Or, Why Four in a Row Is Not Enough.

The failure of Novak Djokovic to covert his 2016 Wimbledon opportunity on the way to a historic Grand Slam, winning all four slam events in the same calendar year, the only “Grand Slam" there is – and the resultant fulminations of Djokovic partisans and other purveyors of imprecise thought, mathematical and otherwise – proved once again the need for a discussion about why winning four consecutive slams is not the same as winning the Grand Slam.

Going into Wimbledon, Djokovic held all four slam titles, 2015 Wimbledon, 2015 US Open, 2016 Australian Open and 2016 French Open.  This is an astounding feat, one that had not been accomplished on the men’s side since Rod Laver won all four in 1969, and Djokovic deserves enormous credit for what is one of the most dominant twelve months of tennis in the history of the sport.  Unlike Laver, who lost quite a few matches during his Grand Slam run, Djokovic was virtually unbeatable, scooping up not only all four slams but also five of the nine ATP Masters 1000 tournaments and a Year End Championship as well.

Once Djokovic lost Wimbledon, however, his chorus of supporters immediately began to suggest that there was no difference between any four straight and the real Grand Slam.  After all, four in a row is hard enough (well, it is difficult, to be sure), and the imposed requirement of all four in a calendar year was unfairly arbitrary.  Hence, their hero should be awarded his gold star without caveat.  The same thing happened with Serena Williams a few years back, and it has happened before as well.  Martina Navratilova once won six slams in a row, perhaps an even more impressive accomplishment than a Grand Slam, but she did not win four within one calendar year, so there was no Grand Slam.

Four Is Not Enough

But to the point, are Djokovic’s fans correct?  Is any old four in a row the same as winning all four in one calendar year?  Well, no.  It’s not the same, and here’s why.

It’s very simple, really.  Each year a player gets four chances to begin a run of four straight slam wins.  But every year, that same player has one and only one opportunity to win all four slams in that calendar year.  So the odds are – Oh, oh, teacher, I know.  Call on me!! – four times less likely.  Surely even the most simple minded can understand the mathematics of that statement.  Although apparently not, as one reads the intellectual wasteland that is Internet forums.

Well then, what’s so special about the calendar year?  The answer is that, like other sports, tennis has seasons, and in the case of tennis the season is defined by the calendar year, January to December.  Life is like that.  We pay taxes on a yearly basis and we don’t hold New Year’s Eve parties on June 5 (the date of the 2016 French Open final, where Novak Djokovic completed his career Grand Slam, in case you’re wondering).  The slams give out trophies with the year inscribed thereupon, surely a meaningful hint.  Tennis holds men’s and women’s year end tournaments, and then that year’s tennis season is over.  Davis Cup is played on an annual basis, with a year-end winner.  Traditionally, the best player for a particular year is said to be the one who holds the number one ranking position at year's end.

Which is why the Grand Slam is all four in one calendar year – and why four in a row, as special as it is, falls a bit short.

Which brings us, parenthetically, to the matter of the imprecision of language used to describe these events.  For the record, they are slam events, not grand slams.  One cannot listen to five minutes of slam television commentary without hearing one of the talking heads refer to the event as a “grand slam".  Well no, there is only one Grand Slam and its meaning is unambiguously defined as winning all four slam events in one calendar year.  I suppose calling each slam tournament a grand slam adds to the hype, but really!  All it does is cheapen the language.  You people are supposed to be professionals.  Get it right or go home.

A Golden Era

Returning to the question of Djokovic’s historic accomplishment – holding all four slam titles simultaneously – it’s time to put that feat in perspective.  Where does it fit in the overall scheme of men’s tennis?  Well for starters, in absolute terms it stands just behind Rod Laver’s 1969 pro Grand Slam, since no man other than Laver has won four in a row at the professional level.  Don Budge won the first Grand Slam, in 1938, but in that era tennis was a mixed affair, with some players turning pro and some remaining amateur.  The Open Era at the slams did not arrive until 1968; thus Budge won his four slams as an amateur, as did amateur Ron Laver in 1962 – the only man to do it twice.

Further, Djokovic’s point total from slams, ATP Masters 1000 wins, 2016 ATP Year End Championship and other tournaments is probably the highest in history over the period in question, making it possibly the most dominant 12 month period in men’s tennis history.  That accomplishment stands alone and leaves little margin for anyone to surpass him.

Having said that, one must also examine context.  Context does not negate or diminish Djokovic’s accomplishments, but it does put them in perspective.  In this case, context encompasses Djokovic’s era and his peers at the pinnacle of the sport, Roger Federer and Raphael Nadal.  It must be noted in fairness to Djokovic that he is still very much in his prime with respect to accomplishments whereas his chief rivals are, by any objective accounting, past theirs.  It can be argued – in fact I do argue here – that these three players are the most recent incarnations of a golden age in the sport.  Past golden eras might be composed of Sampras-Agassi, Connors-Borg-McEnroe-Lendl, Gonzales-Rosewall-Laver, and further back in time, perhaps Budge-Riggs-Kramer and certainly Tilden-Cochet.

The context factors in the relative ages of his rivals as well as the ages at which they reached their peaks and the length of time they remained there.  As of Wimbledon 2016, Djokovic had just turned 29, Nadal had just turned 30, and Federer would be 35 in August.  Thus, Djokovic is one year younger than Nadal and could be said to be very close to being exact rivals if only age is considered, irrespective of age of onset of maturation.  Federer, on the other hand, is a different story.  He lacks only two months being five years older than Nadal and lacks only three months being six years older than Djokovic.  These differences are not insignificant.

Federer won his first slam, Wimbledon, in 2003, just a month short of his 22^nd birthday, and from that point on he was a dominant, record setting force in men’s tennis.  Prior to 2017, the last year he took two slams was 2009, bookending a period of peak ability lasting six years.  When no further slam followed his Australian open win in 2010 most commentators assumed that his career was over.  However, he pulled off another Wimbledon in 2012, a month short of his 31st birthday -- and incredibly, an Australian Open title in 2017 at age 35 and an eighth Wimbledon a month shy of 36, endurance matched by only a scant few, among them Andre Agassi and Ken Rosewall, the latter winning three slams after reaching 35.

Nadal, on the other hand, won his first French Open in 2005 at the age of 19 and continued winning almost continuously through 2014 with only one break due to knee problems.  During this decade, he won at least one slam every year, the longest span on record, exceeding the previous record holder, Pete Sampras, by one year.  Incredibly, he added another French Open in 2017, at age 31.  Nadal's two slam period began in 2008 and ended in 2013, a six year peak performance span, similar to Federer. 

Although Djokovic is only one year younger than Nadal, he did not win his first slam until the 2008 Australian Open, a few months shy of age 21, and he did not win another until 2011, just short of 24, as the dominance of Federer and Nadal continued.  At that  point, Roger Federer ceased to be a perennial slam winner and Djokovic reached the top of the game, winning a total of eleven of 22 slams from the 2011 Australian Open through the 2016 French Open – exactly half of the slams contested.  He won three in 2011 but won only one in each of 2012, 2013 and 2014.  Finally, in 2015 came three and two more in 2016, including a historic four in a row.

Interestingly, the span beginning with three slams in 2011 and ending with two in 2016 constitutes a six year period of dominance, analagous to the arcs of Federer and Nadal.  Recently beset by injury problems, Djokovic now holds none of the four consecutive slam titles he won in 2015-16.  It remains to be seen whether he will have a resurgence similar to Federer and Nadal.  With the gains made by Murray and Wawrinka -- as well as the rise of younger players -- and Djokovic's reaching age 30, the next few years will reveal much about Novak Djokovic's place in the pantheon of tennis greats.

 The Big Picture

This leaves a perhaps forever unanswerable question.  Was Novak Djokovic a late bloomer or did he simply begin to win after Federer and Nadal were past their primes?  No one who has watched Djokovic play can question that he is one of the all-time greats.  By any metric – slam titles, ATP Masters titles, Year End Championships, weeks at number one – or just based on sheer shot making ability, Djokovic is one of the best ever.  Many think he is, for example, the best returner of serve ever to play the game, period.

But, having won four slams consecutively, his name will inevitably be put forward by his supporters as the “greatest of all time," the GOAT.  For beginners, that conversation is premature; Djokovic is still short of other players, some of whom, like Federer and Nadal, are still active.  Unless and until he sends all extant records into oblivion – one must defer assigning his place in the all-time tennis hierarchy.  And, if it turns out that the records of his predecessors are not obliterated convincingly, then points raised with respect to competition against his age group peers, as well as those of other eras, become meaningful.

Federer, Nadal and Djokovic reached their peaks at different ages and held them for different lengths of time.  This means that they played, and still play each other at different maturity levels in their respective careers, a fact that certainly has a strong influence on their respective head-to-head match records.  For instance, Federer defeated Djokovic more times than not, on most surfaces, until Federer was past his prime.  Federer always held a slight edge on Nadal on fast surfaces.  On hard surfaces Nadal and Djokovic were more evenly matched because Djokovic's two-handed backhand tended to neutralize Nadal's left-handed forehand.

Surface and matchup tendencies undeniably skewed head-to-head results.  Nowhere is this more forcefully illustrated than in the clay court matchup of Raphael Nadal’s huge, looping left-handed topspin forehand against right-hander Roger Federer’s one-handed backhand.  Federer’s clay court victories against Nadal have been few in number, and have never come at the French Open, where they have met five times, four of them in the final.

The last observation above brings context into sharp focus.  For much of the prime of his career Roger Federer was the second best clay court player on the planet – as well as being the best grass court player, the best hard court player, and the best overall player in the world.  It is even more certain that Raphael Nadal’s nine French Open titles – an unprecedented accomplishment – as well as his nineteen clay court ATP Masters wins out of a total of twenty-eight, solidify Nadal's status as far and away the best clay court player in the history of the sport, surpassing Bjorn Borg in that regard.

Thus, Federer – himself a candidate for greatest ever, who matured relatively later than Nadal – was unlucky enough to be paired with unarguably the greatest clay court player ever, who matured at a freakishly early age by modern standards, thus effectively closing the age gap and forever denying Federer the opportunity to completely dominate his era in his prime.  Had Nadal not been there, Federer would likely have won two Grand Slams, in 2006 and 2007.  Significantly neither Federer or Djokovic won the French Open with a fit Nadal in his prime on the other side of the net.

Given the extent of Federer’s many records and Djokovic’s present age, 29, along with the onset of injuries, it seems doubtful that Djokovic will be able to amass sufficient accomplishments to unambiguously identify him as the clear cut best ever.  Going into 2017, Federer had won only one slam since he hit 29 and Nadal none.  Pete Sampras captured his final US Open at age 30, and Andre Agassi won two Australian Opens once past 29.

However, much remains to be seen, as both Federer and Nadal won two slams each in 2017 and Nadal returned to world number one.  From that unlikely turn of events, one may infer that Djokovic's final chapter is yet to be written.  However it turns out, none of the above will invalidate his objective career accomplishments as one of the all-time greats – but it will influence how followers of the sport judge those accomplishments relative to the records of others.

 How Hard Is It?

Given the paucity of Grand Slams, and even four-in-a-row occurrences in the open era, it might be instructive to contemplate the odds against and compare them to what has actually been observed in practice.  Of course, such an exercise can never be more than speculation since there is no way to determine probabilities with any degree of accuracy.  But let's try to at least see where the idea leads.  The first step would seem to be to set out the conditions under which a player might have a chance of completing the Grand Slam.  For starters, the following seems reasonable:

• Capable of winning slams on all surfaces (hard, grass, clay)

• No dominant player on any one surface who can block the candidate

• Ability to win two slams in multiple years or three slams in one year

As to odds, for players who win two slams in one year, the probability (greatly simplified, see below) of winning each individual slam in that year is 0.5.  This allows us to calculate the probability of winning four slams in a row as:  0.5 * 0.5 * 0.5 * 0.5 = 0.06.  The probability of winning the Grand Slam is 1/4 of that, 0.015, since there is only one opportunity each year to start a Grand Slam run of four slams.  Put into words, this says that a player good enough to win two slams in a year has only one and a half chances in a hundred of winning the Grand Slam!  No wonder it is so rare!

For players able to win three slams in one year, the probability of winning one slam in that year is 0.75.  From this we calculate the probability of winning four slams in a row as:  0.75 * 0.75 * 0.75 * 0.75 = 0.32.  Once again, the probability of winning the Grand Slam is 1/4 of that, 0.08, as there is only one opportunity each year to start a Grand Slam.  To repeat the analogy from above, a player capable of winning three slams in a year has only eight chances in a hundred of winning the Grand Slam.

In actual fact, the Open Era,which has lasted 48 years so far, 1968-2017, has seen one Grand Slam, or a rate of about 0.02, and two instances of four-in-a-row, a rate of about 0.04, despite a significant number of opportunities on the part of quite a number of players, as the table below shows.

In reality, the above calculations are based on some rather strong simplifying assumptions.  The first is that a player has an equal probability of winning on each different slam surface.  This is almost never true, so the chances of winning the Grand Slam must in reality be conditioned on probabilities that are virtually impossible to quantify, including surface differences, player fatigue as the year progresses, the possibility of injury, and the apparently very real intangible psychological pressure of the historical magnitude of the accomplishment.  All of these work to lower the probability of continuing a winning streak.  More subtly, in the case of starting a four-in-a-row streak the above calculations assume that each probability carries over into the following year, which may or may not be valid.

In the final analysis, the calculations shown simply serve to illustrate the magnitude of the difficulty of winning the Grand Slam, and to perhaps put into context why so many have failed along the way.  It does also give one a greater appreciation for Rod Laver's accomplishment -- at the age of 31, no less!  We conclude by listing qualifying candidates in the open era in the table below, along with relevant aspects of their records.

Men Grand Slam Candidates in the Open Era (1968-2016)*
Player	Could win on all Surfaces?	Blocked by Other Player?	Viability at Career Peak	Notes
Laver	Yes	No	Yes	Grand Slam 1969
Conners	Yes (won 1976 US Open on clay)	No	Yes (denied entry into 1974 French Open)	Wimbledon, US Open, Australian 1974
Borg	Not at US Open	McEnroe at US Open	No	French/Wimb 3 times
McEnroe	Not at French	Lendl at French Open	No	Wimb/US 3 times
Lendl	Not at Wimbledon	--	No	French/US twice
Wilander	Not at Wimbledon	--	No	Three slams 1988
Sampras	Not at French	--	No	Two slams 4 times
Agassi †	Yes	Sampras on hard & grass	Only with Sampras absent	Career Grand Slam, two once
Federer	Yes	Nadal at French Open	Only w/Nadal absent	Career Grand Slam, 3 3-times
Nadal	Yes	No	Yes, but frequently injured	Career Grand Slam, 3 once
Djokovic	Yes	Nadal at French at his peak	Only w/Federer & Nadal past peak	Career G/S, 3 twice, 4-in-a-row
* Candidates are players who won two slams at least twice or three slams at least once in a calendar year during their careers.        † Players who won two slams once:  Agassi, Newcombe (not at French), Vilas & Courier (not at Wimbledon)