Caroline is probably close. Wozniacki over Errani.
 
Fourth Quarter -- Azarenka, Kvitova, Stosur, Ivanovic. Her left-handed serving and stroking power give Petra Kvitova the ability to sweep any opponent for a set or perhaps more. But, supported by our indicators, Azarenka's abilities to blunt Petra's big game long enough to bring the errors seems clear. Azarenka over Kvitova.
 
Semi-final -- S. Williams vs. A. Radwanska. Serena defeated Agnieszka in straight sets at both Miami and Toronto this year, both on hard courts. Agnieszka should resist well and will probably show the fewer errors. Serena Williams over A. Radwanska.
 
Semi-final -- Azarenka over Wozniacki. Victoria won in two close sets in Cincinnati despite yielding seven double-faults. She holds the huge edge in our indicators. Azarenka should be able to dominate behind her stronger first serve. Azarenka over Wozniacki.
 
Final -- S. Williams vs. Azarenka. Serena holds a 12-3 career W-L edge over Victoria, and has dominated through most of her great run of 2012-2013. But Victoria won closely in Cincinnati and also in their other hard-court meeting of 2013, in Doha. Our indicators uniformly point to Serena, who has the power to establish dominance and the mobility to blunt Victoria's. Serena knows from Cincinnati that she must be bold in attacking. It could become a classic final. Serena over Azarenka.
 
Recapping the predictions:
 
Champion: S. Williams
Runner-up: Azarenka
3rd-4th places: A. Radwanska, Wozniacki
5th-8th places: Kerber, Li, Kvitova, Errani
Nation winning most matches: U.S.A.
 
Wide strength in the early rounds among the American women, along with a strong likely contribution from Serena Williams in singles and from several U.S. players in doubles and mixed, should lift the U.S. to first place in the tally of matches won at the Open. The usually strong contingent from Russia will be weakened by the absence of Sharapova. The German women should finish third and could surpass the Russkayas for second place. Czech Republic, third last year, should again perform well behind excellent strength in doubles and a late-round finish by Kvitova in singles.
 
THE ATTACKING GAME AT THE OPEN
 
We can expect that play at the Open will mirror the styles seen in the recent hard-court tournaments. Power serving and stroking will be the wide standard, where points become contests for dominance in search of striking positions closer to net than opponent's. Closer striking positions (1) improve angle opportunities, (2) reduce opponent's time in replying, and (3) keep opponent moving and defending. When both opponents are very strong, resolve in forcing one's way forward can bring victory even to the slower or more error-prone player.
 
Both men and women will balance patience with First-Strike tennis -- i.e., attacking at first opportunity, often exploiting opponent's weak second serve or return of serve. Extreme power to a corner can be point-ending for both male and female pros, the latter's lesser striking power balanced by the less powerful movement of her opponents. Confidence -- overcoming fear of error and enabling the player to wield his or her big game -- comes from not missing previously.
 
Close matches, including some between players considerably different in rank, will often be won by the player able to find the mentality needed to produce his or her best, forceful tennis, especially at critical stages. Expertise in drop shots, net play, and lobbing will please the gallery and enhance the attacking game. Deception in shot-making will be needed.
 
The fast courts at the Open can be expected to favor servers. Foot traction should be excellent. Sizzling weather can be expected for part of the period. Convertible roofs will be absent but are in planning.
 
WRAP
 
The coming of U.S. Open 2013 brings memories from the past -- of walking these same grounds as a pre-teenager at the World's Fair in 1939, of watching Kramer and Schroeder defend the Cup at nearby Forest Hills in 1947 after the intervening years of horror, of the Twin Towers that for years dominated the city skyline in the near distance. Tennis has come far over these years. But it remains yet a rarity in big-time sports, strengthening decency and respect among peoples worldwide and maintaining its high integrity. These are what count most.
 
--Ray Bowers, Arlington, Virginia, U.S.A.