Women's Tennis Rankings FAQ

by Robert Waltz

2001 Edition

Please note that, due to changes in the 2002 ranking system, the ranking tables in this document no longer apply for 2002.

Contents:
Introduction
Part I: Points
Part II: Converting Points to a Ranking: The Current System
Part III: Past Ranking Systems
Part IV: The "Ideal Ranking System"
Part V: Doubles Rankings
Part VI: Questions

Introduction

Well, this isn't really a FAQ (though there is a list of questions at the end). This is an explanation -- an attempt to explain the system by which female professional tennis players are ranked.

Part I: Points

The essence of the ranking system is points. When players play tournaments, they are awarded points. Rankings are calculated based on these point totals. (More on this below.)

Points are of two types: "Round Points" and "Quality Points" (the latter also called "Bonus Points"). Round points are based on how far you advance in a tournament. Quality points are based on the players you beat along the way.

To calculate a player's round points, you must know the "Tier" of a tournament. Wins in higher-tier tournaments are worth more than wins in lower-tier tournaments. Unfortunately, the Tiers are not really numbered consecutively; the actual tiers are (in descending order of significance) Grand Slam, Year End (Chase) Championship, Tier I, Tier II, Tier IIIA, Tier IIIB, Tier IV (see note below the points table for the history of these designations). Challenger and Satellite events are not regarded as part of the regular Tier system, although they also earn the player points. (With the important note that points from these lesser events do not go on the rankings until one week after the event is played.)

The table below shows how points are awarded in events of each tier. (Note that not all events will have as many rounds as are shown here. No matter what the tier of the event, points are awarded based on wins. If you lose your opening match, you receive only one round point, no matter whether you lose in the Round of 128 or the Round of 16. Exceptions: In the Grand Slams, a first-round loss is worth two points; at the Chase Championships, where only sixteen players play, a first-round loss is worth 54 points)

TABLE OF RANKING POINTS FOR TOUR EVENTS

Tier	Round reached
	Win	F	SF	QF	R16	R32	R64
Grand Slam	520	364	234	130	72	44	26
Championship*	390	273	175	97	54
Tier I	260	182	117	65	36	22	13
Tier II	200	140	90	50	26	14
Tier III	155	110	71	39	20	11
Tier IV	140	98	63	35	18	10
Tier V	80	56	36	20	10	6

NOTE on tournament names and tiers: The numeration of tournaments changed in 2001. The following list shows the current and past names for the various Tiers (approximate -- the Tier III was granted more points in 2001):

2001 Tier Name	2000 Tier Name	1998 Tier Name
Slam	Slam	Slam
Championship	Championship	Championship*
Tier I	Tier I	Tier I
Tier II	Tier II	Tier II
Tier IIIA	Tier III	Tier III
Tier IIIB	Tier IVA	did not exist
Tier IV	Tier IVB	Tier IV

* In 2000 and earlier, this was the Chase Championship. In 2001 it is moving to Munich

NOTE on ranking points for Tier III events: The above table was instituted in 2001. The prior table was:

Tier	Round reached
	Win	F	SF	QF	R16	R32	R64
Grand Slam	520	364	234	130	72	44	26
Chase Champ	390	273	175	97	54
Tier I	260	182	117	65	36	22	13
Tier II	200	140	90	50	26	14
Tier III	140	98	63	35	18	10
Tier IVA	110	77	50	27	14
Tier IVB	80	56	36	20	10	6

Complete tables of points awarded for all events, including qualifying rounds and challenger events, can be found at sites such as the WTA web site and Tennis Corner. The WTA site also includes the complete ranking rules (though the rules are neither clear nor entirely free of ambiguities). A table of points for qualifying rounds can be found in Part VI.

Round points, as the name implies, are earned based solely on the round one reaches in a tournament. In some instances, one can earn round points without even playing a match (if your opponent gives you a walkover. You must, however, play at least one match to earn round points at a tournament). Quality points, by contrast, are based on whom you play, not the round you play. If you beat the #1 player in the world, you get the quality points whether it's the first round or the last round. For quality point calculations, all that matters is the ranking of the player you beat.

The following table shows the basic values for quality points awards. (These values are modified for Slams; this is known as the Grand Slam bonus, and the details are in the next section. In addition, doubles quality points are awarded based on the combined ranks of the opponents; see Section V.)

Rank of Player Defeated	Quality Points Earned
1	100
2	75
3	66
4	55
5	50
6-10	43
11-16	35
17-25	23
26-35	15
36-50	10
51-75	8
76-120	4
121-250	2
251-500	1
>500	0

Observe that quality points do not vary from Tier to Tier. (Exception: Grand Slams calculate quality points according to the Grand Slam bonus.) That is, if you beat the #1 player, you earn 100 points whether the event is a Tier I or a Tier II or even a Tier IVB (if you could somehow lure the #1 player into a Tier IVB).

At this point, an example is probably in order. In fact, let's take three. The first is for Martina Hingis's win at the Pan Pacific Tournament 1999, the second for Venus Williams's win at the Hamburg in that same year; the third is not a win, but rather Dominique Van Roost's appearance in the finals of Luxembourg 1999.

Example 1: Martina Hingis, Pan Pacific 1999

The Pan Pacific is a Tier I tournament. A win there is therefore worth 260 round points.

To win the event, Hingis had to beat the following players:
Round of 16: Sugiyama (world #25)
Quarterfinal: Graf (#7)
Semifinal: Novotna (#3)
Final: Coetzer (#15)

For beating the world #25, Hingis earned 23 quality points. For beating #7, she earned 43 quality points. The win over #3 Novotna was worth 66 quality points. And the win over #15 Coetzer supplied 35 quality points. So Hingis earned a total of 23+43+66+35=167 quality points at the Pan Pacific. Adding in her 260 round points gives us a total of 427 points earned by Hingis at the Pan Pacific.

Example 2: Venus Williams, Hamburg 1999

Hamburg is a Tier II event. A win there is therefore worth 200 round points.

Williams beat the following players:
Round of 16: Serna (#26)
Quarterfinal: Coetzer (#16)
Semifinal: Sanchez-Vicario (#6)
Final: Pierce (#8)

Beating #26 was worth 15 points. #16 earned 35 points. #6 is worth 43 points, as is #8. So Williams earned a total of 15+35+43+43 = 136 quality points at Hamburg. Adding this to her 200 round points gives a total of 336 points.

Example #3: Dominique Van Roost, Luxembourg 1999

Luxembourg is a Tier III event. A win would therefore have been worth 140 round points (in 1999; in 2001, this increased to 155 points), but Van Roost did not win the event. She lost in the final. Therefore she earned finalist points -- that is, 98 round points (now increased to 110).

Van Roost's route was as follows:
Round of 16: Beat Sidot (#35)
Quarterfinal: Beat Pisnik (#96)
Semifinal: Beat Krasnoroutskaya (#546)
Final: Lost to Clijsters (#83)

Van Roost, of course, does not earn quality points for losing to Clijsters. So she earns 15 quality points for beating #35 Sidot, 4 quality points for beating #96 Pisnik, and 0 quality points for beating Krasnoroutskaya (since the latter was ranked outside the Top 500). So Van Roost earned 15+4=19 quality points, plus 98 round points, for a total of 117 points.

The above shows how to calculate points for any given tournament. This part of the system has been relatively stable for many years. The only change has been the recent split of Tier IV events into Tier IVA and Tier IVB, and the renumbering of the Tier IVA/IVB, which was accompanied by an increase in the points awarded. However, points from a given tournament are not all there is to a ranking. They simply contribute to the player's ranking. The remainder of the system has changed four times since 1995....

Part II: Converting Points to a Ranking: The Current System

Simply knowing how many points a player earned in a particular event does not determine her ranking. The ranking is based on a whole year of scores. Well, sort of....

In addition to the calculation of points described above, there are two additional details one must know to use a given ranking system. One is the Grand Slam Bonus, and the other is the Calculation Method.

The Grand Slam Bonus is a modification of the Quality Points rule. Just as wins at Slams are worth more round points than equivalent wins at lesser tournaments, so victories at the Slams are worth more quality points.

Under the present ranking system (instituted 1998), the Grand Slam Bonus is a factor of two. That is, if you beat a player at a Slam, you get twice as many quality points as you would had you beaten her at any other event. The bonus for beating #1 therefore becomes 200 quality points (as opposed to 100 anywhere else), the bonus for beating #2 goes up to 150 points, #3 is worth 132 points, etc.

Here again, an example may be in order. Let's take Steffi Graf's win at the 1999 French Open.

Example 4: Steffi Graf, Roland Garros 1999

Round	Opponent	Opponent's Ranking	"Ordinary" Quality Pts	Grand Slam Quality Pts
1R	Maleeva	(unranked)	0	0
2R	Gorrochategui	112	4	8
3R	Carlsson	92	4	8
4R	Kournikova	18	23	46
QF	Davenport	2	75	150
SF	Seles	3	66	132
F	Hingis	1	100	200

Thus, in an ordinary tournament, Graf would have earned 0+4+4+23+75+66+100=272 points for beating these opponents. But since this was a Slam, she received twice this total: 544 points. Adding this to the 520 round points for winning a Slam gives us a total of 1064 points.

Knowing exactly how many points players earn at each tournament, we turn to the Calculation Method. The purpose of the Calculation Method is to produce a single number which is the player's "Ranking Total." Players are ranked in descending order based on Ranking Total.

The Calculation Method for 2001 is known as "Best 17." That is, players are ranked based on the scores they earned in eighteen tournaments where they had the highest scores. (This is a minor modification of the ranking system for 1998-2000, known as "Best 18.")

Not all players play more than seventeen tournaments, of course. In that case, the Ranking Total is simply the total points they earned in the seventeen or fewer events they did play.

Again, an example is in order. The following shows Amanda Coetzer's tournaments in 2000.

Example 5: Amanda Coetzer's Scores in the Year 2000.

Week Ending	Event	Points Earned
1/16/2000	Sydney	41
1/30/2000	Australian Open	46
2/7/2000	Pan Pacific	80
2/28/2000	Oklahoma City	94
3/19/2000	Indian Wells	1
4/3/2000	Ericsson	110
4/17/2000	Amelia Island	46
4/24/2000	Hilton Head	84
5/7/2000	Hamburg	194
5/14/2000	Berlin	283
5/21/2000	Antwerp	134
6/11/2000	Roland Garros	82
6/25/2000	Eastbourne	58
7/9/2000	Wimbledon	30
7/30/2000	Stanford	28
8/6/2000	San Diego	49
8/20/2000	Canadian Open	32
8/26/2000	New Haven	145
9/10/2000	U. S. Open	56
10/8/2000	Filderstadt	96
10/15/2000	Zurich	51
11/12/2000	Philadelphia	58
11/19/2000	Chase Champ	132

Counting the above list, we see that Coetzer played 23 events in this period (a fairly typical number, actually a bit below what she played in past years). We need to know the best seventeen of these. If we sort them, we find:

Position Number	Date	Event	Points Earned
1	5/14/2000	Berlin	283	These events count toward Coetzer's Best 17
2	5/7/2000	Hamburg	194
3	8/26/2000	New Haven	145
4	5/21/2000	Antwerp	134
5	11/19/2000	Chase Champ	132
6	4/3/2000	Ericsson	110
7	10/8/2000	Filderstadt	96
8	2/28/2000	Oklahoma City	94
9	4/24/2000	Hilton Head	84
10	6/11/2000	Roland Garros	82
11	2/7/2000	Pan Pacific	80
12	6/25/2000	Eastbourne	58
13	11/12/2000	Philadelphia	58
14	9/10/2000	U. S. Open	56
15	10/15/2000	Zurich	51
16	8/6/2000	San Diego	49
17	1/30/2000	Australian Open	46	<-- Tournament 17
18	4/17/2000	Amelia Island	46	These events do not count
19	1/16/2000	Sydney	41
20	8/20/2000	Canadian Open	32
21	7/9/2000	Wimbledon	30
22	7/30/2000	Stanford	28
23	3/19/2000	Indian Wells	1

Thus Coetzer's seventeen best are the tournaments ranging in value from Berlin (where she earned 283 points) to the Australian Open (or Amelia Island), where she earned 46. The total of these seventeen scores is 1752. The remaining six scores (46 at Amelia Island, 41 at Sydney, and so on down to 1 at Indian Wells) are simply ignored.

Example 6: Venus Williams's Scores in the Year 2000

Week Ending	Event	Points Earned
5/7/2000	Hamburg	58
5/21/2000	Rome	59
6/11/2000	Roland Garros	228
7/9/2000	Wimbledon	1098
7/30/2000	Stanford	331
8/6/2000	San Diego	343
8/26/2000	New Haven	316
9/10/2000	U. S. Open	1056
10/22/2000	Linz	205

Since this list contains only nine tournaments, which is less than seventeen, we calculate Williams's score by simply adding up the eleven events, for a total of 3694 points.

To calculate the ranking list, one simply lists players in descending order of point totals. The more points you have under Best Seventeen, the higher your ranking.

Footnote: Players with the Same Score. It will periodically happen that players end up with the same score. In that case, the player with the most quality points receives the higher ranking. In singles, this has never failed to break the tie among high-ranked players. In doubles, however, it will sometimes happen that two players play all their events (or all their events which count) together, so they have the same total and the same quality points. If this happens, the player with the most points in her non-counted tournaments receives the higher ranking. (This happened for a brief time in 2000, when Lisa Raymond and Rennae Stubbs had the same best 14 events, and so tied on points and quality points. Raymond had more tournaments, and so was given the #1 ranking.) If even this fails to resolve the tie, the two receive the same ranking. (This has usually been true for the Williams Sisters, for instance.)

Footnote: Walkovers. A player who wins via a walkover does not earn quality points. (Note, however, that if you play even one game, it counts as an official match, and you earn the round points.) A player who wins via walkover does receive round points, with an exception: You must win at least one match at a tournament to earn more than the minimum number of points. So a player who receives a bye in the first round and a walkover in the second, then loses in the third round does not receive any round points (other than the bare minimum 1 or 2 for playing a match). If, however, the player wins one match, then receives a walkover in the second round, the player does receive the round points for winning both matches.

Part III: Past Ranking Systems

The present system was adopted only in 2001. Prior to that, they had a similar system in 1998-2000, but before that the system had changed yearly for three years.

In 1998-2000, the ranking system was "Best 18" -- exactly identical to the Best 17 system used in 2001, except that eighteen tournaments counted rather than seventeen.

In 1997, the WTA used a "total points" ranking system: You simply added up every point you had earned in the last year and ranked based on that.

In addition, the Grand Slam bonus in 1997 was only a factor of 1.5, rather than the present factor of two. That is, whereas in 1999 a win over the #1 player earns 200 quality points at a slam (as compared to 100 points at any other event), in 1997 it would only have been worth 150 points.

In practice, the 1997 system did not differ significantly from the 1998 and 2001 systems, as almost no one earned enough points in tournaments 19 through whatever to make any difference. (To date, Martina Hingis is the only player ever to have more than 100 points in a non-counting tournament.)

The 1998 and 1997 system would produce different ranking totals for some players, however. Let's return to the example of Amanda Coetzer, and assume she had achieved identical results under the 1997 rules:

Example 7: Amanda Coetzer's Scores in the year 2000, calculated under the 1997 ranking system

Week Ending	Event	Points Earned
1/16/2000	Sydney	41
1/30/2000	Australian Open	41	<-- was 46; reduced due to smaller Slam bonus
2/7/2000	Pan Pacific	80
2/28/2000	Oklahoma City	94
3/19/2000	Indian Wells	1
4/3/2000	Ericsson	110
4/17/2000	Amelia Island	46
4/24/2000	Hilton Head	84
5/7/2000	Hamburg	194
5/14/2000	Berlin	283
5/21/2000	Antwerp	134
6/11/2000	Roland Garros	72.5	<-- was 82
6/25/2000	Eastbourne	58
7/9/2000	Wimbledon	29	<-- was 30
7/30/2000	Stanford	28
8/6/2000	San Diego	49
8/20/2000	Canadian Open	32
8/26/2000	New Haven	145
9/10/2000	U. S. Open	53	<-- was 56
10/8/2000	Filderstadt	96
10/15/2000	Zurich	51
11/12/2000	Philadelphia	58
11/19/2000	Chase Champ	132

To get Coetzer's score, we simply add up all the numbers, to produce the total 1911.5.

While the 1997 ranking system differed only trivially from the 2001 system, the same cannot be said of the 1996 ranking system, which was completely and fundamentally different. Whereas, in 1997 and beyond, the ranking was a sum, prior to 1997 the ranking was an average -- the average number of points earned in a tournament. To calculate this, one simply adds up the points and then divides by the number of tournaments. So in the case of Coetzer in the example above, for instance, her total points were 1911.5 and she played 23 tournaments. Therefore her score ranking total would be 1911.5/23 = 83.1 (to three significant digits).

There was a twist, however, known as the "minimum divisor." Players are expected to play a certain number of tournaments. If they don't, they are treated as if they did. In 1996, the minimum divisor was 14. If a player played fewer than fourteen tournaments, her score was still divided by 14.

We can again take Venus Williams as an example. We'll just silently recalculate her quality points as they would have been under the 1996 system (in 1996, as in 1997, the Grand Slam Bonus was only a factor of 1.5):

Example 8: Venus Williams's Scores in the Year 2000, calculated according to the 1996 point allocation system

Week Ending	Event	Points Earned
5/7/2000	Hamburg	58
5/21/2000	Rome	59
6/11/2000	Roland Garros	203.5
7/9/2000	Wimbledon	953.5
7/30/2000	Stanford	331
8/6/2000	San Diego	343
8/26/2000	New Haven	316
9/10/2000	U. S. Open	922
10/22/2000	Linz	205

Adding up these scores, we get a total of 3391. But in only nine tournaments! So although Venus's points per tournament were 3391/9 = 376.8, her actual ranking score would have been 3391/14 = 242.2.

The 1995 system (which was also in use for some years prior to 1995) was identical to the 1996 system, except that it used a minimum divisor of 12. So under this system, Venus's ranking score would have been 3391/12 = 292.6.

All of this makes a very real difference. I demonstrate some of the differences in the questions and answers section. But let's conduct a final set of examples to prove our point.

The following takes the 2000 Top Ten (as of the time the Tour shifted to Best 18, i.e. December 25, 2000), and gives their ranking totals under each of the five ranking systems. (Note: For simplicity, I have not recalculated the quality points from the Slams. In all cases, the Slam bonus is assumed to be 2.) This is followed by the list of the Actual Top Ten under all of these systems.

Example 9: The 1999 Top Ten as they would appear under other ranking systems

WTA Rank	Player	Total Points	# of Tourns	2001 Score	1998 Score	1997 Score	1996 Score	1995 Score
1	Hingis	6394	20	6044	6180	6394	319.7	319.7
2	Davenport	5022	18	5021	5022	5022	279.0	279.0
3	VWilliams	3694	9	3694	3694	3694	263.9	307.8
4	Seles	3255	15	3255	3255	3255	217.0	217.0
5	Martinez	2837	20	2752	2795	2837	141.8	141.8
6	SWilliams	2306	11	2306	2306	2306	164.7	192.2
7	Pierce	2162	13	2162	2162	2162	154.4	166.3
8	Sanchez-Vicario	2132	18	2131	2132	2132	118.4	118.4
9	Kournikova	2414	26	2098	2158	2414	92.8	92.8
10	Tauziat	2033	26	1918	1963	2033	78.2	78.2

Therefore we get the following ranking lists (an * marks a change in the rankings from the 2001 system):

THE TOP TEN UNDER THE 1998-2000 RANKING SYSTEM

Rank	Player	Score
1	Hingis	6044
2	Davenport	5021
3	VWilliams	3694
4	Seles	3255
5	Martinez	2752
6	SWilliams	2306
7	Pierce	2162
*8	Kournikova	2158
*9	Sanchez-Vicario	2132
10	Tauziat	1918

THE TOP TEN UNDER THE 1997 RANKING SYSTEM

Rank	Player	Score
1	Hingis	6394
2	Davenport	5022
3	VWilliams	3694
4	Seles	3255
5	Martinez	2837
*6	Kournikova	2414
*7	SWilliams	2306
*8	Pierce	2162
*9	Sanchez-Vicario	2132
10	Tauziat	2033

THE TOP TEN UNDER THE 1996 RANKING SYSTEM

Rank	Player	Score
1	Hingis	319.7
2	Davenport	279.0
3	VWilliams	263.9
4	Seles	217.0
*5	SWilliams	164.7
*6	Pierce	154.4
*7	Martinez	141.8
8	Sanchez-Vicario	118.4
*9	Mauresmo	101.9
*10	Kournikova	92.8

THE TOP TEN UNDER THE 1995 RANKING SYSTEM

Rank	Player	Score
1	Hingis	319.7
*2	VWilliams	307.8
*3	Davenport	279.0
4	Seles	217.0
*5	SWilliams	192.2
*6	Pierce	166.3
*7	Martinez	141.8
8	Sanchez-V	118.4
*9	Mauresmo	101.9
*10	Kournikova	92.8

Thus we observe that only two ranking positions (#1/Hingis, #4/Seles) remained the same under all five ranking systems, and that only nine players are found on all four Top Ten lists (Tauziat drops off the 1996 and 1995 lists, to be replaced by Mauresmo). And this is actually low; based on some year's results, as many as three players might switch out of the Top Ten.

Part IV: The "Ideal Ranking System"

In light of the above, is it possible to produce an ideal ranking system?

The theoretical answer is, "it depends." The practical answer is probably, "No."

The present ranking system assesses a player's performance over the last year. Yet it is used to predict future performance (in the form of seeds). As long as this discrepancy is maintained, the ranking system will be under opposing pressures. Separating these functions (e.g. by seeding by surfaces) would help, but is unpopular; only Wimbledon does it, and the players complain even so.

In addition, the ranking system is currently used almost as a weapon, forcing players to play more. This function must be served by other incentives if a fair ranking system is to be achieved.

A final problem with the system is the way points are allocated. Neither round nor quality points are actually proportional to the effort needed to earn them.

In the case of round points, there are two examples of this: The gap between the Slams and everything else, and the gap between Tier II and Tier III tournaments. The Slams are inflated for reasons not having directly to do with their difficulty (since Slams have large draws spread out over a long period, it is actually physically easier to win a typical match at a Slam, where you are rested and have lower-ranking opponents, than at a lesser tournament, where your opponent is sure to be ranked higher and you have had less rest). The gap between Tier II and Tier III events, by contrast, is too small in terms of points. There are Tier II events (e.g. Filderstadt, San Diego) where every player who earned direct entry was in the Top 25; there are Tier III events where no one is in the Top 20. Yet the Tier III is regarded as worth more than 75% of the round points of the Tier II!

In the case of quality points, the problem is that what you earn for beating a player is based solely on the player's ranking. #1 is worth 100 quality points, and #2 is worth 75, regardless of whether they are 3000 points apart, or only one.

The ideal system will, therefore, award both round and quality points in a way proportionate to the task at hand. Only in this case can the rankings be truly ideal.

It probably won't happen, though. Such rankings are difficult to calculate, and -- more to the point -- they have little commercial appeal.

Part V: Doubles Rankings

Doubles rankings are much like singles rankings, with two basic exceptions: Quality point awards and number of tournaments.

In doubles, quality points are awarded based on the combined (doubles) rankings of your opponents. That is, you add the rankings of your opponents and look up the appropriate number. If your opponents are ranked #3 and #5 in doubles, for instance, their combined rank is 8, and so you receive 43 quality points for beating them.

(Note the obvious effect of this: The highest possible ranking of a doubles team is #1+#2=3. And so forth down the rankings. Quality points have very little importance in doubles; there just aren't enough of them available.)

Let's work an example. Let's take the path Martina Hingis and Nathalie Tauziat followed to win the 2000 Canadian Open. Their path was as follows (doubles rankings in brackets):

First round: BYE
Second round: def. Grande [41]/Habsudova [47]
Quarterfinal: def. Huber [30]/Schett [18]
Semifinal: def. Po [20]/Sidot [38]
Final: def. Halard-Decugis [4]/Sugiyama [5]

Round points in doubles are the same as in singles: Winning the Canadian Open, a Tier I, is worth 260 points. Now for the quality points. Grande is ranked 41, Habsudova 47; total: 88. So beating them is worth 4 quality points. In the next round, Huber's #30 and Schett's #18 combine to 48, i.e. 10 quality points. Po/Sidot gives 20+38=58, so another 8 quality points. Halard-Decugis and Sugiyama give 4+5=9 for a combined ranking, yielding 43 quality points. So Hingis/Tauziat earned 4+10+8+43=65 quality points for winning the Canadian Open, for a total of 370+63=325 points. (Note how small the ratio of quality to round points is: Hingis and Tauziat beat two seeded teams, including the #1 seeds Halard-Decugis and Sugiyama, and still earned 80% of their points from round points!)

The other difference between singles and doubles is the number of tournaments which count. Singles is Best 17; you add up seventeen tournaments. Doubles is only Best 13; you count only your best thirteen tournaments. (This became the rule in 2001; in 2000, doubles used Best 14, and prior to that, singles and doubles both used Best 18, and they also used the same system while the divisor was in force.)

As far as I know, no official reason for the shift from Best 18 to Best 14 was announced (the shift from Best 14 to Best 13 coincided with the shift in singles from Best 18 to Best 17, and was justified as a help for injured players), but I believe it is in response to Martina Hingis's doubles Grand Slam in 1998. Hingis won all four Slams -- but still wound up #2 in doubles behind Natasha Zvereva. Zvereva had half again as many doubles tournaments as Hingis, and led Hingis by a stunning 2% in points. Under Best 14, Hingis would generally have been #1 in doubles.

Part VI: Questions

Q: What does it mean to "defend points"?
A: You might think of points as having a freshness date: They expire after a year. If a player wants to maintain her point total, she must come up with new points to replace those which expire. This is the essence of defending points. If you earned a lot of points in a given week last year, you must play the same tournament (or another one) and earn new points, or else you lose them.

Q: My favorite player was #6 last week, and this week I see that she has fallen to #10. What happened?
A: Chances are that the player had a lot of points to defend the previous week (see the preceding question), and failed to defend them. It can sometimes happen, too, that a tournament will be rescheduled, meaning that a player can lose the points before she can defend them. This happened, for instance, in 2000, when about a quarter of the year's tournaments (from Indian Wells to Wimbledon) were rescheduled in such a way that the points came off before players could defend them.

Q: What does it mean to "Qualify" or be a "Qualifier"?
A: Only a finite number of players can play at any given tournament -- 128 at a Grand Slam, and a smaller number (most typically 28) at other events. Most of these players get in by "direct entry" -- their rankings are high enough that they are granted automatic admission to the tournament.
The problem with giving everyone direct entry is that it would result in the same players playing every event. There would be no "new blood."
The solution is the "qualifying tournament." Players who are ranked too low to gain direct entry into an event are allowed to play a "pre-event" (usually of three rounds) to earn one of three to twelve spots in the "main draw" reserved for qualifiers.
Unlike regular tournaments, a qualifying draw does not have a single winner; rather, the players who win all three of their matches are admitted to slots in the main draw. These players are known as "Qualifiers," and they are said to have "qualified" for the main draw.
Since qualifying matches are played against tour opponents, they do carry points. As with main draw matches, players earn both round and quality points. The round points are strictly limited, though. (Probably more than they should be; it's worth more to win three matches in Challengers than in qualifying for Tour events. This actually encourages players to play Challengers rather than Qualifying.) The following tables show the qualifying points for various Tiers of events:

QUALIFYING EVENTS WITH THREE ROUNDS:

               Qualifier    3R(finalist)  2R    1R Loss
Grand Slam     22           18            10       2*
Tier I         16            9            5        1
Tier II        12            7            4        1
Tier III        9            5            3        1
Tier IV         8            5            3        1
Tier V          4.5          3            2        1

* Formerly 16.5

QUALIFYING EVENTS WITH TWO ROUNDS:

               Qualifier    2R(finalist)  1R Loss
Tier I          9            5              1
Tier II         7            4              1
Tier III or IV  5            3              1

(Note: The WTA may sometimes treat a two-round qualifying draw as if it had three rounds. An example is Indian Wells 2000, where there were only two rounds of qualifying, but the qualifiers received 11 points and the finalists received 6.)

Fractional points are awarded for results in qualification rounds for Challenger events. Full details, again, are found at the WTA site.

Q: What is a "Lucky Loser"?
A: Not all players who are admitted to a main draw actually play. Many tournaments lose one or more players at the last moment (usually to injury). These players (if they withdraw between the creation of the draw and the completion of the first round) are replaced by Lucky Losers.
A Lucky Loser is a player who lost in the final round of qualifying but is able to get into the main draw when another player withdraws. Lucky Losers are admitted to the draw in direct ranking order (based on the rankings at the time tournament entries closed). Thus, the highest-ranked player to lose in the final round of qualifying gets the first open position, the next-highest gets the second position if there is one, and so on down. (Note: Lucky losers have to be on hand when the player withdraws.)
Although these players are called "lucky," getting into a tournament as a lucky loser is not purely lucky. Lucky losers who win a main draw match suffer a penalty: They forfeit the round points (though not the quality points) earned in the qualifying rounds. If they lose their opening main draw match, however, they keep all the qualifying points. Since points in the main draw are always greater than those in qualifying, this is not a large penalty -- but it is a penalty. [Thanks to Geert P. Calliauw for figuring out the way the WTA actually applies this rule. The official rules are somewhat contradictory.]
We should add that, if a player withdraws after completing her first round match, her opponent simply earns a walkover.

Q: What is a "Wildcard"?
A: Most of the players in a tournament are given direct entry or earn their way in by qualifying. This can result (especially at low-Tier events) in a field without much "fan appeal." To liven up their tournaments, organizers are allowed a handful of "wildcards" -- players who are allowed into the main draw simply at the whim of the organizers.
Wildcards usually fit one of two descriptions: High-ranked players who didn't register for the tournament in time, or low-ranked players from the local area of the tournament (the latter being otherwise ineligible to enter the tournament).
There is a third category: High-profile burnouts. Examples include Jennifer Capriati, Iva Majoli, and Tracy Austin -- players who were very popular for a while, then stopped playing and/or winning. But few players retain enough popularity after bombing off the Tour for this situation to come up.
Tour rules restrict the number of wildcards one can take in a year, though it is very rare for a player to use up her wildcards. (The only recent example, to my knowledge, is Jennifer Capriati in 1998, who used six wildcards to get into tournaments but did so poorly that her ranking did not rise.)

Q: How do I earn a ranking?
A: You talk someone into letting you play recognized tournaments. If you have good school results, it will probably be possible to get into a satellite event.
Once you have played three professional events, you will receive a ranking (though it will probably be very low). You cannot be ranked until you have played three events.

Q: What is the purpose of the rankings?
A: This has several answers. The direct use of the rankings is to seed tournaments, and determine who gains entry into a tournament. A normal Tier II tournament, for instance, has room for 28 players. Under current rules, three or four of these players are qualifiers and two or three are wildcards. The remaining 21 or 22 players are given "direct entry." "Direct entry" is given to the highest-ranked of the players who ask to play in the tournament. The highest-ranked of these players are then granted seeds.
However, the rankings also confer boasting rights, and in many cases also monetary privileges, as players earn more for their endorsements as they earn higher rank. For these purposes, it hardly matters what ranking system is used; #1 is #1 no matter how silly the system. But from the standpoint of seeding and admittance, it is obviously desirable that the rankings produce a #1 player who can reasonably be regarded as the best in the world.

Q: You say that the major change in the ranking system came between 1996 and 1997, even though the system also changed between 1995 and 1996, and again between 1997 and 1998 and between 2000 and 2001. What makes the 1996/1997 change so much more important?
A: Prior to 1997, the system was an averaging system. From 1997 on, the system switched to a lump sum form, under which you could increase your ranking simply by playing more tournaments. Prior to that, the only way to increase your score (once you reached the minimum divisor) was to post more good results.
The net result of the change has been to cause the mid-range players (roughly, those ranked from #8 to #50) to play more, in order to preserve their ranking. This, in turn, affects the lower-ranked players, who can no longer get into such strong tournaments as before (meaning that they earn less).

Q: Why did the WTA shift from the divisor to the Best nn ranking system?
A: The WTA and the players actually had different reasons. The WTA wanted the top players to play more. The mid-ranked players thought (incorrectly) that the new ranking system would improve their rankings and/or income. Most top-ranked players reportedly opposed the system, which tries to force them to play more.

Q: What is the advantage of the Best nn ranking system over the divisor?
A: Under the divisor, if you lose early in a tournament, your average goes down. In other words, losses hurt. Under Best nn, if you lose early, it just means that your point total stays the same. In other words, losses don't count. So you can play lots of tournaments without fear: If you win, your ranking improves; if you lose, it doesn't hurt you. This is perceived as benefitting the Tour, because it encourages the top players to play more.

Q: What is the advantage of the divisor over Best nn?
A: Under the divisor, losses count (for the reasons outlined under the previous question). So you can't lose five or ten matches in a row and have your ranking stay the same (or even, as sometimes happens, go up). Best nn, in essence, ranks players based on how many matches they win. The divisor, in effect, ranks based on win-loss percentage.
Best nn can descend to the point where it ranks little more than endurance, while the divisor always ranks based on the ability to actually win consistently. Thus a side effect of Best nn is that it can allow a player who is good on only one surface to equal the ranking of a player who is successful on all surfaces.
Anecdotal evidence suggests that the shift to Best 18, by inducing players to play more, has caused players (especially players who play most of their matches on hardcourts) to suffer more injuries. This has not, however, been formally demonstrated; as far as I know, no one has attempted to study the correlation between frequency of injury and frequency of play. I would guess that such a study will never be done; those who prosper under the present system (including the WTA Tour officialdom) would be afraid of what the study might show.

Q: Why can't the WTA come up with a ranking system and stick with it?
A: There is no clear-cut answer to this, but probably the best answer is that the ranking system is being asked to do no fewer than three different things. One is to admit seed players and determine who gets into tournaments. A second is to provide actual rankings. And a third is to control the extent to which players play. Since these are not really compatible objectives, there is constant pressure to change the system.

Q: What difference do these different ranking systems make?
A: It can be a lot! In 1997, Martina Hingis became #1 on April 1, but if the 1996 ranking system had still been in use, Hingis would not have become #1 for an additional five weeks after that. Even more extremely, Lindsay Davenport became #1 on October 12, 1998, and held the ranking until February 8, 1999 -- but had the 1996 ranking system been in effect, Davenport would never have overtaken Hingis at all. And it's not just the top ranking that is affected. After the 1997 Australian Open, for instance, Karina Habsudova was #11 in the world, but would have been #15 under the old ranking system, while Monica Seles was #6 in the world, but would have been #3 under the 1996 rules.
As an illustration of how significant all this is, the following table illustrates the changes in the #1 ranking from the beginning of 1997 to the time I wrote this question (May 22, 2000). The table shows the date, the #1 player under the WTA (Best nn) ranking system, and the player who would have been #1 under the divisor (editorial opinion: In every case, where the two differ, the divisor was a more accurate assessment of who was actually #1 at the time, based on winning percentages, strength of tournaments won, etc.)

TIME PERIOD	WEEKS	#1 BY WTA RANK	#1 ACCORDING TO DIVISOR
Jan 1-Ma 24, 1997	12	Graf	Graf
Ma 25-Ap 27, 1997	5	Hingis	Graf	<<<<<<<<<<<
Ap 28-De 31, 1997	35	Hingis	Hingis
Jan 1-Oc 11, 1998	39	Hingis	Hingis
Oc 12-De 31, 1998	13	Davenport	Hingis	<<<<<<<<<<<
Jan 1-Feb 7, 1999	5	Davenport	Hingis	<<<<<<<<<<<
Feb 8-Jul 4, 1999	21	Hingis	Hingis
Jul 5-Aug 8, 1999	4	Davenport	Davenport
Aug 9-De 31, 2000	22	Hingis	Hingis
Jan 1-Feb 6, 2000	5	Hingis	Hingis
Feb 6-Mar 5, 2000	4	Hingis	Davenport	<<<<<<<<<<<
Mar 5-19, 2000	2	Hingis	Hingis
Mar 19-Ap 2, 2000	2	Hingis	Davenport	<<<<<<<<<<<
Ap 2-May 7, 2000	5	Davenport	Davenport
May 8-14, 2000	1	Hingis	Davenport	<<<<<<<<<<<
May 15-21, 2000	1	Davenport	Davenport
May 22, 2000-	1+	Hingis	Davenport	<<<<<<<<<<<

Later footnote: Hingis regained #1 under the divisor at Wimbledon, and Davenport did not regain the ranking in 2000 -- though Venus Williams would briefly have been #1 under the divisor following the U.S. Open, and then for a time in 2001. Hingis, of course, was #1 under Best 18 for this entire period.

Q: Why is there a Grand Slam Bonus?
A: The basic answer to this is, "Because the Slams are Slams." There is no mathematical basis for this; indeed, those who have examined the basis for the ranking system most closely tend to think that it is a poor idea. But the Tour has declared that the Slams are worth twice as much as other tournaments. It's just the way they do things. The purpose is to make the Slams more important in the rankings than other events. Whether you regard this as a good idea depends, of course, on how you feel about the Slams.
The one observation we can make is, very few people like the Slam Bonus. Those who view the ranking system from a mathematical standpoint tend to regard it as too high. Those who think Slams are the entire purpose of the Tour think it is too low. This argues that, at least from the psychological standpoint, it is about right.
A very strong argument can be made that the Slam Bonus MUST not be more than two. Even this large a bonus leaves the other events very much in the shadow of the Slams. Now that may seem reasonable -- but it is the lesser events which provide the "cannon fodder" for the Slams by allowing lower-ranked players to make a living. Make the lesser events too insignificant, and the Slams will no longer be viable, because there won't be any players to play them.

Q: Why are rankings calculated over the course of a year?
A: It would be very difficult to calculate accurate rankings over a period of less than one year. Many players are "specialists"; they earn a disproportionate share of their points on one particular surface. In 1999, for instance, Arantxa Sanchez-Vicario earned 59% of her points on clay (the typical value is 23%), while Serena Williams earned 82% of her points on hardcourts (44% is typical). Assume these players always earned the same results, year after year. If you took only, say, three months of results instead of a year, a player's ranking would fluctuate wildly even if her results stayed the same. At the start of the clay season, for instance, Sanchez-Vicario would be around #20 in the world, while at the end of the season she might rise as high as #4. This even though her results had not changed at all.
As long as the Tour moves from surface to surface, one year is the absolute minimum acceptable period for an overall ranking scheme. (This is a large part of why the men's "race" rankings are such an abomination.) You could, of course, rank over a longer period -- two years or three years or more -- but this would reduce the "responsiveness" of the rankings; I doubt the idea would be popular.

Q: All of this discussion is about singles. What about doubles?
A: Doubles rankings are calculated in much the same way as singles rankings; when you play a match, you earn round and quality points for winning.
There are two minor differences for doubles. First, the quality points awards must be adjusted to reflect the ranking of the opposing TEAM, as opposed to a particular opponent. To calculate quality points in doubles, you add the doubles rankings of the two players and look up the points in the quality points table.
Unfortunately, using the singles quality point table much reduces the importance of quality points in doubles. This is because teams will inherently have a lower combined rank than the individual players. Even if the top two players in the world team up in doubles, their combined rank is 3. In other worlds, beating the best possible doubles team is worth no more than a win over the #3 singles player. This means, in turn, that doubles point totals are lower, and that quality points play a much smaller part in one's scores. Whereas quality points in singles represent about 35-40% of a typical player's total, in doubles the figure is closer to 20%. It would be almost as accurate to abolish quality points for doubles.
For further details and an example, see Section V: Doubles Rankings.

Q: And what about men's rankings?
A: Don't make me laugh.
The men don't have a ranking system. They have a "race." The best thing to do about men's rankings is ignore them.
The men, in fact, use two "ranking systems," the "race rankings" and the "entry rankings." Race rankings -- what the ATP Tour attempts to fob off as "the rankings" -- are based on results gained in the current year only. This produces three problems: First, it artificially inflates the rankings of people who play a lot in the early part of the year; second, it artificially penalizes players who have not been able to play on their favorite surfaces; and third, it completely ignores the problem of injuries. The race rankings are intended to forecast who will be the year-end #1. What they achieve is to demonstrate that the ATP Tour doesn't understand its own ranking system. In the later parts of the year (starting around Wimbledon), the race rankings begin to have some validity (though less than one would think, even after the U.S. Open), but they are not accurate until the end of the year. And even then, they use a! badly biased ranking system which essentially ignores smaller tournaments (only five events below the Masters Series level count; since most players play ten to fifteen such events, the results are nearly meaningless).
The other system used by the ATP is "entry rankings." These, unlike the "race rankings," are a valid ranking system; they take into account all results over the past year. But they have only one purpose: To determine entry and seeding in tournaments. And they, like the Race Rankings, count only five lesser tournaments, making them inaccurate as a predictor of actual tournament success.
We might note that the chief side effect of this ranking system (and, indeed, any ranking system in which losses do not count) is to encourage "tanking" -- deliberately losing a match so one does not have to continue competing (usually after collecting an appearance fee). This is because losses at lower-tier events don't matter in any way. In essence, the ATP has told its lesser tournaments, "You don't count and we don't care if you survive." The lesser tournaments already had to pay appearance fees to bring in players, but could at least hope the players would be willing to play for points. Now, with few if any points on the line, the players have no incentive to do more than collect their fees.
The "slotted" rankings also have the drawback that they are very hard on injured players. Miss, say, Roland Garros and Wimbledon, and you cannot earn back those points in any other way.

Q: How are mixed doubles rankings determined?
A: There aren't rankings for mixed doubles. There are seedings, of course; these are based on the men's and women's doubles rankings. As in "ordinary" doubles, the rankings of the two players are combined, and the teams sorted (and hence seeded) on that basis.
This has two slight problems: First, it means that past success in mixed doubles does not affect one's mixed doubles seeding. The classic example of this was in 1998, when Venus Williams and Justin Gimelstob won two Slams in mixed but were not seeded at the next two Slams; neither had the results in ordinary doubles to gain a seed.
The other problem is that the two Tours calculate doubles rankings differently. This is a relatively minor point, but the two systems do not reward the same sorts of results.
Both of these facts mean that a mixed doubles team may be ranked very high without being particularly good at mixed doubles (where the disparity in skills between the team members is generally much higher than in ordinary doubles). Still, given that relatively few top players play mixed doubles, this is not a major concern. If mixed doubles were upgraded to a more real discipline (e.g. by adding mixed doubles events at Sydney, Indian Wells, and the Ericsson, all of which feature both men and women), the problem would be much more important.

Q: What effect do Fed Cup have on the rankings?
A: None. Federation Cup matches are official WTA matches, but they have no effect on the rankings.
This may sound unfair, but in fact it would be more unfair if they did affect the rankings. There are two reasons for this. One is the matter of qualification. Players don't get into Fed Cup the way they do into other tournaments. We may offer an example from the round of May 2000. The United States was not involved in this round (it had a bye), but suppose it had been. Four women would have been selected: #1 Lindsay Davenport, #3 Venus Williams, #6 Serena Williams, and #7 Monica Seles. This left out, among others, #13 Jennifer Capriati. At any normal tournament, Capriati would have been offered automatic admission; she would have been seeded at the majority of events. But she can't play Fed Cup unless one of the higher players goes down. Meanwhile, some teams such as Slovakia are playing teams of non-Top-Fifty players (Karina Habsudova, Henrietta Nagyova) -- players who could not get into a normal Tier II tournament. In other words, the players playing in Fed Cup a! re not proper opponents.
There is also the matter of awarding points for results. In a normal tournament, each match is worth more round points than the match before, because the opponents will get tougher. This does not follow in Fed Cup, where (in any given round) you play opponents in a random order.
It would be possible to make up rankings based on Fed Cup. But they would involve a completely different set of rules from normal rankings. Better to keep Fed Cup "off the books" than to cause such bending of the rules.

Q: What effect do the Olympics have on the rankings?
A: As with Fed Cup, there is no effect. As with Fed Cup, this is as it ought to be. The key reason why Fed Cup does not count applies to the Olympics as well (only a limited number of players from each country may participate, and they are not selected based on overall rankings). In addition, there is the fact that the Olympics are played every four years, meaning that there would be a skew in the rankings every four years. (With the Olympics not counting, there is a counter-skew because players ignore other events to play the Olympics, but the schedule has been reconstructed to reduce the significance of this.)
The men have adjusted their rankings so that points are awarded for the Olympics. Yet more proof, as if it were needed, that the men don't understand what a ranking should be.

Q: I think a certain player will win a particular upcoming tournament. Can I predict her ranking afterward?
A: Not unless you can predict the exact list of players she will beat along the way. This is because of quality points. If you know the draw, you can determine the maximum possible points a player will earn, but it is highly unusual for a player to earn these points.
Consider the smallest "standard" tournament: The 28-draw Tier I or Tier II event. Our hypothetical winner can face any of fourteen opponents in the final, seven potential opponents in the semifinal, four possible quarterfinal opponents, and two possible Round of 16 opponents. That means that a winner has 784 different possible paths to the final. (And if you think that's a big number, realize that there are 134,217,728 separate possible outcomes to the tournament as a whole; it's just that these outcomes don't affect the winner's route to the final.) Since players earn different numbers of quality points depending on their opponents, predicting the result of a tournament depends almost as much on who you play as on how many rounds you win.

Q: What do the rankings mean? Do they really reflect who is the best player?
A: Not automatically -- consider the example given above where Hingis and Davenport were frequently ranked differently under the divisor and Best 18 ranking systems. It is almost always true that a Top Ten player is better than a player ranked outside the Top Twenty. (The only minor exception is the case of a player who, through injury or youth, has not played a full schedule. This player may be significantly under-ranked.) Again, a Top Twenty player is consistently better than a player outside the Top Fifty. But beyond that, it gets hazy. "Luck of the draw" can have a major effect on one's rankings, particularly at a Slam where the points are doubled. If you have the bad luck to draw a seed in the first round of three of the four Slams, you won't get much chance to earn points (and since there is one chance in eight of drawing a seed, this will happen to someone every few years on average).
There is no perfect cure for this problem -- particularly since there is no consensus on what it means to be the "best" player. Because of the Slam Bonuses, both the WTA and ATP have in effect declared that the best player is almost always the one who does best at the Slams. (And yes, this was true even in 2000, when Martina Hingis was #1 without winning a Slam. Although she didn't have a Slam title, she had more Slam match wins -- twenty -- than any other player.) But it is by no means certain that this player with the best Slam results will have the best winning percentage, or win the highest fraction of tournaments she enters. And for lower-ranked players, who tend not to post strong results at Slams, the correlation between rankings and winning rates is, if anything, even lower.
There are a number of "alternate ranking systems" floating around, such as the SRI (Spectral Radius at Infinity) and ELO rankings. Most of these have some sort of divisor element, and so correspond more closely with divisor and won/lost sorts of rankings. I myself would prefer a "zero-sum" system in which the total points were constant, and each match involved a transaction in which points were transferred from loser to winner. The difficulty with all these schemes is that they are not as easy as the WTA rankings. Still, it would be relatively easy to create an improved system with a won/lost component. The basic components would be three: First, bring back the divisor. Second, increase quality points relative to round points (especially at lower-Tier tournaments where the fields are weak). And finally, reduce the Slam Bonus (this, for some reason, seems the most controversial of the three proposals). This would produce a system which more accurately re! flects wins and losses. It would not, however, particularly resemble the current ranking system.

Q: Why does all this seeding business matter anyway? You have to beat everyone to win the tournament!
A: There are two objections to this: First, you don't have to beat everyone; you simply have to beat a representative selection. If you have a difficult draw, you'll expend more energy -- and perhaps not have enough left for the final. Then, too, there may be certain people you don't much like playing. You're better off if someone else can eliminate them before you play those people.
Second, not everyone wins the tournament. The vast majority of players do not. But they still produce results, and get paid based on how far they advance. So draws matter to the losers.

Q: I've heard it said that it's harder to remain #1 than to become #1. Is this true?
A: It's worth noting that something can be true for psychological reasons when it is not physically true. For example, a #1 player is under intense pressure to defend her points, and will also have lots of players hoping to knock her off. How important these are will, obviously, depend on the player's mental attributes.
But there is a mathematical reason why it is harder to remain #1 than to become #1: Quality points. If you aren't #1, you can beat the #1 player and earn the quality points for that accomplishment. If you ARE #1, you can only beat players ranked #2 or lower. This means you have fewer quality points available.
This generally doesn't matter much. But in a tight contest for #1, where the top two players are very close and playing each other regularly, the #2 player does have an advantage because she can earn more points for defeating her opponent. So it is harder (slightly) to remain #1 than to become #1.

Q: Where do I find the rankings online?
A: As of the time this is written, the official online source for the current singles rankings is:

http://64.157.1.99/rankings/printable_rankings.asp

This information subject to change without notice and at the whim of the WTA (they often forget to update the thing); it's not under my control.